Given: $K_{\mathrm{b}}$ (dimethylamine) $=7.4\times {10}^{-4} \mathrm{M}$. A buffer is made by mixing ${\left({\mathrm{CH}}_3\right)}_2\mathrm{NH}$ and ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{NH}}_2\mathrm{Cl}$.The range of buffer to which this buffer can be used is

$\mathrm{p}{K}_{\mathrm{b}}^{\circ }=-\log \left(7.4\times {10}^{-4}\mathrm{M}\right)=3.13$   Buffer range is $14-\mathrm{p}{K}_{\mathrm{b}}-1$to $14-\mathrm{p}{K}_{\mathrm{b}}+1$, i.e.  $9.87$to $11.87$  A buffer should have a pH range that is one pH unit on each side of the ${\mathrm{pK}}_{\mathrm{a}}$ value of the weak acid. If a buffer's pH deviates from this range, it loses its capacity to endure substantial pH changes.