The pH of a salt solution formed from a weak acid and a weak base can be calculated using the formula:

$\mathrm{pH}=7+\frac{1}{2}p{K}_a-\frac{1}{2}p{K}_b$

Given: pK_a = 3.2 and pK_b = 3.4

Step 1: Substitute the values into the formula:

$\mathrm{pH}=7+\frac{1}{2}\left(3.2\right)-\frac{1}{2}\left(3.4\right)$

Step 2: Calculate the terms:

$\frac{1}{2}\left(3.2\right)=1.6$

$\frac{1}{2}\left(3.4\right)=1.7$

Step 3: Substitute back:

$\mathrm{pH}=7+1.6-1.7$

Step 4: Perform the arithmetic:

$\mathrm{pH}=7+1.6=8.6$

$8.6-1.7=6.9$

Therefore, the pH of the salt solution is 6.9.

Related Topics and Formulae

Salt Hydrolysis: When a salt is formed from a weak acid and a weak base, both the cation and anion hydrolyze, affecting the pH of the solution. The extent of hydrolysis depends on the relative strengths of the acid and base, quantified by their pK_a and pK_b values.

Key Formula: For a salt AB formed from weak acid HA and weak base BOH, the pH is given by:

$\mathrm{pH}=7+\frac{1}{2}p{K}_a-\frac{1}{2}p{K}_b$

This formula is derived by considering the hydrolysis equilibria of both ions and the water dissociation constant (K_w).