Question

Acetic acid is the principal ingredient in vinegar that's why it tastes sour. At equilibrium. a solution contains $\left[C{H}_{3}C{O}_{2}H\right]=0.0787M$ and $\left[H_3{O}^{+}\right]=\left[C{H}_{3}C{O}_2^{-}\right]=0.00118M.$ what is the values of $K_a$ for acetic acid?

• A. $1.77\times {10}^{-5}$
• B. $2.55\times {10}^{-6}$
• C. $2.77\times {10}^{-5}$
• D. $2.77\times {10}^{-7}$

Answer 1

The correct option is A $1.77\times {10}^{-5}$

We are asked to calculate equilibrium constant from equilibrium concentrations. At equilibrium, the value of the equilibrium constant is equal to the reaction quotient for the reaction:
$C{H}_{3}C{O}_{2}H\left(aq\right)+H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}\left(aq\right)+C{H}_{3}C{O}_2^{-}\left(aq\right)K_a=\frac{\left[H_3{O}^{+}\right]\left[C{H}_{3}C{O}_2^{-}\right]}{\left[C{H}_{3}C{O}_{2}H\right]}=\frac{\left(0.00118\right)\left(0.00118\right)}{0.0787}=1.77\times {10}^{-5}$
Hence, the values of $K_a$ for acetic acid is $1.77\times {10}^{-5}$