Question

The pH of sodium formate solution in terms of Kₐ and the concentration of the electrolyte C is:

• A. pH = 7 - (1)/(2) pKₐ - (1)/(2) C
• B. pH = 7 - (1)/(2) pKₐ + (1)/(2) C
• C. pH = 7 + (1)/(2) pKₐ + (1)/(2) C
• D. pH = 7 + (1)/(2) pKₐ - (1)/(2) C

Hint:

To avoid confusion with formulas: - Salt of Weak Acid + Strong Base: pH = 7 + (1)/(2) pKₐ + (1)/(2) C (Basic) - Salt of Strong Acid + Weak Base: pH = 7 - (1)/(2) pKb - (1)/(2) C (Acidic)

Answer 1

The Correct Option is C

Concept:
Sodium formate (HCOONa) is a salt formed from a weak acid (formic acid, HCOOH) and a strong base (sodium hydroxide, NaOH). In aqueous solution, the salt undergoes anionic hydrolysis, making the resulting solution basic (pH > 7).

The hydrolysis reaction is:
HCOO⁻ + H₂O ⇌ HCOOH + OH⁻

The hydrolysis constant is given by:
K_h = K_w / K_a

For a salt of concentration C, the hydroxide ion concentration is:

[OH⁻] = √(K_h × C) = √(K_w/K_a × C)

Taking negative logarithm on both sides:

pOH = ½ (pK_w − pK_a − log C)

Since pH + pOH = pK_w (which is 14 at 25°C):

pH = pK_w − pOH pH = pK_w − ½ (pK_w − pK_a − log C)

pH = ½ pK_w + ½ pK_a + ½ log C

Since pK_w = 14:

pH = 7 + ½ pK_a + ½ log C