pH and pOH of a solution

Question

A 0.660 M solution of a weak acid (HA) is made. The Ka for this acid is 2.17⋅10^−9. 

How do I find the pH and pOH given Ka and M of the solution? I don't know what I'm doing wrong; initially I got 13.82 pH and 0.18 pOH and that is wrong.

Answer 1

So, to find the pH and pOH, we need to find the [H+] and/or the [OH-]. We can do this if we know the Ka of the weak acid, and the concentration of that acid. Here is how you do it.

We write the Ka expression as follows: Ka = [H⁺][A^-] / [HA]

We then fill in what we know and solve for the unknown: 2.17x10^-9 = (x)(x) / 0.660 - x

If we assume x is small compared to 0.660 M, we can ignore it and avoid using the quadratic equation.

We then have...

2.17x10^-9 = (x)(x) / 0.660

x² = 1.43x10^-9

x = 3.78x10^-5 M = [H⁺] .. and note that this is indeed small compared to 0.660 so our assumption is ok

pH = -log [H+] = -log 3.78x10^-5

pH = 4.42

pOH + pH = 14

pOH = 14 - pH = 14 - 4.42

pOH = 9.58

Done !!!