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PRINCIPLES OF ALCHEMY
FIRE

Chemical reactions change substances.

Chemicals are transformed by breaking and making bonds.

The "dance of electrons" is explained by valency and redox.

Balancing equations is important to all Alchemists.

Many things influence the rates of chemical reactions.

Equilibrium determines the yield of a chemical reaction.

Enthalpy changes are involved in chemical reactions.

Blame the disorder of the universe on entropy.

Gibbs energy explains all chemical reactions.

Fire is a chemical reaction and so is life itself!

You mean there is a fire burning in me? Keeping me alive?

Well, yes, in a sense. It isn't a flame like on a candle, but chemical reactions "power" living things. You and me and mice and other living things can be thought of in two ways. Dead or alive. A dead thing is just a bag of chemicals like the atoms and molecules we talked about in the earlier sections. But living things are a series of chemical reactions! Chemical reactions are the subject of our last Ancient Element, FIRE.

Great. You've mentioned chemical reactions a lot already. What exactly are they?

Chemical reactions CHANGE chemicals, making a new chemical from another.

Hey, what exactly is a chemical?! Exactly.

Hmmm. You know it's funny I hadn't mentioned it before, but chemicals are just about everything!. The word "chemical" can refer to any substance - as atoms or molecules or even the purity or state it is in.

How about ice melting into water? Is that a chemical reaction?

Yes, it is. When ice melts, what happens to the molecules?

They move around. Move apart. The water molecules in the ice are in solid regular groups, so ice is made of crystals of water. When it melts, the pattern falls apart and flows. It becomes a liquid. Only the weak forces change. Do weak forces count?

Of course they count. That change from a regular pattern, a crystal, to a drop of water is a chemical change. Weak forces are responsible for a great deal of Alchemy. Including many of the weak interactions that we call life.

I think chemical reactions are the real exciting part of Alchemy. It allows an Alchemist to make new chemicals from old ones. Right?

Right. The making of another molecule, a synthesis, (pronounced "sin-the-sis") is at the very core of an Alchemist's work. We do that by causing and controlling chemical reactions. Chemical reactions can turn atoms into molecules (making bonds), molecules into atoms (breaking bonds) or molecules into other kinds of molecules (breaking old bonds and making new ones). Plus we must not forget the weak forces.
You can think of chemical reactions as the making and breaking of bonds. Weak bonds, strong bonds and metal bonds. All bonds! All this bond making and breaking in chemical reactions involves energy.

What exactly is energy?

Energy is "the ability to do work".

Like harvest crops or clean the room?

Well, more like the work of the universe. The universe has its own kind of work and "rules" of work.

The universe has rules?

Oh, yes. The rules of the universe (often called "the laws of nature") are the foundation upon which our universe is built and works. The universe isn't concerned about the harvest or your room. "Work" to the universe is things like heat, light, sound and electricity.

Sounds complex.

Well, it can be, but we aren't going to go deeply into it. I don't want to turn this into a physics class.

Good. Do all chemical reactions need energy to make them go? Do all of them need heat to go?

Ah, now you have asked two different things and both are complex. Heat is only one form of energy. There is also energy hidden in the chemicals and sometimes that hidden energy can be huge. Lets take this one step at a time in order to keep it simple. First we will talk about heat as if it were the only kind of energy Then we will go on to consider the hidden energy too.

That sounds like a good idea to me. I understand heat. It's so obvious.

Yes, it is. OK, lets concentrate on heat.
Some chemical reactions need you to add heat to them to make them "go". They need to absorb heat to make them run. Chemical reactions that absorb heat are called endothermic.
You seem to know a lot about ancient words. What do you think "endothermic", means?

Ah, "endo" means "under" and "thermic" has something to do with temperature, I think.

Right. So endothermic means "under temperature".

Cold!

Right! Endothermic reactions suck heat out of their environment (their neighborhood) to make the endothermic reaction "go". That makes the environment colder. Cold is just the lower energy in the environment caused by the endothermic reaction.

I bet all chemical reactions are endothermic because you need to add energy to make anything "go". It just makes sense. It takes energy to harvest crops and it takes energy to clean my room.

Quite a lot of energy. But the rules of the universe can play pleasant tricks on you. You see you said "energy" when you should have said "heat". You are confusing the two. Let's stick to heat. Some chemical reactions PRODUCE heat!

How?

Chemicals have a hidden "on board" energy stored in them. That energy is mostly hidden in the bonds - the kind of bonds they are, the amount of wiggle in them and so on. Also, some energy is stored in the molecules' wiggles or vibrations. There's a lot of hidden energy in chemicals! (And much more energy hidden in the nuclei of the atoms, but that's nuclear physics.)
Can you imagine a way a chemical reaction might give off heat?

Let's see. A chemical reaction changes one chemical into another, so....
Hmmm... let me guess.
If the starting chemical has more energy than the new chemical, the chemical reaction will give off the extra energy. Perhaps as heat. Is that how it happens? It kind of makes sense.

Yes! That is exactly what happens in an exothermic reaction. Exothermic reactions produce energy from the chemical change and release that energy as heat.

I see.
Exothermic reactions burn off some heat as they make a lower-energy molecule.
Endothermic reactions take in heat to make a new molecule with more "hidden" energy stored away.

Right.

Hey. Wait a minute. Is fire an exothermic or endothermic reaction?

What do you think? Think about how a fire starts and progresses.

That's what confuses me. All I need is a tiny flame to turn a pile of wood into a huge amount of heat. I put in a tiny amount of heat but I get out a huge amount of heat. The fire pays me back a million fold in the heat it produces, but it needs my help to get it started.

That's right. DO NOT confuse the energy change caused by the chemical reaction with the conditions that started it. True, you need a tiny flame to start a big fire, but the fire "pays you back" many times over. So the whole chemical reaction eventually gives off heat.

So fire is an exothermic reaction.

Right. Fire gives off heat, so it is an exothermic reaction.

OK. That makes sense. But why does it need me to get it started? Why the tiny flame?

A piece of wood must first be heated to very high temperatures before it begins to burn. Once it is burning it produces heat of its own, from the chemical reaction (chemical changes). It is this "self generated heat" which then feeds energy to the rest of the wood causing it to burn. This is why fires, once started, can get out of control. Can't they?

They sure can. Hey, what about an explosion? What causes an explosion?

Well, an explosion is caused by a very fast reaction. The energy is given off very quickly as heat, light, and sound. The sound produces a shock wave that carries away the energy in a destructive "blast".

So explosives are dangerous and useful because they are fast chemical reactions?

Yes, exactly. Explosives, like dynamite and fireworks, are very fast reactions. A similar but slower chemical reaction occurs in a flame. A candle flame produces heat and light. And even a wee bit of sound.
DON'T put your HEAD close to a flame to listen to it! You'll set your hair on fire!

OK. OK! Sorry.

Another inch and you would be! Trust me, candles make wee sounds. Anyway, a flame is usually a slow, steady reaction.
The difference between an explosion and a flame is the SPEED of the chemical change. Some chemical changes occur very rapidly and the release of energy is fast and impressive - like a firecracker. A candle flame is slower. Some chemical reactions are so slow you hardly notice them from one day to the next - like rust.

Oh. Rust is a chemical reaction. So a poorly kept sword rusts because of a chemical reaction?

Yes. The iron in a sword is a metal and it is pretty good at picking up oxygen. The iron atoms in the sword pick up oxygen atoms to produce iron oxides. Rust!
Let's start talking and writing like a proper Alchemist.
The material at the start of the chemical reaction is the reactant and is placed on the left side of the equation. An arrow points the way to the final products. Like this
REACTANTS ------> PRODUCTS

I see. So the chemical equation for ruining a sword is
SWORD + AIR ------> RUSTY SWORD

Yes, but how would an Alchemist explain and write it?

Oh, well, like this
iron + oxygen ------> iron oxide
Or even better would be to use the symbols.

Yes, but for now, I think we should go slow. Any questions about rusty swords?

Yeah. Why does a sword rust faster if it's wet? The oxygen comes from the air. Right?

Right. That's a very good question. The water helps the iron to rust into iron oxide, but it doesn't end up in the product. Some important parts of Alchemy work that way. More on that later.
What about a copper coin? Or the copper wire heated in the flame?
What would that be in terms of the atoms involved and the words Alchemists use?

Ah, let's see. The coin and wire are copper (Cu, just the metal) and it is what we start with so it is the reactant.

Right.
And the copper oxide?

That's the product and it is made of copper oxide (CuO).

Right. So what would the chemical equation look like?

Like this
Cu -----> CuO
I suppose it gets the oxygen from the air.

You suppose correctly. However, the equation you wrote is incomplete. It is missing an important ingredient. The oxygen! Without the oxygen you could not make the copper oxide. So let's include the oxygen from the air. Remember, a molecule of oxygen is O2.

I remember. I just need to write in the oxygen as a reactant (on the left side). So the "complete" equation is
Cu + O2-----> CuO
Right?

Right! That is a complete equation. It shows all you need to make a copper coin "rust". It is complete, because it has all the reactants and products, but it is NOT balanced. A balanced equation has the correct NUMBER of the needed ingredients and the substances they produced. Have you noticed that the left side of the equation has two oxygen atoms (in the one oxygen molecule)?

Yeah, but there's only one oxygen on the right side in the "rust". Where did the other oxygen atom go?

Good question. Where do you think it went?

I don't know. Maybe to another copper atom?

Yes, another copper atom is used up. It makes another molecule of copper oxide (CuO).

I need two atoms of copper to make that the two molecules of copper oxide. I'll just rewrite the equation to include two copper atoms to begin with, as reactants. And that will give me two molecules of copper oxide (2CuO) as products.
2Cu + O2-----> 2CuO
Right?

Right. In 2Cu + O2-----> 2CuO, the copper and oxygen atoms are all accounted for. That is a complete and balanced chemical equation. All students of Alchemy must learn how to make complete, balanced equations.

Looks easy enough. It's just a puzzle.

Yes it is. Some puzzles are easier than others. That one was pretty easy. Later on I'll teach you how to do the harder ones.

Anything else I should know about writing equations?

