Determine the number of moles of $NaOH$ to add to $1.0\; L$ of a buffer $0.10\;M$ in methylamine and $0.10\;M$ in methyl chloride to increase the $pH$ of one unit.
Before the addition:
$pH$ $=$ $pKa$ $+$ $log\frac{0.1}{0.1}$
$pH=pKa$ (1)
The addition of $x$ mol $NaOH$ decreases the number of moles methylammonium by $x$ and increases the number of moles of methylamine by $x$.
After addition:
$pH+1$ $=$ $pKa$ $+$ $log\frac{0.1+x}{0.1-x}$ (2)
(1) and (2):
$pKa+1$ $=$ $pKa$ $+$ $log\frac{0.1+x}{0.1-x}$
$10$ $=$ $\frac{0.1+x}{0.1-x}$
$x$= number of moles to be added =
$8.2\cdot 10^{-2} \;mol$
