Question

The Ka of a monoprotic weak acid is 8.58 × 10-3. What is the percent ionization of a 0.178 M solution of this acid?

Answer 1

Let the weak acid be HA

HA dissociates as:

HA -----> H+ + A-

0.178 0 0

0.178-x x x

Ka = [H+][A-]/[HA]

Ka = x*x/(c-x)

Assuming x can be ignored as compared to c

So, above expression becomes

Ka = x*x/(c)

so, x = sqrt (Ka*c)

x = sqrt ((8.58*10^-3)*0.178) = 3.908*10^-2

since x is comparable c, our assumption is not correct

we need to solve this using Quadratic equation

Ka = x*x/(c-x)

8.58*10^-3 = x^2/(0.178-x)

1.527*10^-3 - 8.58*10^-3 *x = x^2

x^2 + 8.58*10^-3 *x-1.527*10^-3 = 0

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

a = 1

b = 8.58*10^-3

c = -1.527*10^-3

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 = 6.183*10^-3

roots are :

x = 3.502*10^-2 and x = -4.36*10^-2

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

x = 3.502*10^-2

% dissociation = (x*100)/c

= 3.502*10^-2*100/0.178

= 19.7 %

Answer: 19.7 %