The pK b of dimethylamine and pK a of acetic acid are 3 . 27 and 4 . 77 respectively at T ( K ) . The…

${\mathrm{pk}}_{\mathrm{b}}$ of dimethylamine $=3.27$
${\mathrm{pk}}_{\mathrm{a}}$ of acetic acid $=4.77$

Dimethylammonium acetate is salt of weak acid and weak base for which $\mathrm{pH}$ is:

$\mathrm{pH}=7+\frac{1}{2}{\mathrm{pk}}_{\mathrm{a}}-\frac{1}{2}{\mathrm{pK}}_{\mathrm{b}}$

$=7+\frac{1}{2}\times 4.77-\frac{1}{2}\times 3.27$

$=7.75$