BALANCING SIMPLE EQUATIONS

8.2. BALANCING SIMPLE EQUATIONS

If you know the reactants and products of a chemical reaction, you should be able to write an equation for the reaction and balance it. In writing the equation, first write the correct formulas for all reactants and products. After they are written, only then start to balance the equation. Do not balance the equation by changing the formulas of the substances involved. For simple equations, you should balance the equation “by inspection.” (Balancing of oxidation-reduction equation will be presented in Chap. 14.) The following rules will help you to balance simple equations.

1. Before the equation is balanced, there are no coefficients for any reactant or product; after the equation is balanced, the absence of a coefficient implies a coefficient of 1. Assume a coefficient of 1 for the most complicated substance in the equation. (Since you are getting ratios, you can assume any value for one of the substances.) Then work from this substance to figure out the coefficients of the others, one at a time. To prevent ambiguity while you are balancing the equation, place a question mark before every other substance.

2. Replace each question mark as you figure out each real coefficient. After you get some practice, you will not need to use the question marks. If an element appears in more than one reactant or more than one product, balance that element last.

3. Optionally, if a polyatomic ion that does not change during the reaction is involved, you may treat the whole thing as one unit, instead of considering the atoms that make it up.

4. After you have provided coefficients for all the substances, if any fractions are present, multiply every coefficient by the same small integer to clear the fractions.

CHEMICAL EQUATIONS

[ CHAP. 8

5. Eliminate any coefficients equal to 1.

6. Always check to see that you have the same number of atoms of each element on both sides of the equation after you finish.

EXAMPLE 8.4. Sulfuric acid, H 2 SO 4 , reacts with excess sodium hydroxide to produce sodium sulfate and water. Write a balanced chemical equation for the reaction.

Ans. Step 1: Write down the formulas for reactants and products. Assume a coefficient of 1 for a complicated reactant or product. Add question marks:

1H 2 SO 4 + ? NaOH −→ ? Na 2 SO 4 + ?H 2 O

Step 2:

Balance the S

1H 2 SO 4 + ? NaOH −→ 1 Na 2 SO 4 + ?H 2 O

Balance the Na

1H 2 SO 4 +

2 NaOH −→ 1 Na 2 SO 4 + ?H 2 O

Balance the H

2 NaOH −→ 1 Na 2 SO 4 + 2H 2 O Since the coefficient of H 2 SO 4 is 1, there is one sulfur atom on the left of the equation. Sulfur appears in

1H 2 SO 4 +

only one product, and so that product must have a coefficient of 1. The one Na 2 SO 4 has two Na atoms in it, and so there must be two Na atoms on the left; the NaOH gets a coefficient of 2. There are two H atoms in H 2 SO 4 and two more in two NaOH, and so two water molecules are produced. The oxygen atoms are balanced, with six on each side. Step 4 is not necessary.

Step 5: We drop the coefficients of 1 to finish our equation.

2 NaOH −→ Na 2 SO 4 + 2H 2 O Step 6: Check: We find four H atoms, one S atom, two Na atoms, and six O atoms on each side. Alternatively

Eliminate the 1s

H 2 SO 4 +

(step 3), we count four H atoms, one SO 4 group, two Na atoms, and two other O atoms on each side of the equation.

EXAMPLE 8.5. Magnesium metal reacts with HCl to produce MgCl 2 and hydrogen gas. Write a balanced equation for the process.

Ans. Step 1:

? Mg + ? HCl −→ 1 MgCl 2 + ?H 2

We note that hydrogen is one of the seven elements that form diatomic molecules when in the elemental state.

Step 2:

1 Mg + 2 HCl −→ 1 MgCl 2 + ?H 2

1 Mg + 2 HCl −→ 1 MgCl 2 + 1H 2

Step 5:

Mg + 2 HCl −→ MgCl 2 + H 2

Step 6: There are one Mg atom, two H atoms, and two Cl atoms on each side of the equation. EXAMPLE 8.6. Balance the following equation:

CoF 3 + NaI −→ NaF + CoI 2 + I 2

Ans. Step 1:

Steps 4 and 5:

2 CoF 3 + 6 NaI −→ 6 NaF + 2 CoI 2 + I 2