Questions: Systematic Treatment of Equilibrium (Charge and Mass Balance)

Question 1

Which is the correct charge balance for an aqueous solution of phosphoric acid, H₃PO₄?

• A. [H⁺] = [H₂PO₄⁻] + [HPO₄²⁻] + [PO₄³⁻] + [OH⁻]
• B. [H⁺] = [H₂PO₄⁻] + 2[HPO₄²⁻] + 3[PO₄³⁻] + [OH⁻]
• C. 3[H⁺] = [PO₄³⁻] + [OH⁻]
• D. [H₃PO₄] = [H₂PO₄⁻] + [HPO₄²⁻] + [PO₄³⁻]

Answer: (B)

Positive charge comes only from H⁺. Each anion contributes its concentration times its charge, so HPO₄²⁻ counts twice and PO₄³⁻ three times. The last option is a mistaken mass balance, not a charge balance.

Question 2

In a charge balance, the concentration of a 2− ion is multiplied by 2.

• T. True
• F. False

Answer: True

One mole of a 2− ion carries two moles of negative charge. Neutrality requires the total positive charge to equal the total negative charge, so each concentration is weighted by the size of its charge.

Question 3

A solution is made with 0.050 mol of acetic acid per liter. Which mass balance is correct?

• A. 0.050 = [CH₃COOH]
• B. 0.050 = [CH₃COO⁻]
• C. 0.050 = [CH₃COOH] + [CH₃COO⁻]
• D. 0.050 = [H⁺] + [CH₃COO⁻]

Answer: (C)

All the acetate groups added must be present as either the undissociated acid or the acetate ion. The mass balance adds every form of the same group.

Question 4

Use the charge balance and Kw = 1.0 × 10⁻¹⁴ to find the pH of 1.0 × 10⁻⁸ M HCl.

Model answer: About 6.98

Charge balance: [H⁺] = [Cl⁻] + [OH⁻] = 1.0 × 10⁻⁸ + Kw/[H⁺]. Solving [H⁺]² − (1.0 × 10⁻⁸)[H⁺] − 1.0 × 10⁻¹⁴ = 0 gives [H⁺] ≈ 1.05 × 10⁻⁷ M, so pH ≈ 6.98. Water's own H⁺ dominates.