This is a situation analogous to the calculation of pH with weak acids that we discussed in the previous point. Weak bases in solution do not completely dissociate as strong bases do, so an equilibrium is established between the base and its dissociated species. This equilibrium is evaluated through the basicity constant, which will allow us to calculate the concentration of free hydroxide ions in the medium. Once this concentration is found, we proceed to calculate the pOH, and with its relationship with the pH we obtain the latter.
Let's see an example: Calculate the pH of a 0.0025 M solution in methylamine. ($K_b=4.2x10^{-4}$).
We begin by writing the dissociation equilibrium of methylamine:
$CH_3NH_2 + H_2O \rightarrow CH_3NH_3^+ + OH^-$
Initial 0.0025 -------- ---------
Equilibrium 0.0025-x x x
Taking the equilibrium composition to the constant:
\begin{equation}K_b=\frac{[CH_3NH_3^+][OH^-]}{[CH_3NH_2]}=\frac{x^2}{0.0025-x}=4.2x10^{-4}\end{equation}
Clearing x from the quadratic equation:
$x=[OH^-]=8.4x10^{-4}\;M$
$pOH=-log[OH^-]=3.08$
$pH=14-pOH=10.92$