Effects of Ka on the Half-Equivalence Point

Question

I'm new to studying chemistry at a university level and am currently reviewing acid-base titrations. I am wondering about the relationship between your ionization constant for a weak acid ($K_\mathrm{a}$) and both the volume of strong base needed to reach the half equivalence point and the $\mathrm{pH}$ at the half-equivalence point.

Assuming these two weak acids are of the same concentration, if you had a higher $K_\mathrm{a}$ value for one of them, my reasoning is that your $\mathrm{pH}$ at the half equivalence would be lower than that of the weak acid with a lower $K_\mathrm{a}$ value because given the equation

$$\mathrm{pH} = -\log[\ce{H3O+}],$$

a greater hydronium ion concentration (from being present in larger amounts as a product given the larger $K_\mathrm{a}$ value) would result in a lower $\mathrm{pH}$ overall.

However, I am not entirely sure if this is correct, and I am also unsure as to how the volume of strong base titrant needed to reach the half equivalence point would be affected.

Answer 1

If we consider $\ce{HA}$ as a weak acid, then at the half equivalence point, $$\mathrm{p}H = \mathrm{p}K_\mathrm{a}$$ As $$\mathrm{p}H = \mathrm{p}K_\mathrm{a} + \mathrm{p[\ce{HA}]} -\mathrm{p[\ce{A-}]}$$ and for the half equivalence point,
$$\mathrm{p[\ce{HA}]} =\mathrm{p[\ce{A-}]}$$ So the higher the $\mathrm{p}K_\mathrm{a}$ is, the higher is $\mathrm{p}H$ at the half equivalence.