HA dissociates as:
HA -----> H+ + A-
0.138 0 0
0.138-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 ((8.12*10^-3)*0.138) = 3.347*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)
8.12*10^-3 = x^2/(0.138-x)
1.121*10^-3 - 8.12*10^-3 *x = x^2
x^2 + 8.12*10^-3 *x-1.121*10^-3 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 8.12*10^-3
c = -1.121*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 = 4.548*10^-3
roots are :
x = 2.966*10^-2 and x = -3.778*10^-2
since x can't be negative, the possible value of x is
x = 2.966*10^-2
% dissociation = (x*100)/c
= 2.966*10^-2*100/0.138
= 21.49 %
Answer: 21.5 %
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