Question

How do you determine the Ka of a weak acid or the Kb of a weak base?

Answer 1

How else but by measurement?

Explanation:

Typically, a weak acid is titrated by a strong base, or a weak base is titrated by a strong acid. In order to measure `K_a` (or more usually `-log_10K_a=pK_a`).

We use the relationship:

`pH=pK_a+log_10{[[A^-]]/[[HA]]}`

So do the measurement, i.e. the titration of weak acid by a strong base, and measure the `pH` as you add increments of the titrant. At the point of HALF EQUIVALENCE, i.e. when `[A^-]=[HA]`, we use the given equation:

`pH=pK_a+log_10{1},` i.e. `pH=pK_a`, because `log_(10)1=0`.

Satisfied?

See here for details of the buffer equation.