Yes. Sometimes you will see chemical reactions written with an arrow pointing BOTH ways like this
REACTANTS <------> PRODUCTS
The double arrow is to remind you the reaction is "reversible".

Reversible! I bet you don't get too many of those!

You bet wrong! Chemical reactions are reversible if you change their conditions. The hard part is changing the conditions to make the reaction run in the other direction. It's easier said than done.

So it is a worthless idea, these reversible reactions!

Not worthless. Priceless! There's a difference.
In theory, all chemical reactions are reversible. In practice few are.
Alchemists spend a great deal of time making (synthesizing) molecules which would rather not be made. Some molecules that Alchemists make are very hard to synthesize. So Alchemists search for the right conditions of temperature, pressure and other things that will force a chemical reaction to go one way instead of another.

I see what you mean. If you could find the conditions which would reverse the rusting of a sword, you would have a magic recipe.

In mythical terms, yes. But modern Alchemists have replaced chants and mysticism with reaction conditions.

There must be millions of chemical reactions. How do you remember them all?

I don't! No one does. The methods for making new chemicals from old chemicals are called synthesis techniques. By the 21st century, Alchemists had discovered millions of ways to make millions of chemicals. All those "magic recipes" can be found in libraries.

Do you have some way to keep track of them all?

Yes. Many ways. It all boils down to the special words Alchemists use to describe molecules and how to make them.
All chemical reactions can be classified as one of three types: combination, decomposition or replacement.
Combination joins two (or more) substances to create a more complex substance.

Like copper and oxygen combining to form copper oxide (2Cu + O2 ------> 2CuO)?

Right. That's a combination. The opposite reaction is decomposition. Decomposition breaks a substance into two (or more) simpler substances.

So it is the reverse reaction from before. 2CuO ------> 2Cu + O2 is an example of decomposition.

Right. Combination and decomposition are the reverse of each other. They don't always refer to the same reactions but they can. For example
2Cu + O2 ------> 2CuO
is a combination reaction.
But the decomposition reaction is
2CuO ------> 2Cu + O2
The combination of copper and oxygen into copper oxide is the reverse of the decomposition of copper oxide back to oxygen and copper. If the reaction conditions are right, you get more combination than decomposition and you end up with copper oxide being produced.

So the reaction can go either way.

Right. It's reversible.
Under standard reaction conditions you end up with copper oxide because combination "wins out" over decomposition in this example of copper and oxygen.

What is this "standard conditions" all about?

Those are the "standard" temperatures and pressures. Alchemists like to think in terms of standard conditions in order to keep clear (to each other) what conditions they are talking about. Most Alchemists define standard conditions as zero degree centigrade (0oC) and one atmosphere of pressure (1 atmos).

So, standard conditions are just normal pressure and a cold day.

Ah, yes, but we Alchemists are more specific and define it as 0oC and 1 atmos. Alchemists agreed on those as the standard conditions because they are so common (on Earth).

Let me get this straight. Under standard conditions copper combines with oxygen to form copper oxide. Right?

Absolutely. Copper oxide forms under standard conditions. However, if we change the conditions to something "non-standard" we could reverse the reaction. For example, at a different temperature decomposition "wins" and the copper oxide will not form. You're left with copper and oxygen.

Exactly, what "non-standard" conditions will cause copper oxide to decompose?

I don't know, off-hand. However, I'm sure it is known and can be found in a library. Those specifics aren't important (now) in your education. OK?

OK. Combination and decomposition are reversible examples of the same chemical equation.

Right. They illustrate the reversibility we have been talking about. But most of the time one or the other "wins".

And which one "wins" depends upon the reaction conditions. Under standard conditions, combination "wins". Does combination always "win" under standard conditions?

No, no! Each chemical reaction is different. In the equation
2Cu + O2 ------> 2CuO
this combination will occur under standard conditions.
However, the break up of hydrogen peroxide into oxygen and water is a completely unrelated decomposition reaction
2H2O2 ------> O2 + 2H2O
and it occurs at standard conditions. (At 0oC and 1 atmos hydrogen peroxide decomposes.)

I see what you mean. Combination and decomposition describe what happens in a reaction and they are reversible examples. Sometimes combination "wins" and sometimes decomposition "wins". It's the conditions of the reaction that decide which one "wins".

Right. Under standard conditions copper oxide is made from copper and oxygen (a combination) while under those same standard conditions hydrogen peroxide decomposes. Under "non-standard" conditions (of some sort) these reactions will reverse. Got it?

Yeah. You really have to keep track of which equation you are talking about and which conditions.

Absolutely! That is the main "work" of an Alchemist - discovering the right equations and reaction conditions that will give him what he wants.
By the way, about this chemical equation I have written for the decomposition of hydrogen peroxide
2H2O2 ------> O2 + 2H2O
Is it a complete and balanced equation?

Ah, lets see..... No! The oxygens don't balance.

Don't they? How many oxygens are on the left, in the reactant?

Two in each molecule of hydrogen peroxide gives a total of four oxygens in the reactant. But the product has two oxygens in the one molecule of oxygen molecule and one in both water molecules......
Oh, that's four oxygen atoms on both sides! The oxygens balance.
Maybe the hydrogens don't balance. Let's see. The two molecules of hydrogen peroxide have a total of four hydrogens. And the hydrogens in the products are all in the water molecules. Two hydrogens in each water molecule and two water molecules are in the product so the total product has four hydrogens too!

Right! It's a balanced (and complete) chemical equation for hydrogen peroxide's decomposition.
2H2O2 ------> O2 + 2H2O

I see.
You know, you really have to work it out. It kind of looks wrong at first, but they do add up to the same atoms in the reactant as in the product.

That's right and that's an important lesson. Most of the time you can't tell if an equation is balanced (or complete) by just a casual glance. You have to work on it to prove it to yourself.

OK. You said there were three chemical reactions.

Oh, yes.
The third type of chemical reaction is a replacement reaction. Replacement substitutes one atom or part of a molecule for another.

For example?

For example, if you dropped a piece of copper into sulfuric acid the copper atoms would replace the hydrogens. Like this
Cu + H2SO4 ------> CuSO4 + H2

I see. Atoms are traded around.
Is replacement a reversible reaction?

Of course! All simple chemical reactions are reversible.

But you said there were only three types. If the replacement reaction has a reverse reaction there would be four types. The forth reaction would be a "unreplacement" reaction.

No. You've got yourself confused. Easy enough to do with this lesson.
The equation I have written is reversible. All equations are reversible, even the ones that have been written to look as if they only go one way. I wrote it in one direction because that is the direction that "wins" under standard conditions. Can you tell me the reverse equation (under some "non-standard" conditions)?

Sure, it is just the reverse.
CuSO4 + H2 ------> Cu + H2SO4

That's right. Now tell me, is that a combination, decomposition or replacement reaction?

Ah, it's not really a combination reaction because you don't end up with a more complex molecule, just a different one. And it isn't a decomposition reaction because you don't end up with a simpler molecule, just a different one. Actually, it's another replacement reaction!

Right, and now you have your answer to your question. Replacement reactions are their own reverse! It just depends...

...upon the reaction conditions! I get it.
So all chemical reactions are either combination, decomposition or recombination. And they are all reversible if you change the reaction conditions.

Aye, that's right. Be aware, that some chemical reactions are very complex. There can be mixtures of thousands of chemical reactions of these three types. However, we can always see one or more of these three types of reactions in any reaction, if we look close enough. Also be aware that while all chemical reactions are reversible if you change the reaction conditions, it isn't always easy to do that.

So, that's all there is to chemical reactions?

Oh, goodness, no! There's plenty more. This has been a good introduction to the general ideas. Let's get into some details.

OK. What is happening with these bonds breaking and reforming? It must involve the electrons. Right?

Aye, it certainly does. We spoke of chemical reactions as involving any kinds of bonds, including the weak forces. That is certainly true, but most Alchemy involves changes in the strong bonds. That's not to say that weak forces and bonds are not important. They are! But changes in weak bonds are often so simple or delicate that we will not use them as a subject to study here.

So I will learn only about the strong bonds? That doesn't sound like a complete education. You're cutting corners, wizard.

No, I'm making things simple. The chemical reactions involving the strong bonds are the focus of most introductory Alchemy classes because once you understand them, the reactions involving weak bonds are very easy. Although the weak forces operate differently, the overall ideas are similar.

So, you'll teach me all about chemical reactions involving strong bonds, but I can figure out the weak bond reactions from what I learn.

Yes. Chemical reactions involving strong bonds rearrange the electrons, and thus the atoms' arrangements, making new molecules.
Chemical reactions involving weak bonds don't rearrange the electrons, so no new molecules are made. Changes in weak bonds usually change things like the state of the substance.

OK, I see. I would much rather learn the details of strong bond changes because I'm more interested in changing molecules than in changing states.

Me too. Exactly how and why the strong bonds break and reform is the main subject of Alchemy. Especially synthesis Alchemy.

OK, I'm convinced.

Good. I want to go into detail about the breaking and making of strong bonds. Let's just call them "bonds" for the rest of the lesson. OK?

OK by me.

Good. Imagine a simple molecule. The simplest molecule in the universe, H2. The bond joining two atoms (H-H) is like a vibrating spring. The "average bond length" is the average distance between the two atoms, but it varies slightly as they vibrate back and forth.

We talked about bond lengths in the last section (in EARTH).

That's right. And you will recall that the atoms are only as close together as their outer electron shells will allow. Do you remember why?

Yeah, the electrostatic repulsion of the outer shell electrons eventually stops them from getting any closer.

Correct. The minimum distance between two atoms is determined by the electrostatic repulsion of their outer shells. What would happen if you pushed the two hydrogen atoms closer to each other than their average bond length?

Eventually they would push against each other's electron shell and repel each other.

Right. To move the two atoms closer to each other than their average bond distance you would have to exert energy against the electrostatic repulsion of their (outer) electron shells.

I see what you mean. I bet the closer together you tried to push them, the more they would resist and the harder you would have to push.

That's absolutely right. Nuclear Alchemists in the 20th century have worked very hard to come up with ways to push two hydrogen atoms so close together that they fuse into one atom! But it takes huge amounts of energy to do that.
Tell me Arthur, what would you get if you pushed two hydrogen atoms together completely? Assuming you had plenty of energy to do it.

