CH3NH2 dissociates as:
CH3NH2 +H2O -----> CH3NH3+ + OH-
5*10^-2 0 0
5*10^-2-x x x
Kb = [CH3NH3+][OH-]/[CH3NH2]
Kb = x*x/(c-x)
Assuming x can be ignored as compared to c
So, above expression becomes
Kb = x*x/(c)
so, x = sqrt (Kb*c)
x = sqrt ((4.4*10^-4)*5*10^-2) = 4.69*10^-3
since x is comparable c, our assumption is not correct
we need to solve this using Quadratic equation
Kb = x*x/(c-x)
4.4*10^-4 = x^2/(5*10^-2-x)
2.2*10^-5 - 4.4*10^-4 *x = x^2
x^2 + 4.4*10^-4 *x-2.2*10^-5 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 4.4*10^-4
c = -2.2*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 = 8.819*10^-5
roots are :
x = 4.476*10^-3 and x = -4.916*10^-3
since x can't be negative, the possible value of x is
x = 4.476*10^-3
So, [OH-] = x = 4.476*10^-3 M
Answer: D
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