The following procedure is guaranteed to produce an accurately balanced reaction equation for any redox reaction that occurs in aqueous solution. In fact, it will even work for reaction equations in which no redox occurs, but then it's pretty tedious compared to balancing a metathesis reaction. The only thing you have to know to begin is the chemical identity of the major reactants and products of the reaction. Let's take the following example: a popular WW-II German rocket propellant was nitric acid (HNO3) and hydrazine (N2H4). As a general rule, unless stated otherwise, nitrogen will wind up as elemental nitrogen (N2), carbon will wind up as carbon dioxide (CO2), and hydrogen and oxygen are specifically treated below. For any other elements, the problem at hand must give you both reactants and products.

  1. Write a "skeleton" reaction equation, one with no stoichiometric coefficients.

    HNO3 + N2H4 = N2

  2. Pick out an unusual element from the skeleton reaction (non-hydrogen, non-oxygen unless that's all you have). Write a skeleton "half-reaction," one involving only species of that element. Elemental oxygen (O2) and hydrogen (H2) may appear only if they are included explicitly in the problem.

    HNO3 = N2

  3. Insert stoichiometric coefficients to balance the number of atoms of that element on each side of the half- reaction.

    2 HNO3 = N2

  4. Insert species from the original reaction to take care of other non-H, non-O elements (if any). Balance the half-reaction with respect to the non-H, non-O element (if any).

    (Not applicable to this problem)

  5. Insert enough H2O molecules on the side that's short of O atoms to balance the O atoms.

    2 HNO3 = N2 + 6 H2O

  6. Insert enough H+ ions on the side that's short of H atoms to balance the H atoms.

    2 HNO3 + 10 H+ = N2 + 6 H2O

  7. Total up the electrical charge on each side of the half-reaction equation.

    (+10 on left, 0 on right)

  8. Add enough electrons to the side that's too positive (or not negative enough) to make the net charge balance.

    2 HNO3 + 10 H+ + 10 e- = N2 + 6 H2O

  9. Check to make sure that atoms of each element are balanced and that charge is balanced in the half-reaction.

    (2 N, 12 H, 6 O, 0 charge)

  10. Pick another unusual element in the original skeleton equation and write a skeleton half- reaction for it. Go through steps 3-9 again; that is, balance the unusual elements, then balance O using H2O, then balance H using H+, then balance charge using e-.

    N2H4 = N2

    N2H4 = N2 + 4 H+

    N2H4 = N2 + 4 H+ + 4 e-

    (2 N, 4 H, 0 charge)

  11. The electrons are the key to balancing redox reactions. In a redox reaction electrons are transferred from one reactant to another, so the number of electrons in the first half-reaction must equal the number in the second. If they don't, just multiply each half-reaction by an integer chosen so that the electrons do balance.

    (Multiply first reaction by 2 and second reaction by 5 to give 20 electrons)

    4 HNO3 + 20 H+ + 20 e- = 2 N2 + 12 H2O

    5 N2H4 = 5 N2 + 20 H+ + 20 e-

  12. Add the two half-reactions together, canceling the electrons and as many H+ and H2O as possible.

    4 HNO3 + 5 N2H4 = 7 N2 + 12 H2O

  13. Double check that the number of atoms of each kind are balanced and that the total charge is balanced.

    (14 N, 12 O, 24 H, 0 charge)

The half-reaction with electrons on the right is called the oxidation. Since electrons are lost in this process, we use the acronym LEO: Lose Electrons Oxidation. The half-reaction with electrons on the left is called the reduction. GER stands for Gain Electrons Reduction. When we speak of "the oxidation" or "the reduction," we are speaking of half-reactions, but when we are speaking of reactants, the situation is reversed.

Everyone knows that an insurance agent causes others to be insured. Similarly, the reactant that causes another reactant to be oxidized is called the oxidizing agent, or oxidant. The reactant which causes another reactant to be reduced is called the reducing agent, or reductant. If you stop to consider the matter, you will realize that the oxidant is the one that is, itself, reduced and vice versa. In the previous example HNO3 is the oxidant and N2H4 is the reductant.

