a)
NH3 dissociates as:
NH3 +H2O -----> NH4+ + OH-
1.1 0 0
1.1-x x x
Kb = [NH4+][OH-]/[NH3]
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 ((1.8*10^-5)*1.1) = 4.45*10^-3
since c is much greater than x, our assumption is correct
so, x = 4.45*10^-3 M
% dissociation = (x*100)/c
= 4.45*10^-3*100/1.1
= 0.4045 %
Answer: 0.40 %
b)
NH3 dissociates as:
NH3 +H2O -----> NH4+ + OH-
0.1 0 0
0.1-x x x
Kb = [NH4+][OH-]/[NH3]
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 ((1.8*10^-5)*0.1) = 1.342*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)
1.8*10^-5 = x^2/(0.1-x)
1.8*10^-6 - 1.8*10^-5 *x = x^2
x^2 + 1.8*10^-5 *x-1.8*10^-6 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 1.8*10^-5
c = -1.8*10^-6
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 = 7.2*10^-6
roots are :
x = 1.333*10^-3 and x = -1.351*10^-3
since x can't be negative, the possible value of x is
x = 1.333*10^-3
% dissociation = (x*100)/c
= 1.333*10^-3*100/0.1
= 1.333 %
Answer: 1.3 %
c)
CH3NH2 dissociates as:
CH3NH2 +H2O -----> CH3NH3+ + OH-
0.8 0 0
0.8-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 ((4.38*10^-4)*0.8) = 1.872*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)
4.38*10^-4 = x^2/(0.8-x)
3.504*10^-4 - 4.38*10^-4 *x = x^2
x^2 + 4.38*10^-4 *x-3.504*10^-4 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 4.38*10^-4
c = -3.504*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 = 1.402*10^-3
roots are :
x = 1.85*10^-2 and x = -1.894*10^-2
since x can't be negative, the possible value of x is
x = 1.85*10^-2
% dissociation = (x*100)/c
= 1.85*10^-2*100/0.8
= 2.313 %
Answer: 2.3 %
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