Question

What is the fraction of association (α) for the following potassium propionate solutions? Ignore activities. The Ka of propanoic acid is 1.34 × 10-5.

(c) 5.00 × 10-12 M K(C2H5CO2)

Answer 1

use:

Kb = Kw/Ka

Kw is dissociation constant of water whose value is 1.0*10^-14 at 25 oC

Kb = (1.0*10^-14)/Ka

Kb = (1.0*10^-14)/1.34*10^-5

Kb = 7.463*10^-10

C2H5CO2- dissociates as:

C2H5CO2- +H2O -----> C2H5COOH + OH-

5*10^-12 0 0

5*10^-12-x x x

Kb = [C2H5COOH][OH-]/[C2H5CO2-]

Kb = x*x/(c-x)

Assuming x can be ignored as compared to c

So, above expression becomes

Kb = x*x/(c)

so, x = sqrt (Kb*c)

x = sqrt ((7.463*10^-10)*5*10^-12) = 6.108*10^-11

since x is comparable c, our assumption is not correct

we need to solve this using Quadratic equation

Kb = x*x/(c-x)

7.463*10^-10 = x^2/(5*10^-12-x)

3.731*10^-21 - 7.463*10^-10 *x = x^2

x^2 + 7.463*10^-10 *x-3.731*10^-21 = 0

This is quadratic equation (ax^2+bx+c=0)

a = 1

b = 7.463*10^-10

c = -3.731*10^-21

Roots can be found by

x = {-b + sqrt(b^2-4*a*c)}/2a

x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 5.718*10^-19

roots are :

x = 4.967*10^-12 and x = -7.512*10^-10

since x can't be negative, the possible value of x is

x = 4.967*10^-12

fraction = (x)/c

= 4.967*10^-12/0

= 0.9934

Answer: 0.9934