The pK_b of dimethylamine and pK_a of acetic acid are 3.27 and 4.77 respectively at T (K). The correct option for the pH of dimethylammonium acetate solution is :

We are asked for the pH of an aqueous solution that contains the salt dimethylammonium acetate. This salt is formed from the weak base dimethylamine (B) and the weak acid acetic acid (HA). In water the cation dimethylammonium (BH⁺) can donate a proton, while the anion acetate (A⁻) can accept a proton.

First we need the acid dissociation constant of the cation BH⁺. The given pK_b of dimethylamine is 3.27. For a conjugate acid‑base pair we have

Taking negative logarithms (pK = –log K) gives

At 25 °C, pK_w ≈ 14. Therefore

The acid dissociation constant of the acetic acid is already given as pK_a(HA) = 4.77.

For a solution that contains only the salt of a weak acid and a weak base, the pH can be approximated by the average of the two relevant pK values:

Substituting the numbers:

Thus the pH of the dimethylammonium acetate solution is 7.75, which matches the provided correct option.