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

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

Step-by-step explanation:

Concentration of sodium stearate acid : c

Moles of sodium stearate =
`(3.96 g)/(306 g/mol)=0.01294 mol`

Volume of the solution = 10.0 mL = 0.010 L

`c=(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* 10^(-5)`

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

`K_a=([C_(17)H_(35)COOH][OH^-])/([C_(17)H_(35)COO^-])`

`K_a=((x)^2* x)/((c -x))`

`1.3* 10^(-5)=(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.