Ah, hydrogen is just a proton, so if you pushed two together you would have one atom with two protons. Helium.

Right. Fusing atoms is nuclear fusion and requires a huge amount of energy. (But then it gives off a huge amount of energy too.) Most Alchemists don't have that kind of energy to work with. Nuclear fusion is not a chemical reaction in a strict sense and we will not discuss it further.

So it takes energy to push atoms closer than their average bond distance. What happens if you try to pull them apart?

Good question! If you try to stretch the bond between two atoms you have to tug on them to pull them away from each other. But the atoms don't want to be pulled apart. Do you know why?

Well, if you pulled H2 apart you would have two atoms of hydrogen (2H). You would be breaking their covalent bonds.

Right. Recall that the covalent bond holding them together is formed in order for the two atoms to reach a noble electron configuration.

Yeah. Together, in a covalent bond, both hydrogens share their electrons so they have the electron configuration of helium.

Right again. Both hydrogens would rather be together than apart. That "desire" to reach the noble state is a powerful force.
It is this "desire" that causes the hydrogen atoms in H2 to resist being pulled apart.

So I would need energy to pull the two hydrogens apart, just like I need energy to push them together.

That's right. These two opposing forces balance themselves out as an average bond length.

So the average bond length uses the least energy of all.

Exactly! That's why most H2 molecules have an average bond length. Any other length would take energy.
Let's draw an "Energy Diagram" to help us think about it.

Looks complex!

That's because it's new to you. Don't let that frighten you. We'll go through it one step at a time. I've included the diagram of bond lengths in our drawing to help you understand this graph. We "plot" the position of the two atoms along the horizontal.

So the distance between the two atoms is along the "horizon".

Aye. In this diagram, I have put one atom at the far left side and won't move it. The other atom is moved horizontally to indicate the distance between them.

OK. What this up and down part of the diagram?

The up and down part (or vertical part) of the diagram shows how much energy is needed to put the atom in that position. It indicates the amount of energy needed to push or pull the atoms together.

I see that the lowest part of the diagram, the valley, is the average bond distance.

That's right. The average bond distance is the energy "minimum". That's where most bonds end up - at the energy minimum.
Look at what happens if you push two atoms together, starting at the average distance.

The amount of energy goes up.

Why?

Because you are working against the electrostatic repulsion of the electron shells. That takes energy. The closer you push the together the more energy you must use.

Right. To push them completely together (to fuse the atoms) takes so much energy I can't even draw it on this scale. What do you think would happen if you pushed the atoms a wee bit closer together than their average bond length and then released your grip?

Ah, I bet they would push away from each other because of the electrostatic repulsion. And they would return to their average bond distance because that is the point of minimum energy.

Very good, Arthur. By pushing the two atoms together you are using energy to push them "up-hill". When you release the energy the atoms spring back to the average bond length as if they had rolled back down into the "valley". Now tell me what would happen if you pulled the two atoms apart a wee bit?

Well, if you pulled them apart you would be increasing the bond distance. But the atoms want to be together to keep a noble electron configuration, so it takes energy to pull them to a longer bond length.

Right. What would happen if you released your grip on those two atoms that you had pulled a wee bit apart.

They would snap back to their average bond length! They would go back into the "energy valley".

Exactly!

Hey, I got a question. What about ionic molecules like NaCl? The sodium has a positive charge and the chlorine has a negative charge so they are attracted to each other by electrostatic attraction. Why don't they fuse?

Good question. Even though the atoms in an ionic molecule are drawn to each other by electrostatic attraction, they can only come so close to each other before their outer electron shells begin to rub.
Remember, the sodium ion (Na+) has a single positive charge, but it also has a shell of electrons. The cation's positive charge is buried in the nucleus. So the anion (Cl-) is drawn close to the cation (Na+) but only so far as their outer shells allow.

I see what you mean. So an ionic bond's minimum length is caused by the same forces that cause the covalent bond to have a minimum length. Electrostatic repulsion keeps all atoms from getting too close to each other.

Right. But tell me about the maximum length. What happens when you pull the cation and anion a wee bit apart?

Ah, now that is different. The two ions are held together by electrostatic attraction. You would have to use some energy to pull on them. If you pulled them a wee bit apart and then released your grip, they would spring back to their average bond length because of the attraction of their opposite charges. But they wouldn't go colliding into each other because their outer shells would keep them apart.

Very well said. An important point here is that this energy diagram would look much the same for either covalent or ionic bonds. Weak bonds also have similar energy diagrams. There is always a minimum energy point at an average bond length. The minimum bond length is caused by electrostatic repulsion. The maximum bond length is caused by the actually mechanism that causes the bonds to form anyway. That is true of all bonds including the weak ones. Do you see what I mean?

I think so. All bonds have an average bond length and they can be understood by the energy needed to position the two atoms in the bond. It takes energy to force the atoms closer, because the electrostatic repulsion is always there. It takes energy to pull them apart because you are working against the force that makes the bond in the first place!

Right. The energy diagram can be used to understand any bond (including the weak ones).
In chemical reactions we are concerned about pulling atoms apart, so we tend to think about the energy needed to increase the bond distances. If you pull hard enough you actually break the bond.

Any bond?

Yes. All bonds have a breaking point called the bond dissociation energy. This will stretch the bond to the breaking point. It is the energy needed to overcome the force of the (ionic, covalent, hydrogen, etc.) bond.
H2 (that is H-H) + bond dissociation energy ------> 2H (that is H and H as separate atoms).

Do all bonds have these properties?

Yes. Here I've added another energy diagram. This one is for HF.

It looks a lot like the one for H2. But the valley for HF is lower than the valley for H2.

That's a very good observation, Arthur. I think you are getting the hang of reading these energy diagrams. There are differences in the exact details (the bond lengths are slightly different and so are the dissociation energies).
We can use these energy diagrams to understand what is going on in chemical reactions.
Consider this reaction H2 + F2 ------> 2 HF
In this example, the high electronegativity of the fluorine atoms provides the bond dissociation energy for the H2. The fluorines tug the H-H bond apart due to the difference in electronegativity.

Yeah, I remember that H2 and F2 form HF because of fluorine's high electronegativity.

Right. Once the H-H bond has been broken, the atoms will rearrange their electrons to form new bonds with the "best" combination(s) of atoms. H-F bonds are preferred to H-H bonds and F-F bonds, because of fluorine's high electronegativity.

We can combine the energy diagrams of the old bond broken and the new bond formed to make an energy diagram for the entire reaction.

It looks like the path of someone walking over a hill and into a deeper valley.

Yes, it does. The path from reactants to products is an energy map of the path the atoms take as they form the new bond. The horizontal direction is called the reaction co-ordinate and the energy needed to move between the two (reactants to products) represents the energy path to get there. I like to think of these diagrams as reaction paths.

What about the other part of the reaction? What about the F2 being broken up to make the HF?

It would have a reaction path and energy diagram too. But lets just concentrate on the hydrogen as the reactant here in this example.

OK. It looks to me that the hydrogen atom that is going to make the HF has to first climb up a hill. Then it can slide back down into the HF valley.

That's a good way to think about it. Along this reaction co-ordinate is the point of maximum energy called the transition state. As you noticed, this transition state is at the top of an energy hill.

Is the transition state always at the top of an energy hill?

Yes, if there is a hill at all. Sometimes there is no obvious hill in a reaction diagram so there appears to be no transition state at all.

Huh?

Well, some energy paths go from reactants to products with no hill in between. Their path is one long downhill slope.

So you don't need to push energy into the reaction. It runs by itself? Downhill?

Aye! Chemical reactions with no energy hill between the reactants and products are spontaneous.

Meaning they happen automatically?

Right. Actually, there is probably a wee hill along the path but the reaction gets over it with a wee bit of energy from its environment. We just don't notice it. That brings me to why we call this the transition state (instead of the "top of the hill state"). At the transition state the reaction could go either way.

You mean it could go backwards to where it started? Back to the reactants and not make any products?

Yes. The transition state is a funny halfway state. It's a "hybrid" state. You can imagine that both of the atoms are sort of bonded together but not very tight. This group of "confused" atoms are called an activated complex.

It sounds complex!

Don't let it worry you. All it means is that atoms at the transition state are in an activated complex and they end up rolling either to the left or the right. If they roll to the right you get the product. If they roll left you go back to the reactant and that reactant can be used again to try to go up to the transition state.
Here's the diagram again, but I made the valleys flat at the bottom. (For the rest of the course we will ignore the idea of pushing atoms closer than their average bond distance and just concentrate on breaking the old bond and making a new one.)

Once it gets to the transition state it may or may not go to the right, to make a product. It could go back where it came to (re)make the reactants.

Right. This might go on thousands of times each second, so eventually most of them go to the right. Once they get to the right side of the hill, they are products and are not as likely to return to reactants (on the left side of the hill) because that's a higher hill to climb.

Is there a name for the energy needed to climb up this hill?

Yes. The difference in energy between the reactant and the transition state is called the activation energy.

Because it is the energy needed to make an activated complex!

Exactly. The activation energy is the energy needed to make the reaction "go".
If the reaction path carries the reactants UP to the transition state, the activation energy is really an energy barrier. This barrier must be overcome to make the reaction "go". This energy must be added to push the reaction over the barrier.
Some reaction paths have no (real) energy barrier, their path being entirely downhill.

Those downhill reactions are "spontaneous" and will occur without doing anything? Right?

Right. You're learning a great deal about the names of these important parts of the reaction path and how to understand them.

But it IS confusing. The transition state is the "halfway" point in the reaction where it can go either way. Right?

Right. It is the point where a transition may occur. That's how it got its name.

And it is at the transition state that this activated complex is found. Right?

Right again.

And the activation energy is the energy you need to get to the activated state.

Absolutely! The activation energy is the energy needed to make the reaction "go".

But not all reactions have an energy barrier to climb. They may be downhill all the way. Then they don't need additional energy (they don't need activation energy) they just happen spontaneously.

Yes! I think you've got it!

Well, I'm going to read my notes on this diagram about a million times before I think I've got it!

