Multiple Choice
A solution with a hydroxide ion concentration of 4.15 × 10⁻⁵ M is considered a weak base. What is the hydrogen ion concentration of this solution?
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17. Acid and Base Equilibrium
pH of Weak Bases
Multiple Choice
Calculate the pH of a 0.400 M NaF solution, given that the Ka of HF is 6.4 x 10^-4.
A
7.00
B
8.20
C
9.40
D
5.80
Verified step by step guidance1
Identify that NaF is a salt derived from a weak acid (HF) and a strong base (NaOH). In solution, NaF will dissociate into Na⁺ and F⁻ ions. The F⁻ ion will act as a base and react with water to form HF and OH⁻.
Write the equilibrium expression for the reaction of F⁻ with water: \( \text{F}^- + \text{H}_2\text{O} \rightleftharpoons \text{HF} + \text{OH}^- \).
Use the relationship between the acid dissociation constant \( K_a \) and the base dissociation constant \( K_b \) to find \( K_b \) for F⁻. The formula is \( K_w = K_a \times K_b \), where \( K_w \) is the ion product of water \( 1.0 \times 10^{-14} \). Solve for \( K_b \) using \( K_b = \frac{K_w}{K_a} \).
Set up an ICE table (Initial, Change, Equilibrium) for the reaction \( \text{F}^- + \text{H}_2\text{O} \rightleftharpoons \text{HF} + \text{OH}^- \) to find the equilibrium concentrations. Assume initial concentration of F⁻ is 0.400 M, and changes in concentration are represented by \( x \).
Use the expression for \( K_b \) to solve for \( x \), which represents the concentration of OH⁻ at equilibrium. Then, calculate the pOH using \( \text{pOH} = -\log[\text{OH}^-] \) and convert to pH using \( \text{pH} = 14 - \text{pOH} \).
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