Multiple Choice
Which formula can be used to calculate the pH of a weak acid given its pKa and concentration?
17. Acid and Base Equilibrium
pH of Weak Acids
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The venom of stinging ants contains formic acid, HCOOH, with a dissociation constant (Ka) of 1.8 × 10⁻⁴ at 25 °C. What is the pH of a 0.055 M solution of formic acid?
A
5.28
B
2.37
C
3.45
D
4.12
Verified step by step guidance1
Identify the dissociation reaction of formic acid in water: \( \text{HCOOH} \rightleftharpoons \text{H}^+ + \text{HCOO}^- \).
Write the expression for the acid dissociation constant \( K_a \): \( K_a = \frac{[\text{H}^+][\text{HCOO}^-]}{[\text{HCOOH}]} \).
Set up an ICE (Initial, Change, Equilibrium) table to determine the concentrations of the species at equilibrium. Initially, \([\text{HCOOH}] = 0.055 \text{ M}\), and \([\text{H}^+] = [\text{HCOO}^-] = 0\).
Assume \( x \) is the change in concentration for \([\text{H}^+]\) and \([\text{HCOO}^-]\) at equilibrium. Therefore, \([\text{H}^+] = x\), \([\text{HCOO}^-] = x\), and \([\text{HCOOH}] = 0.055 - x\).
Substitute the equilibrium concentrations into the \( K_a \) expression: \( 1.8 \times 10^{-4} = \frac{x^2}{0.055 - x} \). Solve for \( x \), which represents \([\text{H}^+]\), and then calculate the pH using \( \text{pH} = -\log[\text{H}^+] \).
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