It does require a bit of thinking. But you'll get it. Let's see what else you can learn from energy diagrams.
You noticed right away that the valley for HF was lower than the valley for H2. What do you think that means in terms of the overall energy of the reaction?

Hmmmm,
It takes energy to go up the hill to the transition state (at least in this example, which is not spontaneous). But once you get up to the transition state, it is downhill all the way to the HF.

True. Now think about the total energy put in and the total energy given off.

It looks like you use a little energy to climb the hill, but you get a lot of energy released as you roll down into a deeper valley caused by the formation of the HF.

Right!
Notice that the hill you must climb is just a barrier in the way. But it is the total energy of the reactants and products that tells you the total energy of the reaction.
Reactions in which the total energy of the products is less than the total energy of the reactants will release energy. We call them exergonic reactions because they give off energy. "Ergonic" means "energy".

So an exergonic reaction has extra energy to spare.
I see. No, I think I see. No, I'm confused!
If a reaction gives off energy it is exergonic. But what if it gives off heat? What's that called?

A reaction that gives off heat is exothermic ("above the heat"). Don't confuse that with exergonic ("above the energy"). A reaction with extra energy is exergonic. But it may not always release that energy as heat. It might hide that energy inside the new products.

So an exergonic reaction produces energy but not always as heat.

Right. Some exergonic reactions are exothermic and some are not.

Do all reactions give off energy?

No. Some reactions need more energy than they produce. Reactions in which the total energy of the products is MORE than the total energy of the reactants will require energy to be added and are called endergonic reactions.

I see. "Endergonic" means "below the energy" so they need energy to go. Endergonic reactions need energy to go up the energy hill all the way to products.

Right.

So it is the total energy in or out of the reaction that determines if it is exergonic (releasing extra energy) or endergonic (needing more energy). But a reactions may give off heat (be exothermic) or take up heat (endothermic) from its environment regardless of whether it is an exergonic or endergonic reaction.

Right. Don't get the ideas of energy (ergonic) mixed up with temperature (thermic). Temperature is just one form of energy and chemicals can hide excess energy. (Later we will discuss how they do that.)
Also, don't get the idea of activation energy mixed up with exothermic or endothermic. The reaction might need a wee push to get it over the barrier. That's activation energy. But it is the total amount of energy released or absorbed that determines if it is exergonic or endergonic.

Ahhhh, right. (I better go over that again!)
This gets back to my question about fire.

Yes, it does. You need a small flame to start the reaction.

To get it over the energy barrier. That's the activation energy.

Right. Once it is over the energy barrier fire releases more energy than you put into it. That "new" energy can be used to power another reaction.

Oh, I see! The energy from the first reaction provides the energy needed by the second reaction to push it over its energy barrier! So I don't need to add any more energy.

Right.

And the energy created by that second reaction can power the third reaction.
And so on, and so on.....

Right. That's called a chain reaction. Once started a chain reaction will run all by itself. It will only stop if it runs out of reactant.

I see what you mean. Fire needs oxygen so you can stop a fire by cutting off its supply of that one reactant - oxygen. Or the fire stops when it has run out of fuel.

That's right. Fire and other chemical reactions that are chain reactions can quickly get out of hand because they are able to power themselves.

You know, following these chemical reactions is really just following how the atoms rearrange themselves and that all has to do with the electrons. It's the electrons that make the bonds.
But I suppose it's important to remember the number of bonds each element can make.

Aye, it is! We call that the valence number. An atom's valence number is the number of electrons it uses to form compounds. The valence number can also be thought of as the combining power of an atom and equals the number of hydrogen atoms it could combine with. We often refer to that number as the atom's valency.
Notice that valency has to do with COMPOUNDS!

Yeah? So what?

So valency numbers can only be figured out from compounds.

What's your point?

My "point" is that ELEMENTAL molecules don't count. Atoms in pure elemental form (elemental molecules) have a valency of zero (0).
OK?

Yeah, OK. I get it.

Can you tell me the valence number of some elements involved in compounds?

Sure, it's easy. All the Group I elements have a valency of one (+1) and all the Group II elements have a valency of two (+2). But in their pure state they have a valency of zero (0).

Aye. That's the right way to think about it. But, there's one Group I element which may trick you at times. Do you know which one I'm talking about?

Hydrogen! In some compounds, like in LiH, it can gain an extra electron to form an anion with a charge of -1.

Right. The hydride of hydrogen has a valency of -1. That valency follows from knowing how hydrogen forms ions. You would also know that Group VII elements always have a valency of minus one (-1) in the compounds they make.

Isn't the valency of an atom just the electrons it needs or loses to reach the noble state? Isn't that what Lewis' Octet rule is all about?

Ah, not quite. But close.
That would be taking the Octet rule too far. You see, all atoms seek the electron configuration of a noble element but not all of them reach it. That affects their valency. Think of valency as the number of bonds it CAN make, not the number of bonds it WANTS to make.

How do you mean?

Well, the valency of most atoms, and indeed many Groups, is constant.
Elements in Groups I, II and VII have constant valences of +1, +2 and -1 (in that order).

The Group VIII elements will have a valence number of zero (0) because they don't form any bonds at all!

That's right!
Notice that pure sodium (Na) for example has a valence number of zero. But when you have a compound involving sodium, then the sodium atoms have a valency of +1.

So valency can change?

Yes! Many chemical reactions involve a change in the valency of the atoms involved. In that example, the pure elemental sodium was "changed" into an ion, so it changed its valence number from 0 to +1.

I see. So a good Alchemist knows what the valency numbers are and how they change. The valence number of all elemental molecules is zero, but they change their valence number as they become a compound. The elemental has a value of zero at all times, but the compound has another value. That's easy to remember. Just know what valence number it goes to.

Right. But not all elements have a simple "valence number it goes to". Some elements can form compounds with different valence numbers.

How do you mean?

Take iron (Fe). Iron compounds can have a valence number of either +2 or +3. Do you know what that means?

Yeah, sometimes iron makes ionic compounds by donating two electrons and sometimes it donates three.

Right. It depends on the specific "chemical circumstances" it is in. (It has to do with iron's d orbitals.)
Elements in the middle of the Table are particularly good at having several possible valence numbers. Can you guess why?

Hmmm.
The middle of the Table has a great deal going on in it. Electrons in the outer shell might form ionic bonds with each other, but many of them form covalent bonds too. And metal ones.
The elements from Groups III to Group VI are involved in the "staircase" aren't they?

Yes, they are. Do you recall what forms that "staircase"?

Metals on the bottom, semi-metals over them and nonmetals on top. It all has to do with the metal properties and that has do with how well they conduct electricity. Going down a Group adds extra shells which are more likely to get involved in "super sharing" their electrons (in metal bonds and to carry electrical currents). But going across a Period shrinks the outer shell inward so the electrons aren't as likely to be "super shared".

Right. You've explained how those opposing forces cause the "staircase look" to the Table.

Could those same opposing effects explain why valences in the middle of the Table are so difficult?

Yes. The "basement" orbitals can also have an effect. Like all explanations of electron behavior, the ultimate answer lies in an advanced class. But all a young Alchemist like you needs to know, is that some elements have valences that are easy to understand, but others do not.

Are there any general rules?

Yes. Plenty! You already know one basic rule about predicting an atom's valency. Let's hear it.

Ah. Groups I and II are +1 and +2, Group VII is -1 and Group VIII is zero (0). The valence number of the ion equals the charge, with cations having positive numbers and anions negative numbers.

Right. The elements at the far ends of the Table behave the way you would always expect. You can figure it out from their electron structure and the Octet rule. It's in the middle where things get muddled. In the middle you have elements that can form ionic bonds or covalent bonds, as well as metal bonds.

I see why it gets complex. I hadn't thought about covalent bonds. If an atom's valence number is the number of electrons it uses to form the compound, then the valence number of an atom involved in a covalent bond is just the number of electrons it shares. Right?

Absolutely right.
This may start to sound familiar. You will recall that methane (CH4) is made of four hydrogen atoms, each with a valency of one (1) ......

Oh, yeah, yeah!
And the carbon in methane has a valency of 4.

Right. In covalent compounds, the valence number of an atom equals the number of electrons it contributes to the (shared) covalent bonds.

I remember that some of the elements in the top of Groups V and VI have weird valency numbers.

Right! Keeping track of the bonding among nitrogen (N), phosphorus (P), oxygen (O) and sulfur (S) atoms is sometimes tricky. Sometimes the only way to find out how they are bonding is to do complex experiments.

Sounds difficult!

It is, but you don't have to worry about it. Most Alchemists go through life without really thinking about the difficulty of discovering an atom's valency. All you have to do is KEEP TRACK OF IT.

So, is there complete madness in the middle of the Table?

No, no, not at all. Most transition metals form cations of +1, +2 or +3. You just have to keep track of it or look them up in a book.

What about the normal elements? The ones in Groups III to Group VI?

Most of the Typical Elements follow predictable patterns and you already know most of them.
Carbon in compounds has a valency of 4 because it always forms 4 covalent bonds (by sharing four of its outer electrons and getting four more shared in return).

But carbon can make double and triple bonds. Does that change its valency?

No, not at all. Remember that those bonds are made of several molecular orbitals. If you think about the electrons being shared, you'll see that carbon still shares 4 of its valence electrons in its covalent bonding.

Yeah, I see your point.
Hey, what about graphite and diamonds? Huh?
In diamonds each carbon has four carbons attached to it (in a tetrahedron made of four sp3 hybrid orbitals) but in graphite each carbon is covalently bonded to only three other carbons (in flat triangle sheets made of three sp2 hybrid orbitals). So, what's the valency of carbon?

The valency of carbon is four when it is in a compound, or it is zero when it is elemental. So, Arthur, what is the valency of carbon in diamonds or graphite?

Oops, I forgot about that. I see what you are trying to show me.
Diamonds and graphite are elemental molecules so the carbon in them has a valency of zero.

Aye.

OK, I accept that carbon has a valency of four in the COMPOUNDS it makes. But those four elements at the top of Groups V and VI (N,O,P,S) are strange right? That "NOPS square" has a few weird properties.

Right, but they tend to follow rules most of the time. For example, oxygen has a valency of -2 in all compounds, except in peroxides, where its valency is -1. I mentioned peroxides earlier.

