Multiple Choice
What is the pH change of a 0.220 M solution of benzoic acid (pKa=4.19) if 0.175 M benzoate is added with no change in volume?
17. Acid and Base Equilibrium
pH of Weak Acids
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What is the concentration of H⁺ ions in a 2.0 M solution of acetic acid (HC₂H₃O₂) if the acid dissociation constant (Ka) is 1.8 x 10⁻⁵?
A
4.0 x 10⁻⁵ M
B
3.6 x 10⁻³ M
C
1.9 x 10⁻³ M
D
2.0 x 10⁻⁵ M
Verified step by step guidance1
Start by writing the balanced chemical equation for the dissociation of acetic acid (HC₂H₃O₂) in water: HC₂H₃O₂ ⇌ H⁺ + C₂H₃O₂⁻.
Set up the expression for the acid dissociation constant (Ka) for acetic acid: \( K_a = \frac{[H^+][C_2H_3O_2^-]}{[HC_2H_3O_2]} \).
Assume that the initial concentration of acetic acid is 2.0 M and that the change in concentration of H⁺ ions is x. Therefore, at equilibrium, [H⁺] = x, [C₂H₃O₂⁻] = x, and [HC₂H₃O₂] = 2.0 - x.
Substitute these equilibrium concentrations into the Ka expression: \( 1.8 \times 10^{-5} = \frac{x^2}{2.0 - x} \).
Assume that x is small compared to 2.0, so 2.0 - x ≈ 2.0. This simplifies the equation to \( 1.8 \times 10^{-5} = \frac{x^2}{2.0} \). Solve for x to find the concentration of H⁺ ions.
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