The pK₆ of dimethylamine and pKₐ of acetic acid are 3.27 and 4.77 respectively at T (K). The correct option for the pH of dimethylammonium acetate solution is :

The correct option is 7.75.

Step-by-Step Explanation:

1. Identify the type of salt:
Dimethylammonium acetate is a salt formed from a weak base (dimethylamine) and a weak acid (acetic acid).

2. Formula for the pH of a salt of a weak acid and a weak base:
The pH of a solution containing a salt of a weak acid and a weak base is given by the standard relation:
$\text{pH}=7+\frac{1}{2}({\text{pK}}_{\text{a}}-{\text{pK}}_{\text{b}})$
where:
${\text{pK}}_{\text{a}}$ is the acid dissociation constant exponent of the weak acid (acetic acid).
${\text{pK}}_{\text{b}}$ is the base dissociation constant exponent of the weak base (dimethylamine).

3. Substitute the given values into the formula:
We are given:
${\text{pK}}_{\text{b}}\text{of dimethylamine}=3.27$
${\text{pK}}_{\text{a}}\text{of acetic acid}=4.77$
Substituting these parameters:
$\text{pH}=7+\frac{1}{2}(4.77-3.27)$

4. Perform the calculation:
$\text{pH}=7+\frac{1}{2}\left(1.50\right)$
$\text{pH}=7+0.75$
$\text{pH}=7.75$
Thus, the pH of the dimethylammonium acetate solution is 7.75.