Chemical Quantities and Aqueous Reactions: Balancing Chemical Equations

Chapter 4: Chemical Quantities and Aqueous Reactions

Writing and Balancing Chemical Equations

Chemical equations are essential tools in chemistry for representing chemical reactions, which involve the transformation of reactants into products. Balancing these equations ensures the law of conservation of mass is obeyed, meaning the number of atoms of each element is the same on both sides of the equation.

• Chemical Reaction: A process in which one or more substances are converted into one or more different substances. This involves the rearrangement and exchange of atoms to produce new molecules.

• Chemical Equation: A symbolic representation of a chemical reaction, showing reactants and products.

• States of Matter in Equations: Indicated by (g) for gas, (l) for liquid, (s) for solid, and (aq) for aqueous (dissolved in water).

Example:

• $\mathrm{CH}_4 (g) + \mathrm{O}_2 (g) \rightarrow \mathrm{CO}_2 (g) + \mathrm{H}_2\mathrm{O} (g)$

In this reaction, methane reacts with oxygen to produce carbon dioxide and water.

Balancing Chemical Equations

Balancing a chemical equation ensures that the same number of each type of atom appears on both sides of the equation. This is necessary to satisfy the law of conservation of mass.

• Step 1: Write the unbalanced equation.

• Step 2: Take inventory of the elements and their numbers on each side.

• Step 3: Adjust coefficients to balance the atoms.

• Step 4: Check your work to ensure all atoms are balanced.

Example:

• Unbalanced: $\mathrm{CH}_4 (g) + \mathrm{O}_2 (g) \rightarrow \mathrm{CO}_2 (g) + \mathrm{H}_2\mathrm{O} (g)$

• Inventory: C: 1 (both sides), H: 4 (left), 2 (right), O: 2 (left), 3 (right)

• Balanced: $\mathrm{CH}_4 (g) + 2\mathrm{O}_2 (g) \rightarrow \mathrm{CO}_2 (g) + 2\mathrm{H}_2\mathrm{O} (g)$

• Inventory: C: 1, H: 4, O: 4 (both sides)

Balancing Equations with Fractional Coefficients

Sometimes, balancing requires the use of fractional coefficients, especially when free elements are involved. These can be cleared by multiplying the entire equation by the denominator of the fraction.

• Example: Potassium superoxide reacts with carbon dioxide:

• Skeletal: $\mathrm{KO}_2 (s) + \mathrm{CO}_2 (g) \rightarrow \mathrm{O}_2 (g) + \mathrm{K}_2\mathrm{CO}_3 (s)$

• Balanced (with fraction): $2\mathrm{KO}_2 (s) + \mathrm{CO}_2 (g) \rightarrow \frac{3}{2}\mathrm{O}_2 (g) + \mathrm{K}_2\mathrm{CO}_3 (s)$

• Clear fractions: $4\mathrm{KO}_2 (s) + 2\mathrm{CO}_2 (g) \rightarrow 3\mathrm{O}_2 (g) + 2\mathrm{K}_2\mathrm{CO}_3 (s)$

Strategies for Balancing Equations

• Balance atoms in compounds before atoms in pure elements.

• Balance free elements last by adjusting their coefficients.

• Check the final equation by summing the total number of each type of atom on both sides.

Identifying Balanced Equations

Only equations with equal numbers of each atom on both sides are balanced. For example:

• Unbalanced: $\mathrm{Al} (s) + \mathrm{HCl} (aq) \rightarrow \mathrm{AlCl}_3 (aq) + \mathrm{H}_2 (g)$

• Balanced: $2\mathrm{Al} (s) + 6\mathrm{HCl} (aq) \rightarrow 2\mathrm{AlCl}_3 (aq) + 3\mathrm{H}_2 (g)$

Table: States of Reactants and Products in Chemical Equations

Abbreviation	State
(g)	Gas
(l)	Liquid
(s)	Solid
(aq)	Aqueous (water solution)

Summary

• Balancing chemical equations is fundamental to understanding chemical reactions and stoichiometry.

• Always ensure the law of conservation of mass is obeyed by having equal numbers of each atom on both sides.

• Use coefficients to balance equations, and clear any fractions by multiplying through.