Yeah, what are they?

Peroxides have an unusual form of oxygen - an unstable form. Water is H2O. Hydrogen peroxide is H2O2. In water, the oxygen atom is behaving as expected and has a valency of 2 because it forms two covalent bonds to hydrogens. We make that a minus 2 (-2) to remind us that there is a wee bit of ionic character to the bonds that the oxygen makes.

And the hydrogen's have a valence number of +1 because they are in Group I. (And they are not a halide in water.)

Right, hydrogen has an easy to understand valence number. Let's get back to the oxygens. The oxygen in hydrogen peroxide has a valency of -1. Not -2! As a matter of fact, if you look at the equation for hydrogen peroxide (H2O2) you will realize that the two oxygens MUST have a valency of -1 in order to explain it.

Huh?

Well, hydrogen peroxide (H2O2) is not an ion. It has no charge. The two hydrogens give the molecule a +2 charge so the remaining atoms, the two oxygens, must together supply a total of -2. Otherwise hydrogen peroxide would be an ion.

I see what you mean.
Hmmm. I have a hard time trying to picture what H2O2 would look like. I can imagine that in a water molecule, the two hydrogen atoms are bonded to a single, central oxygen. But how do the oxygens and hydrogens link up in hydrogen peroxide?

They don't link up well at all! That's why hydrogen peroxide is unstable. It breaks up into water and releases the extra hydrogen. I appreciate your enthusiasm to understand the structure of hydrogen peroxide, but it is a difficult subject. For now let's just stick to the fact that oxygens in peroxides have a valence number of -1, and leave the idea of the actual structures to an advanced class.

OK. I don't want to get confused further. I'll just remember that most of the time oxygen has a valency of -2.

Yes. It depends on the specific conditions the atom finds itself in. Nitrogen (N), phosphorous (P) and sulfur (S) also can have weird valence numbers.

I see (I think). It looks like the transition metals and atoms in the "NOPS square" are special.

Yes, they are. Be aware of that but don't let it get you worried. A good Alchemist is aware of them and learns to use them. Approach these valency problems as a puzzle and you will be able to figure them out.

Give me an example of a puzzle to figure out.

OK. Take ferrous chloride. It is FeCl2 and it is NOT an ion (so its total charge must be zero).
What is the valence number of the iron atom in it?

Well chlorine is a Group VII element, so it has a valency of -1, right?

Right. Group VII elements have a valency of -1 in every compound they make.

So, the iron must have a valence number of +2. Right?

Correct! In ferrous chloride (FeCl2) the iron has a valence number of +2. All molecules must have a "balanced" charge (unless they are an ion of some sort), so it makes sense that FeCl2 must be made of iron atoms with a valency of +2. We Alchemist call iron in the +2 state "ferrous". That's why we call FeCl2, ferrous chloride.
Now what is the valency of the iron atoms in ferric chloride (FeCl3)?

Simple. The three negative charges from the chlorines must be balanced by a +3 from the iron. So that iron has a valence number of +3.

Absolutely right! We Alchemists call iron with a valence of +3 "ferric" iron and the molecules it forms with chlorine are called ferric chloride (FeCl3).

Is that the only two valence numbers of iron?

Yes, they are. In COMPOUNDS made of iron. Otherwise they are zero. Right?.

Right. Because atoms that are not involved in compounds have valences of zero.

Correct. Can you remember that ferrous is +2 and ferric is +3?

Sure can. It's like two is a couple ("us") but three's a crowd ("ick").

That's a good way to remember it. I like that. Little tricks like that help you remember. That will work for iron's two valence numbers but it won't work for all metals. Take copper (Cu). Cupric chloride is CuCl2. What is the valence number of the copper?

Ah, +2. Because it must balance the negative charges from the two chlorines.

Right. Notice the "ick" is now the ending on an atom with a valence number of +2, not +3. And here's another one. What's the valence number on cuprous chloride (CuCl)?

Ah, gee. It looks like the copper is now +1. Hmmm. I guess my idea doesn't always work that way.

Sorry, but it doesn't.

So why do Alchemists use those names so badly!?

They use them according to different rules. The "us" and "ick" refer to the amount of valency it has. Both iron and copper can have two different valency numbers in compounds. Copper can be +1 or +2. Iron can be +2 or +3. Alchemists use the "ous" (pronounced "us") ending on the cation with the LOWER valence possibility for that element. Ferrous and cuprous are the lower valence possibilities for the iron and copper atoms. Iron's lowest valence possibility is +2, but copper's is +1. Alchemists use the "ic" (pronounced "ick") ending on the cation with the HIGHER valence possibility for that element. Ferric and cupric are the higher valence possibility with ferric being +3 and cupric being +2.

I get it (I think). I'll have to read that again to make sure.
It looks to me that you must remove an extra electron to turn "us" into "ick".

That's right! If you remove an electron from an "ion-us" you get an "ion-ick".

Do Alchemists have any other naming tricks?

They aren't tricks. They are definitions. Use "ous" for the lower and "ic" for the higher valence cations. That's a definition, not a trick.

OK. Anything else I should know about how Alchemists talk about these things?

Well, yes. To help keep track of changes in valency, Alchemists often include the valence number in parenthesis. Pure copper has a valency of zero, because pure (elemental) metal bonds don't have a real valency. Right?.

Right.

Some Alchemists abbreviate pure copper as Cu(0) to remind them it has no valence. When copper takes on a valency of two (able to make ionic bonds with its +2 charge) the ion can be written as copper (II) and abbreviated as Cu (II).
You probably also noticed that when copper is an ion it is renamed slightly as "cup-something" (pronounced "coop-something"). Kind of like iron being renamed "ferr-something" (pronounced "fair-something") when it is behaving as an ion.

I see. Cupric (Cu+2) can be written as Cu(II). I bet cuprous is Cu(I)

You bet right. What about ferrous and ferric ions?

The ferrous ion is +2 and would be Fe(II). The ferric ion is +3 and would be Fe(III).

By Jove I think you got it!

Good, but I'm getting tired talking about the names. Let's talk about chemical reactions!

Fine. All this "naming" is important to help you keep track of chemical reactions.

But there are only three types of chemical reactions. Combination, decomposition and replacement. Right?

Well, yes and no.

What!?

The three types of reactions you named are one way to look at chemical reactions. And it is true that any chemical reaction can be classified as one of those three types. But there is another way to think about chemical reactions.

How?

By thinking about how the atoms' valences change. Many chemical reactions that involve the breaking and making of strong bonds, often cause a change in valency of the atoms involved. We keep track of those changes by understanding which chemicals are "oxidized and reduced".

What's that?

Oxidation (pronounced "ox-i-day-shun") and reduction (pronounced "ree-duck-shun") are the core to understanding chemical reactions and equations.

What do they mean? I'm confused.

That's understandable. A chemical that undergoes oxidation is oxidized (pronounced "ox-i-dyzed").

And a chemical that undergoes reduction is reduced?

Right. Now let's get deeper into those meanings. Alchemists use to think that all of Alchemy involved the addition or removal of oxygen.

Were they right?

No, but they were close! Oxygen is a very important part of the Alchemy. But it doesn't tell you the whole story. Besides, there are a great deal of chemical reactions that do not involve oxygen but behave as if they do.

Huh?

OK, I can see I'm confusing you so let's back up and start over.
In the past, "oxidation" was the name given to any chemical reaction in which oxygen was combined with a substance. For example, when you "burned" copper wire you combined the raw copper with oxygen from the air to make copper oxide
2Cu + O2 ------> 2CuO.

That's cupric oxide, isn't it? The copper in CuO must have a charge of +2, to balance the -2 of the oxygen. So the copper atom goes from copper metal to copper (II). And because Cu(II) is the highest valence number for copper, it gets the "ick" ending.

Yes! Very good Arthur. You have put your finger right on the important point. Or at least pretty close to it. Notice that the copper metal lost electrons to form cupric ions with a +2 charge.

Yeah. When the electrons left it changed the atoms from copper to cupric.

Right. The valence number of the copper atoms changes from zero (in the metal) to +2 (in the compound). Tell me, how can any atom go from a zero charge to a positive charge?

By losing electrons.

Right. We call that "oxidation".

But it doesn't have anything to do with oxygen. Not directly.

That's right.
As Alchemy matured, Alchemists began to focus on the electrons involved in a reaction.
In oxidation electrons are lost.
2Cu ------> 2Cu+2 + 4e-

I see (I think). Each copper metal atom MUST lose two electrons in order to form ionic bonds to the oxygen. The copper must become a cation in order to form the ionic bonds with the oxygen. Right?

Right. Reactions in which oxygen is gained involve the loss of electrons by one of the chemicals, so oxidation is the loss of electrons. Oxidation increases the valence number (in this case, from 0 to +2).

But the copper is oxidized, not the oxygen! That's hard to follow.

Yes, it can be confusing. Part of the problem is the fact that Alchemists started naming these reactions based upon where the oxygens go and how they behave. But other elements can cause oxidation.

You mean you don't need oxygen to oxidize?

That's right. So instead of thinking of oxidation as the gain of oxygen, we think of oxidation as the loss of electrons.

Boy, that sounds backwards!

Well, it isn't really backwards. It just represents the way that Alchemy has "evolved" through the centuries. It wasn't until the 19th century that anyone knew about electrons. Until then, all that Alchemists had to go by was whether oxygen was consumed or not. So, the old Alchemists thought in terms of oxygen reactions. But the real Alchemy occurs with electrons. Clear?

Yes. Electrons are responsible for the bonds, so electrons are responsible for making compounds.

Exactly! The word "oxidation" is just a leftover from the old days when all of Alchemy seemed to involve oxygen. But 20th century Alchemy uses the word oxidation to refer to loss of electrons.

What about an atom which gains electrons in a reaction? You know, the opposite of oxidation.

That would be reduction. In the past, "reduction" was the name given to any chemical reaction in which oxygen was removed from a substance. For example, the copper in cupric oxide can be returned to its elemental form by reacting with hydrogen gas. Like this
CuO + H2 ------> Cu + H2O
If you look at the electrons transferred in the reaction, you see that electrons are gained by the copper.
Cu+2 + 2e- ------> Cu

I see. The cupric ion (Cu+2) gained two electrons to return to the metal, which then has no charge. And it lost the oxygen in the process. I suppose that the copper atom (with no charge) can't form ionic bonds with the oxygen so the oxygen is released.

