# Effects of Ka on the Half-Equivalence Point

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.

• The half equivalence point is not really a "thing" in chemistry because it would depend on some much else. That said, with a strong base titrant, the acid that had the smaller pKa would also have the lower pH at its half equivalence point.
– MaxW
Mar 25 '19 at 22:59

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.