# Calculate the "pH" of a "0.32 M" solution of acetic acid (K_a = 1.8 xx 10^(-5)) to three sig figs?

Mar 4, 2017

This ${K}_{a}$ is on the order of ${10}^{- 5}$ or less, so to an even better approximation, x=[H"^(+)] is indeed small in comparison to $\text{0.32 M}$.

Thus, we skip over the ICE table and get:

${K}_{a} = 1.8 \times {10}^{- 5} = \left(\left[\text{H"^(+)]["A"^(-)])/(["HA}\right]\right)$

$= {x}^{2} / \left(0.32 - x\right) \approx {x}^{2} / 0.32$

$\to \left[{\text{H}}^{+}\right] = \sqrt{{K}_{a} \left[H A\right]} = 0.0024$ $\text{M}$

and the $\text{pH}$ would just be:

"pH" = -log["H"^(+)] = 2.620

To three sig figs it would then be:

$\textcolor{b l u e}{\text{pH} = 2.62}$