Yes, that's right.
Reactions in which oxygen is lost involve the gain of electrons, so reduction is the gain of electrons. Reduction decreases the valence number (in this case from +2 to 0).

So reduction is the opposite of oxidation.
If an atom loses an electron it is oxidized. If it gains an electron it is reduced.

That's right. In the examples I have shown you , I made a point to use oxygen in the reactions to help you understand how the names of "oxidation and reduction" came about. When the copper metal gained the oxygen Alchemists said it was oxidized. That's because the Alchemists of the past thought only in term of oxygen.

And when the cupric oxide lost its oxygen they said the copper was reduced because it lost the oxygen.

Yes, but we now think in terms of electrons being gained or lost. Oxidation and reduction can occur without oxygens and I will show you some examples of that later. But you must understand that it is the electrons that we keep track of, not the oxygens. Can you remember that?

Sure can. Loss of Electron(s) is Oxidation (LEO). Gain of Electron(s) is Reduction (GER). It's like Leo the lion growing.
Leo says "Ger".

That's a very good way to remember it! Leo says "Ger"!
Loss of Electron(s) is Oxidation (LEO). Gain of Electron(s) is Reduction (GER). I like that!

I need those little tricks to keep it straight. I think this oxidation and reduction stuff is confusing.

Well, yes it can be at first. But if you just follow the electrons and keep track of what you are talking about, all should be OK. OK?

OK.

Good. Now I want you to notice something about the two equations we've been using as examples. Both of them have a reduction occurring AND an oxidation occurring. We've only been looking at one side of the reactions to make it easier.

Easier!

Well, less difficult. Let's take a look at the oxidation of copper again.
2Cu + O2 ------> 2CuO
What can you tell me about this equation?

The copper starts off with no charge because it is a metal. It starts with a charge of zero, Cu(O). But the copper atoms lose two electrons to become ions, Cu(II). Right?

Right. Show me the equation for the electrons involved in copper as it changes.

OK.
2Cu ------> 2Cu+2 + 4e-
That means the copper is oxidized. It loses electrons and loss of electrons is an oxidation reaction. To lose electrons is oxidation (LEO).

That's right. Now, what about the oxygen in that chemical reaction? Write what happens to the oxygen atoms.

OK. The oxygen atoms start off as O2. They are not a compound, so they have a valency of zero. Right?

That's right. O2 is an elemental molecule, so it has a valency of zero. Notice that the two oxygen atoms are held together by sharing two pairs of electrons between them, but they still have a valency of zero (because they're elemental). Now write an equation to show how the oxygen and electrons behave. Remember, the copper atoms give up electrons in the chemical reaction. Think about how those electrons are used by the oxygen.

OK. That would be O2 + 4e- -----> 2O-2
Both oxygens gain two electrons to become the anions. Hmmmm. That means the oxygens are reduced! Gain Electrons Reduced, "GER".
But the coppers were oxidized! The coppers lost electrons. Lose Electrons Oxidized, "LEO"

That's right! And you have discovered an important point. Whenever oxidation occurs, reduction also occurs.

And whenever reduction occurs, oxidation must also be occurring!

You are absolutely right. Oxidation is the loss of electrons and reduction is the gain of electrons. The two reactions, oxidation and reduction, occur at the same time. The chemical undergoing oxidation provides the electrons for the other chemical's reduction.

So you can't have oxidation without reduction and you can't have reduction without oxidation. It's just the swapping of electrons!

Right. This swapping of electrons is so important to Alchemists that we call these "redox reactions". These reactions require both reduction and oxidation to occur.

Redox reactions are just the swapping of the electrons.

Right. We Alchemists like to describe these chemical reactions as TWO reactions occurring at the same time! One is a reduction and the other is an oxidation. Redox! Can you write a pair of redox equations for the oxidation of cupic oxide with hydrogen gas? (That's the equation we were looking at earlier.)

Sure. The "normal" equation is CuO + H2 ------> Cu + H2O
The copper gains electrons to change the cupric ion (Cu+2) to the copper metal (Cu).
Cu+2 + 2e- ------> Cu
The copper gains electrons so the copper is reduced. (GER)

Right. Now try to find the other half of the equation. What is oxidized? Where do those electrons come from?

Hmmm.. I'm not sure, but it looks like the hydrogen molecule (H2) breaks up in this reaction to form the water molecule. Is that right?

Yes, it is. How would you write that break up of H2? How would the electrons behave?

Hmmm.. The hydrogen is just a diatomic elemental molecule held together by the sharing of a pair of electrons. Could it be that the H2 breaks up and releases the two electrons? Like this?
H2 -----> 2H+ + 2e-

Yes, that's right. The hydrogens both give up their electrons so the hydrogen is oxidized.

Let me get this straight. The coppers are reduced because they gain electrons (GER) and the hydrogens are oxidized because they lose their electrons (LEO).

Right!

But what about the oxygens in this equation?

Well, what about them? What do the oxygens do? What happens to their electrons?

That's what confuses me! The oxygen in the reactants (CuO) is bonded to the copper because the oxygen is -2. And the oxygen in the products (H2O) is also -2. The valency of the oxygen does not change.

That's right! Oxygen in any compound (almost) always has a valency of -2.

Oh, yeah, I forgot that's a rule about oxygen! Oxygen (almost) always has a valency of -2.

Right! Except in peroxides where the oxygen is -1 or in its elemental form where it is zero.
Recall that in the previous equation (the one before this one) we talked about the oxidation of copper to form CuO. In that case the oxygen molecule changed its valency from zero to -2, by gaining electrons.

Yeah, the oxygen became reduced! But in this equation, CuO + H2 ------> Cu + H2O, it is the hydrogen molecule being reduced. The oxygen started with a valency of -2 and ended with a valency of -2. The oxygen's valency isn't changed.

Right. In CuO + H2 ------> Cu + H2O the oxygen is not involved in the redox part of the equation because its valency stays the same. The oxygen is not oxidized or reduced.

All the redox magic is in the coppers and hydrogens! The copper is oxidized and the hydrogen reduced. It has nothing to do with the oxygens! That seems wrong.

You're not wrong. You're right! It just "feels" wrong, because we use that old word "oxidation" and you begin to think that the oxygen is involved. But in this example the oxygen is just being passed around. The electrons in the oxygen do not move to other atoms.

So, the oxygen isn't really involved!

Well, it isn't involved in the redox, but it certainly is involved in the final equation. You see, this is where the word "oxidation" is used to say that the hydrogens are "oxidized".

But the hydrogens ARE oxidized! They lose their electrons, so the hydrogens are oxidized!

Right! In the old days, Alchemists said the hydrogen was oxidized because it picked up the oxygen. And they also said the copper was reduced because it lost the oxygen. But in fact we define redox equations according to electrons. Not oxygen.

OK. I get it. Sometimes the oxygen oxidizes and sometimes it doesn't. But if I just follow the electrons instead of the oxygen I can tell what is important in redox reactions.

That's right.

So the copper really is reduced because it gains electrons (Cu+2 + 2e- ------> Cu)
and the hydrogens really are oxidized because they lose electrons (H2 -----> 2H+ + 2e-).

Right! It just so happens that oxygen is involved only as a "bystander". In this equation (reaction) the oxygen isn't oxidized or reduced. It is swapped around as the other two elements are reduced and oxidized!

Phewww! It's a bit twisted but I think I got it. Any other Alchemy up your sleeve you think will confuse me?

Well, there is the subject of "agents" in redox reactions. It's quit simple, really. Once you see how it works. It's just a matter of definitions.

OK, let's have it.

The substance that loses electron(s) is "oxidized" but it is called a reducing agent because it is the agent responsible for reducing the other substance. Reducing agents lose electrons. Of course, the opposite agent must also be present to accept those electrons.

Let me guess. The substance that gains electron(s) is "reduced" but is called an oxidizing agent because it is the agent responsible for oxidizing the other substance. Oxidizing agents gain electrons.

Right! I think you see how this redox thing works.

Hmmm, I'm not too sure. But I'll go through what you just said a couple times and I'm sure I'll get it.

I'm sure you will.

You said we would come back to balancing equations?

Yes, I did. Recall that a balanced chemical equation has equal numbers of each atom including each type, or element, on both sides of the equation.

Yeah, it's like a math puzzle.

Right. You solve the puzzle by adding extra molecules to different sides of the equation until the atoms are all accounted for. "It's the law!" and it makes perfect sense because you can't create new or different atoms (unless you use nuclear chemistry).

What about the electrons? Should the electrons balance?

Well, as a matter of fact they should! That's a point some Alchemists forget.

How could they forget the electrons?! It makes sense that you can't create electrons from nothing! I think you have to have equal numbers of electrons on both sides of the equation.

You're right. Electrons can be released or absorbed by atoms during a chemical reaction, so they must balance too. You have to take account of them.

We balanced a few equations earlier. They were easy. But not all equations are easy to balance, are they?

Well, they take a wee bit of practice. A young Alchemist's first equations are the hardest. After a while you start to get a feel for how to do the balancing. Balancing equations can get tricky and it helps to work slowly, carefully and keep track of everything!
There are no (easy) steps to follow, but there is one important rule ...
the only way to balance a chemical equation is by changing the number of molecules.

How do you mean?

You cannot change the molecules themselves (you cannot change the subscripts on the molecules) so you must change the number of molecules (by changing the coefficient, or number in front, of the molecules).

I see. If you tried to balance an equation by changing the subscripts, you'd be changing the kinds of reactants and products. That's not what you want to do. That's cheating.

And it's wrong. Just keep adding in more of one molecule or another to one side of the equation or the other until they balance. But, of course, you want to add as few as possible. It keeps the equation looking neat and provides the simplest solution.

But are equations of any real use? I mean other than helping you to understand the reactions.

Yes. With a balanced equation you can calculate how many molecules you need to make a certain number of other molecules. It helps you plan your Alchemy.

But how?

