Calculate the concentration of all species in a 0.14 M KF
solution.
Ka(HF)=6.3×10−4
Express your answer using two significant figures. Enter your answers numerically separated by commas.
HF dissociates as:
HF -----> H+ + F-
0.14 0 0
0.14-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 ((6.3*10^-4)*0.14) = 9.391*10^-3
since x is comparable c, our assumption is not correct
we need to solve this using Quadratic equation
Ka = x*x/(c-x)
6.3*10^-4 = x^2/(0.14-x)
8.82*10^-5 - 6.3*10^-4 *x = x^2
x^2 + 6.3*10^-4 *x-8.82*10^-5 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 6.3*10^-4
c = -8.82*10^-5
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 = 3.532*10^-4
roots are :
x = 9.082*10^-3 and x = -9.712*10^-3
since x can't be negative, the possible value of x is
x = 9.082*10^-3
So, [H+] = x = 9.082*10^-3 M
[F-] = x = 9.082*10^-3 M
[HF] = 0.14 - x
= 0.14 - 9.082*10^-3
= 0.13 M
Answer:
H+] = 9.1*10^-3 M
[F-] = 9.1*10^-3 M
[HF] = 0.13 M
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