I'll work three more examples, two easy ones from Natural History and a hard one, but the only way to learn this is to work lots of problems on your own.

Q: Cu + O2 = Cu2O
Q: CH3COOH + Cu = Cu(CH3COO)2 + H2
Q: KClO3 + C12H22O11 = KCl + CO2

I don't think anyone will have an easy time learning to balance redox reactions. Balancing redox reactions is probably one of the two hardest things in first-year chemistry and I give you permission to find it difficult. Curse it, swear at it, grit your teeth at it, but know that if you persevere, you can master it. I have seen people with Velcro shoelaces get this, so I am sure that if you've read this far, you're smart enough to do it. And there are two payoffs; first, this is the hardest thing in the book, so if you get this it'll be smooth sailing from here on; second, you will be able to amuse yourself for hours in your doctor's waiting room. When you finally get in, tell her how much fun you've been having and watch her eyes boggle.

WarningMaterial Safety

A distinction must be made between acute toxicity, the kind in which exposure makes you sick right now, and chronic toxicity, the kind which makes you sick some time in the future. So far, we have considered only acute toxicity. While LD50's determined in test animals may not be quantitatively reliable for humans, they at least provide a measure of relative acute toxicity. Sadly, there is no single, easily understood measure of chronic toxicity. What is clear, however, is that chronic toxicity results from repeated exposure to sub-acute doses of a substance over extended periods of time.

The cigarette is probably the most familiar example of a material which is chronically toxic but acutely non-toxic. How can a cigarette be acutely non-toxic when the LD50 (mice, oral) for nicotine is 230 mg/kg? Each cigarette delivers about 2 mg of nicotine. A little UFA shows that a 100 kg person would have to smoke 11,500 cigarettes in order to have a 50% chance of snuffing it from nicotine poisoning, assuming that the toxicity for inhalation is not too different from that for ingestion and that toxicity for humans is similar to that for mice. No, you just don't hear about people smoking themselves to death in one sitting; it takes years to do that, and taking years to kill you is what chronic toxicity is all about. It bothers me, then, when well-meaning anti-smoking activists list all of the toxic chemicals in tobacco smoke, including carbon monoxide and benzene, but don't tell you the amounts of these chemicals delivered by a cigarette. Just because toxic chemicals are detectable in something doesn't mean that they are present in dangerous amounts. Until people start overdosing on cigarettes the way they do on Heroin or alcohol, there's just not a case to be made for acute toxicity.

As with smoking, chronic chemical intoxication occurs with repeated exposure to sub-acute doses over long periods of time. Consequently we ought to pay the most attention to those situations which bring about such exposure. Occupational exposure is one such situation which attracts and deserves attention. We might hear on the news, for example, that workers in the widget industry are three times as likely to get biglongnamitis as the general public. As terrible as this statistic sounds, it is vital to know whether the incidence of this disease is high or just higher-than-average. If biglongnamitis is a rare disease then even a tripled rate of incidence may be small in comparison to other dangers of widget work.

In no way do I mean to downplay the risks posed by smoking, by occupational hazards, by food additives, or by environmental pollutants. Unfortunately, however, these risks are far more complex than those posed by acute toxins. For chronic toxins there is no measure of risk as straightforward as the LD50 for acute toxins. The bad news, then, is that it is extremely difficult for the general public to distinguish between genuine chronic dangers and alarmist propaganda. The good news is that chronic toxicity is not about the one exposure which came back to bite you twenty years later; it's about years of exposure that finally caught up with you. If the motto for acute toxicity is "the dose makes the poison," then perhaps the one for chronic toxicity ought to be "the longer you live, the sooner you bloody-well die." While you may not be able to avoid exposure to every conceivable chronic hazard, you have time to demand more of your news sources than sensationalistic sound-bites.

You aren't going to get away without a material safety assignment, even though there are no materials involved in this project. Find an MSDS for mercury (CAS 7439-97-6), silica (CAS 14808-60-7), or asbestos (CAS 12001-29-5), and write a paragraph comparing and contrasting the chronic and acute toxicities of the material you have chosen.

NoteResearch and Development

So there you are, studying for a test, and you wonder what will be on it.