pH of acids, bases and salts

Exercise 16

    

Using the simplified formula for the $pH$ of a weak base, calculate the volume of a 22  %  ($\rho_S=$ 0.9164 $\frac{g}{mL}$)  ammonia solution that must be diluted in a volumetric flask $j$ of 250 $mL$ in order to obtain a solution with $pH$ = 11.1.

$NH_3$: weak base Final solution: $pOH$ $=$ $\frac{1}{2}pK_b$ $-$ $\frac{1}{2}log\;c$ $pH$ $=$ $7$ $+$ $\frac{1}{2}pK_a$ $+$ $\frac{1}{2}log\;c$ $c$ $=$ $10^{2pH$ $-$ $14-pK_a}$ = 0.1 $\frac{mol}{L}$ $n_{NH_3}$ = $c_{NH_3}\cdot V_{j}$ = 0.1$\cdot$0.25 = 0.025 $\;mol$ The concentrated initial solution has the same number of moles: Initial solution $S$: $m_{NH_3}$ = $n_{NH_3}\cdot M_{NH_3}$ = 0.025$\cdot$17.03 = 0.426$ \;g$ $m_S$ = $\frac{m_{NH_3}\cdot 100}{\%_S}$ = $\frac{0.426\cdot 100}{22}$ = 1.936$ \;g$ $V_S$ = $\frac{m_S}{\rho_S}$ = $\frac{0.426}{0.9164}$ = 0.465$ \; mL$