An acetic acid solution has a pH of 5.80. What is its [OH⁻]? A) 1.6 × 10⁻²⁰ M B) 6.3 × 10⁻⁹ M C) 1.6 × 10^{− 6} M D) 6.3 × 10⁵ M

Question

Quizplus · Accepted Answer

The pH of the solution is given by $pH = -\log[H^+]$. Rearranging the equation gives $[H^+] = 10^{-pH}$. Since acetic acid is a weak acid, we can assume that it only partially dissociates and use the equilibrium expression $K_a = \frac{[H^+][OAc^-]}{[HOAc]}$, where $OAc^-$ is the acetate ion and $HOAc$ is the undissociated acetic acid. The $K_a$ for acetic acid is $1.8 	imes 10^{-5}$ at 25°C. We can assume that the amount of $OAc^-$ generated from the dissociation of $HOAc$ is small and negligible compared to the initial concentration of $OAc^-$, which is determined by the stoichiometry of the dissociation reaction.

Therefore, we can simplify the equilibrium expression to $K_a \approx \frac{[H^+]^2}{[HOAc]}$. Substituting for $[H^+]$ gives $K_a \approx \frac{10^{-2pH}}{[HOAc]}$. Rearranging the equation to solve for $[OH^-]$ gives $[OH^-] = \frac{K_a}{[H^+]} = \frac{1.8 	imes 10^{-5}}{10^{-5.80}} = 6.3 	imes 10^{-9}$.

Thus, the answer is B, 6.3 × 10−9 M, which is the [OH^-] of the acetic acid solution.

An Acetic Acid Solution Has a PH of 5