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

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Answer 1 · 2017-03-04T19:32:01

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 $"0.32 M"$ .

Thus, we skip over the ICE table and get:

$K_a = 1.8 xx 10^(-5) = (["H"^(+)]["A"^(-)])/(["HA"])$

$= x^2/(0.32 - x) ~~ x^2/0.32$

$-> ["H"^(+)] = sqrt(K_a[HA]) = 0.0024$ $"M"$

and the $"pH"$ would just be:

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

To three sig figs it would then be:

$color(blue)("pH" = 2.62)$

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