29)
(CH3)2NH dissociates as:
(CH3)2NH +H2O -----> (CH3)2NH2+ + OH-
0.57 0 0
0.57-x x x
Kb = [(CH3)2NH2+][OH-]/[(CH3)2NH]
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 ((5.1*10^-4)*0.57) = 1.705*10^-2
since x is comparable c, our assumption is not correct
we need to solve this using Quadratic equation
Kb = x*x/(c-x)
5.1*10^-4 = x^2/(0.57-x)
2.907*10^-4 - 5.1*10^-4 *x = x^2
x^2 + 5.1*10^-4 *x-2.907*10^-4 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 5.1*10^-4
c = -2.907*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 = 1.163*10^-3
roots are :
x = 1.68*10^-2 and x = -1.731*10^-2
since x can't be negative, the possible value of x is
x = 1.68*10^-2
% dissociation = (x*100)/c
= 1.68*10^-2*100/0.57
= 2.9 %
Answer: a
Only 1 question at a time please
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