Well, in Advanced Alchemy you can learn how to use balanced chemical equations to figure out how many grams of reactant you get from a set amount of product. But that requires a bit more math than I want to go into at this level of Alchemy. I think you'll learn plenty about Alchemy without going that far into the math.

OK. Are some equations easier to balance than others?

Yes. Chemical equations with very simple changes in valency often go unnoticed because they are so easy to balance. This unbalanced equation changes two elemental molecules into a compound.
H2 + F2 ------> HF

This is the equation we talked so much about when I learned about bond breaking and making.

Yes, it is. Here I've written it as an unbalanced equation. Tell me about the valency of the reactants and products.

OK. Each hydrogen's valency is zero.

Right. Each hydrogen makes one covalent bond to the other, BUT H2 is an elemental compound so both atoms in the molecule have a valency of zero.

That's right, wizard. I remembered.
And I also know that each fluorine's valency is also zero for the same reason. But the molecule formed on the right side is a compound. Both the atoms in that compound have a valency of 1 because they both form one covalent bond to another atom. To each other. The hydrogen has a valence of +1 (because it is Group I) and the fluorine has a valency of -1 (because it is Group VII).

How do you know that the hydrogen isn't a hydride? What makes you so sure its valency in HF is +1 and not -1?

Because if the hydrogen was -1 it wouldn't bond to the fluorine anion. Two anions would be repelled from each other, not attracted!

Absolutely right Now, go on and balance it.

Easy! It's a simple matter to balance this by simply counting the number of atoms. The atoms going into the equation MUST equal the atoms coming out. In any chemical equation, the atoms on the right must equal the atoms on the left.
H2 + F2 will provide enough H and F to make two molecules of HF. Placing a 2 in front of the molecule means that two molecules of HF are made.
H2 + F2 ------> 2HF

Very good Arthur. This equation is now balanced. There are two hydrogens and two fluorines on both sides of the equation. Notice that the hydrogens have lost their electrons, changing their charge from zero to +1.

Yeah. Both of the hydrogens in the H2 lose their electrons, so they are oxidized ("leo"). Also, the two fluorines have each gained an electron, changing their charge from zero to -1. Both the fluorines gained an electron, so they are reduced ("ger"). So all the electrons balance too!

Very good Arthur. That was an easy one. All you had to do was double the number of product molecules. Often, you must "go back" and change other coefficients (the numbers in front of the molecules) again and again until all the atoms balance. But here, you only had to add an extra molecule and it was a balanced equation.

Easy!

True, but complex changes in valency are more difficult to balance. When there is a major change in valence, balancing the equation becomes more difficult. You must remember that the total number of electrons gained (by the oxidizing agent) MUST equal the number of electrons lost (by the reducing agent).

"It's the law!"

Yes, and it is the base on which we "balance" chemical equations involving a change in valency.

OK. And, of course, the atoms which go into the equation must also equal the number and kinds of atoms which come out of it

Right. You can use your knowledge of redox to get to the details in an equation. All chemical reactions involving a change in valence can be broken down into TWO reactions - one oxidation and the other reduction.
The oxidation of copper can be pictured as a two processes occurring together.
Reduction is O2 + 4e- ------> 2O-2
The oxygen changes from a covalent (sharing electrons) elemental molecule (valence of zero) to a pair of anions (valence -2) by reduction.
Oxidation is Cu ------> Cu+2 + 2e-
The copper metal changes from a metallic bonded ("super shared" electrons) elemental metal (valence of zero) to a cation (valence +2) by oxidation.

I see. Those two "half reactions" together form the equation
Cu + O2 ------> CuO
But that's unbalanced.

Yes, but it is a good place to start. These "half reactions" are also called "half equations" and together they form a "redox couple". They occur at the same time (simultaneously) but it is good to think of them as two separate reactions (equations). Now tell me about the atoms and electrons involved in that reaction.

Well, the oxygen molecule needs 4 electrons to reduce both oxygen atoms but the copper atom only produces 2 electrons.

Right. If you were to combine those two half equations you would see that there are not enough electrons to balance it. To produce a balanced equation you MUST have equal numbers of electrons transferred. So, what do you do?

To produce the 4 electrons needed to reduce the oxygen molecule, you must reduce TWO atoms of copper (both producing 2 electrons for a total of 4 electrons).

Right. By doubling the amount of copper you double the amount of electrons given up in the reaction.
Doubling the amount of the reducing agent (the copper loses electrons so it the reducing agent) gives this half reaction
2Cu ------> 2Cu+2 + 4e-

I see. Now, the number of electrons produced by the oxidation of two copper atoms equals the number of electrons needed to reduce the oxygen molecule.

That's right. We can now add the two half reactions like this
Reduction is O2 + 4e- ------> 2O-2
Oxidation is 2Cu ---------> 2Cu+2 + 4e-
---------------------------------------------------------
Total Redox is 2Cu + O2 ------> 2Cu+2 + 2O-2

I see that there are 4 electrons on the left and 4 electrons on the right side of these two half equations, so the number of electrons lost (by the copper atom) EQUALS the number gained (by the oxygen molecule). But why aren't they in the total redox equation?

Well, they are there. You can think of these 4 electrons on opposite sides of the equation as "canceling out" each other. It would be all right to include them. But most Alchemists leave the electrons out of the final balanced equation.

I see. You use the half equations to make sure the electrons are accounted for. To make sure they balance. But once you are satisfied that you have all the electrons, don't bother writing them.

Yes. We can use the electrons and half equations to help us get the right proportions, the right balance, of reactants and products. But we don't normally include the electrons in the final equation.

What do you mean by "don't normally"?

Well, I would only include the electrons in the equation if they were important to help me understand what is going on. For example, if I were writing a balanced equation for a chemical reaction that produced electrons, I would include them in the equation.

Hey, wait a minute! How can you have a chemical reaction "produce" electrons?! You can't make them out of nothing. Right?

Right. What I mean is a chemical reaction that releases electrons from the reactants like this
Reactant ------> Products + electrons
Actually the electrons are products too, so I guess that should be
Reactant ------> Products (including electrons)

But where do these electrons come from? What kind of chemical reaction releases electrons?

Well, some redox reactions can be used to "make" electrons. Actually, those reactions release electrons from the reactants.

The reactants are oxidized.

Yes. Those reactions are used in chemical vessels called "batteries". When the reactant has given up all the electrons can, the battery goes "dead".

I'm not sure what you are talking about with these batteries. Are they important.

Well, they can be. Batteries and similar chemical reactions are part of a special filed of Alchemy called ElectroAlchemy. It can be pretty advanced.

Then I think we will just deal with "normal" chemical reactions.

That's fine by me. But you should be aware that some reactions produce electrons by releasing them from the reactants.

OK. Now getting back to the oxidation of copper to copper oxide, it's the transfer of these electrons which causes the product to form. Right?

That's right. The two ions created in this redox (the Cu+2 and the O-2) are drawn together by electrostatic attraction and held together by ionic bonds.
2Cu+2 + 2O-2 ------> 2CuO.

And the reaction is balanced because the net charges (electrons transferred) AND the number of atoms is equal on both sides of the equations.
2Cu + O2 ------ > (2Cu+2 + 2O-2) ------> 2CuO

Absolutely.

You know. I could have balanced this equation without even thinking about the electrons or changes in valency. The atoms just "add up" right, so the equation is balanced.

True, but you should always be aware that valency changes are going on. When you balance an equation, you are looking for an answer but at the same time it lets you learn the details of the reaction. If there is a change in valency you should always check to see that the electrons "add up" too. In this example, the balancing might appear to be obvious, but some equations involving changes in valency can get tricky. Always check out the electrons as well as the atoms. Sometimes an equation is not written correctly and you may discover, using redox balancing, that a product or reactant is not correct. It acts as a way to check your work.

OK. How about some harder equations to balance? I can handle this stuff.

Good. Very complex changes in valency are more difficult to balance. But I'm sure you can do it. Like all equations, you start with a rough equation, adjust it to balance the atoms and then adjust it again to balance the electrons (if they need balancing). Or you can first balance the electrons and then the atoms.

For example...?

For example, iron (III) chloride (FeCl3) and sodium sulfite (Na2SO3) in water form iron (II) chloride (FeCl2) and sodium sulfate (Na2SO4) plus hydrochloric acid (HCl).

Wow, that's a mouth full!

True. Let me right that as an unbalanced equation.
FeCl3 + Na2SO3 -----> FeCl2 + Na2SO4 + HCl

I recall that iron in the +3 state is written as Fe(III) and called ferric, while the iron in the +2 state is written as Fe(II) and called ferrous. But what is this with sulfite and sulfate?

Ah, yes. The "ites" and "ates".

What are you talking about?

Oxygen! That's what I'm talking about when I use "ites" and "ates" at the end of the anion. I'm talking about oxygens.

You mean the oxygens attached to the sulfur?

That's right. The sulfur-oxygen anion called sulfite (SO3-2) has one less oxygen than the sulfur-oxygen anion called sulfate (SO4-2).
The "ite" anion contains less oxygen than the "ate" anion. That's another "naming rule".

You sure name things a lot!

True, but it helps me keep track of it all. Especially when talking about radicals.

Radicals? What are radicals?

We've been talking about them already but just haven't given them a name. Until now. A radical is a cluster of atoms held together with covalent bonds, but they contain an excess or deficiency of electrons. So they are ions.

Sounds like radicals are complex ions!

They are. But you get use to them after a while. Here are the names and valence numbers (as superscripts)of some common radicals (they are repeated in the notes)
Ammonium (NH4)+
Acetate (C2H3O2)-
Carbonate (CO3)-2
Bicarbonate (HCO3)-
Chlorate (ClO3)-
Cyanide (CN)-
Nitrite (NO2)-
Nitrate (NO3)-
Phosphate (PO4)-3

Wow, there's a lot of radicals!

Yes. And of course there are sulfite and sulfate too.
If you look carefully you see the sulfur changes its valency along with the number of oxygens bonded to it. Both the sulfate (SO4-2) and the sulfite (SO3-2) have the same -2 charge but they have different numbers of oxygens. Tell me about the oxygens in those two anion radicals and how they affect the sulfur.

OK. Oxygen in all compounds is always -2 unless it is a peroxide, which this isn't (in this example). So it must be the sulfurs that are changing valency.

