Question

Enter your answer in the provided box. Sodium stearate (C17H35COONa) is a major component of bar soap. The Ka of the stearic acid is 1.3 × 10−5. What is the pH of 10.0 mL of a solution containing 3.96 g of sodium stearate?

Answer 1

Answer:

11.61 is the pH of 10.0 mL of a solution containing 3.96 g of sodium stearate.

Explanation:

Concentration of sodium stearate acid : c

Moles of sodium stearate = $\frac{3.96 g}{306 g/mol}=0.01294 mol$

Volume of the solution = 10.0 mL = 0.010 L

$c=\frac{0.01294 mol}{0.010 L}=1.294 M$

$C_{17}H_{35}COONa\rightleftharpoons C_{17}H_{35}COO^-+Na^+$

$[C_{17}H_{35}COO^-]=c=1.294 M$

$C_{17}H_{35}COO^-+H_2O\rightleftharpoons C_{17}H_{35}COOH +OH^-$

initially c

c           0    0

At equilibrium

(c-x)       x    x

Dissociation constant of an acid = $K_a=1.3\times 10^{-5}$

Expression of a dissociation constant of an acid is given by:  

$K_a=\frac{[C_{17}H_{35}COOH][OH^-]}{[C_{17}H_{35}COO^-]}$

$K_a=\frac{(x)^2\times x}{(c -x)}$

$1.3\times 10^{-5}=\frac{x^2}{1.294-x}$

Solving for x;

x = 0.0041 M

$[OH^-]=0.0041 M$

The pOH of the solution:

$pOH=-\log[OH^-]=-\log[0.0041 M]=2.39$

pH = 14 -pOH

pH = 14 - 2.39 = 11.61

11.61 is the pH of 10.0 mL of a solution containing 3.96 g of sodium stearate.