HF dissociates as:
HF -----> H+ + F-
7.8*10^-4 0 0
7.8*10^-4-x x x
Ka = [H+][F-]/[HF]
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 ((6.4*10^-4)*7.8*10^-4) = 7.065*10^-4
since x is comparable c, our assumption is not correct
we need to solve this using Quadratic equation
Ka = x*x/(c-x)
6.4*10^-4 = x^2/(7.8*10^-4-x)
4.992*10^-7 - 6.4*10^-4 *x = x^2
x^2 + 6.4*10^-4 *x-4.992*10^-7 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 6.4*10^-4
c = -4.992*10^-7
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 = 2.406*10^-6
roots are :
x = 4.556*10^-4 and x = -1.096*10^-3
since x can't be negative, the possible value of x is
x = 4.556*10^-4
% dissociation = (x*100)/c
= 4.556*10^-4*100/0.0008
= 58.41 %
Answer: 58.4 %
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