Right. Now use that fact to tell me the valence number of sulfur in sulfates and sulfites.

I don't know how.

Well, all the oxygens have a valency of -2. Right?

Right. So sulfite has 3 oxygens each making two bonds for a total of 6 bonds right?

Right. However, you should think of that as -6, because the valence numbers of all the oxygens are -2 each, for a total of -6.

OK. Now, the sulfite radical (SO3)-2 has a charge of -2. Hmmm. Somehow I think that's important.

It is! Just think about the math involved. What must be the charge on the sulfur atom, when 3 oxygen atoms are attached (each with a charge of -2) which would give you an ion with a leftover charge of -2?

Hmm. I have -6 from the 3 oxygens and must have -2 when I am done, so the sulfur must contribute a valence of +4. Is that right? Does sulfur have a valency of +4?

Yes it does! At least in sulfite. You worked that out very well. Now use the same steps to tell me the valence number of the sulfur in the sulfate radical (SO4)-2.

OK. Sulfate has four oxygens each giving a -2 charge to the molecule. So that's -8 from the oxygens. And the charge on the total anion is -2, so the sulfur must be +6.

Right as rain! Now let's get back to that unbalanced equation.
FeCl3 + Na2SO3 -----> FeCl2 + Na2SO4 + HCl
What happens to the sulfurs as they go from reactants (on the left) to products (on the right)?

The valence number changes from +4 to +6.

Right! What does that mean in terms of the electrons?

Oh, the sulfur loses two more electrons. The sulfur is oxidized (because "leo" tells me that "losing electrons oxidizes").

Correct. Why not write that as a half equation?

Like this?
(SO3)-2 ------> (SO4)-2 + 2e-

That's excellent. The half equation you wrote shows you that sulfur is oxidized. (Don't worry about where the extra oxygen comes from. Not yet.)

So something else in the equation must be reduced. I bet it is the iron. Yeah, that's it! The iron goes from the ferric (+3) to the ferrous (+2) cation. To do that the iron must accept an electron. The iron is reduced because of "ger" ("gaining electrons reduces").

Very good. You have identified both the oxidation and the reduction. That's an important part of Alchemy. Always try to identify the redox couple (if redox occurs).
Now why not write down the two half equations and add them together to see if it makes sense?

OK
(SO3)-2 ------> (SO4)-2 + 2e-
Fe+3 + e- ------> Fe+2
--------------------------------
Hmmm. Nope I have too many electrons produced to make it balance!

Do you know how to give an extra electron a home?

Sure do. Just add another iron. But that must be another whole molecule. A molecule of ferric chloride (FeCl3).

Right. But don't worry about that yet. Go ahead and make that twice as many irons into the half equation.

OK
(SO3)-2 ------> (SO4)-2 + 2e-
2Fe+3 + 2e- ------> 2Fe+2
-------------------------------------
2Fe+3 + (SO3)-2 ------> 2Fe+2 + (SO4)-2 and all the electrons are accounted for!

That's right. But so far you have only included the ions. Lets see the equation with all the molecules shown.

Easy. I'll just rewrite the old equation but include 2 molecules of ferric chloride and ferrous chloride.
2FeCl3 + Na2SO3 -----> 2FeCl2 + Na2SO4 + HCl

Very good. Now you have a balanced equation for the electrons. Do the atoms all add up too?

Hmmm. There are two irons on both the right and the left. Hey, there are three chlorines on the left but only two on the right.

Ah, you're looking at the right problem, but you miss-counted the chlorines. You forgot the coefficients in front of the irons.

Oops! Right. That gives six chlorines on the left and four on the right. The chlorines are unbalanced. Hey, no wait. There's a chlorine in the HCl on the right. Does that count?

It sure does!

OK. But that still doesn't balance! I count a total of six chlorines on the left but only five on the right.

Yes, so do I. How would you correct that? Remember, to make it balance all you have to do is add more of one molecule or another to one side or the other.

Ah, I don't want to mess with the iron chlorides because that would only make the equation more complicated. If I changed the number of iron chlorides I would have to recalculate the half equations and balance the electrons again. I'd rather not do that again!

I see your point! It is difficult. Sometimes you do have to go back and start over. But not this time. Can you see how to add more chlorine without bothering your valence radicals?

Yeah. The HCl is the trick! I'll just have two HCl molecules instead of one.
2FeCl3 + Na2SO3 -----> 2FeCl2 + Na2SO4 + 2HCl
Now there are six chlorines on both sides. The chlorines balance and I didn't have to change anything that has to do with redox so I don't have to worry about recalculating it all over again. (Pheww!)

Right. Now then, is the equation balanced?

Hmmm. The irons, sulfurs and chlorines are OK. And so are the sodiums, because there's two on each side. Oh, but look at the oxygens! There's three on the left (in the sulfite) and four oxygens on the right (in the sulfate). And, hey! Where did this hydrogen come from? There's no hydrogen on the left but there's a hydrogen in the hydrochloric acid (HCl) on the right. Actually I need two hydrogens because I need to make two molecules of HCl. What's going on?

Calm down, Arthur. You are right to notice that you need two more hydrogens. And you also need another oxygen. Did I forget to mention that this chemical reaction is done in water?

Water?!

Yes. Most chemical reactions are done in water. It is such a common thing that I forgot to include it in the equation but it looks like it will be important.

Important! Yes, it is important! If I put one water molecule on the left side, then the equation becomes...
H2O + 2FeCl3 + Na2SO3 ------> 2FeCl2 + Na2SO4 + 2HCl

That's right. And now you have a balanced equation. Check it and see for yourself.

Both sides have two hydrogens, four oxygens (on the left you get one from the water), two iron atoms, six chlorine atoms, two sodium atoms, and one sulfur atom. Yeap, they all are accounted for. And we took care of the electrons earlier when we did the redox part.

Right. We don't have to recount the electrons because you balanced them earlier. The water and the HCl aren't involved in the redox so we can ignore any electrons they carry.

I get it. The valence of the atoms in water or HCl doesn't change in this reaction, so they are not involved in the redox.

Right.

My goodness that was a hard equation!

Yes, that was a difficult one. And you learned some extra Alchemy in the process.

Yeah, about radicals.

Right. Radicals are an important part of Alchemy.
You know, you could have balanced the equation the other way around. You can balance the atoms first and then deal with the electrons. Let's do that same problem again but the other way around. Atoms first.

OK. First I'll write a rough equation to start with
FeCl3 + Na2SO3 -----> FeCl2 + Na2SO4 + HCl
I see there are no hydrogens on the right side! But this reaction occurs in water and that is where the hydrogens come from, so I add the water to give
FeCl3 + Na2SO3 + H2O -----> FeCl2 + Na2SO4 + HCl

Good. Now what?

Next I count atoms. I have a balanced number of iron (1), chlorine (3), sodium (2), sulfur (1) and oxygen atoms (4). BUT I have two hydrogens on the left (in the water) but only one on the right (in the HCl).

Right. How do you correct that imbalance?

Just add an extra molecule of HCl to give
FeCl3 + Na2SO3 + H2O -----> FeCl2 + Na2SO4 + 2HCl
Now the hydrogens are balanced but there are four chlorines on the right (two in the one molecule of FeCl2 and one in each HCl molecule.). So now I must balance the chlorines. I have to add chlorine to the right side of the equation. This is NOT easy because the only way to change the number of chlorines also changes the number of iron atoms!

Yes. That makes it more difficult to follow but you must. So add another molecule of FeCl3 to the left side to give you
2FeCl3 + Na2SO3 + H2O -----> FeCl2 + Na2SO4 + 2HCl

OK. OK. But, now I have too many chlorines on the left (6 of them) and the irons are not balanced either!
Hmmmm. By adding an extra molecule of FeCl2 to the right side, suddenly things balance!
2FeCl3 + Na2SO3 + H2O -----> 2FeCl2 + Na2SO4 + 2HCl

Very good! Now you have the same atoms on the left as on the right. The atoms balance. But do the electrons? Remember, some complex redox is going on here. Notice that the iron changes its valency from +3 to +2.

I remember! We call iron (III) ferric and iron (II) ferrous. In this reaction the iron goes from +3 to +2 by gaining an electron and the electron's negative charge causes the charge to drop by one. Because the iron gains an electron, it is reduced. Something else must be oxidized. That's where the sulfur comes in. The iron is reduced from the ferrous (+3) to the ferric (+2) while the sulfur is oxidized from the sulfite (+4) to the sulfate (+6).

Good. You have now identified the atoms with changing valences and thus identified the atoms responsible for the transfer of electrons. No other atoms in this equation change their valency. So all you have to do is be sure the electrons balance by checking that the electrons gained by the iron equal the electrons lost by the sulfurs.

Right. I see from this equation
2FeCl3 + Na2SO3 + H2O -----> 2FeCl2 + Na2SO4 + 2HCl
that the two ferric atoms (2Fe+3) on the left each takes on an extra electron to become two ferrous irons (2Fe+2), reducing them. The reduction of the irons needs two electrons.
The single sulfur atom in the sulfite (SO3-2) goes from a valency of +4 to +6 by giving up two electrons, so it is oxidized.
In total, two electrons are transferred and the equation is already balanced!

Very good, Arthur. You can balance equations either way. It doesn't matter which you do first, just as long as you check both atoms and electrons. Balancing equations is a lot like doing math problems. Some are simple and obvious. There's only one correct answer but there may be more than one way to get to the same answer. As with math problems, the important point is to work slowly, carefully and be sure you know what you are doing. Once you get the answer, check it to see if it is right, by checking to see that the electrons and atoms balance.

I think I need to read this all again to really understand it.

Good idea. Any Alchemist can expect to get plenty of "balancing problems". Practice makes perfect.

If you want to continue choose the next hyperlink.

PRINCIPLES OF ALCHEMY
FIRE

Part Two

Many things influence the rates of chemical reactions.

Equilibrium determines the yield of a chemical reaction.

Enthalpy changes are involved in chemical reactions.

Blame the disorder of the universe on entropy.

Gibbs energy explains all chemical reactions.


This work was created by Dr Jamie Love and licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Creative Commons Licence.