Question

A solution of caproic acid(HC₆H₁₁O₂) is made by dissolving 1.25 grams of caproic acid in enough water to make a 300 mL solution. The solution has (H⁺) = 1.7 X 10^-3M. What is the K_a for caproic acid?

Answer 1

calculate molarity of caproic acid

molar mass of caproic acid = 116.1583 gm/mole then 1.25 gm = 1.25 / 116.1583 = 0.01076 mole

no. of mole of capric acid = 0.01076 mole

volume of solution = 300 ml = 0.300 liter

molarity = no. of mole / volume of solutiion in liter

Molarity of caproic acid = 0.01076 / 0.300 = 0.0359 M

Caproic acid dissociated as

HC₆H₁₁O₂ + H₂O C₆H₁₁O₂^- + H₃O⁺

K_a = [C₆H₁₁OO^- ][H₃O⁺] / [HC₆H₁₁O₂]

Accoding to dissociation reaction no. of C₆H₁₁O₂^- = H₃O⁺

[C₆H₁₁O₂^- ] = [H₃O⁺] = 1.7 10^-3 M

Substitute the value in equation

K_a = [1.710^-3][1.710^-3]/ [0.0359]

K_a  = 8.05 10^-5