The Ka of a monoprotic weak acid is 5.91 × 10-3. What is the percent ionization of a 0.162 M solution of this acid?
Lets write the acid as HA
HA dissociates as:
HA -----> H+ + A-
0.162 0 0
0.162-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 ((5.91*10^-3)*0.162) = 3.094*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)
5.91*10^-3 = x^2/(0.162-x)
9.574*10^-4 - 5.91*10^-3 *x = x^2
x^2 + 5.91*10^-3 *x-9.574*10^-4 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 5.91*10^-3
c = -9.574*10^-4
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 = 3.865*10^-3
roots are :
x = 2.813*10^-2 and x = -3.404*10^-2
since x can't be negative, the possible value of x is
x = 2.813*10^-2
% dissociation = (x*100)/c
= 2.813*10^-2*100/0.162
= 17.4 %
Answer: 17.4 %
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