Question

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

Answer 1

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)`