1)
a)
use:
pKa = -log Ka
4.756 = -log Ka
Ka = 1.754*10^-5
CH3COOH dissociates as:
CH3COOH -----> H+ + CH3COO-
1.97*10^-3 0 0
1.97*10^-3-x x x
Ka = [H+][CH3COO-]/[CH3COOH]
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 ((1.754*10^-5)*1.97*10^-3) = 1.859*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)
1.754*10^-5 = x^2/(1.97*10^-3-x)
3.455*10^-8 - 1.754*10^-5 *x = x^2
x^2 + 1.754*10^-5 *x-3.455*10^-8 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 1.754*10^-5
c = -3.455*10^-8
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 = 1.385*10^-7
roots are :
x = 1.773*10^-4 and x = -1.949*10^-4
since x can't be negative, the possible value of x is
x = 1.773*10^-4
So, [H+] = x = 1.773*10^-4 M
use:
pH = -log [H+]
= -log (1.773*10^-4)
= 3.7512
Answer: 3.75
b)
Alpa = x / initial concentration
= (1.773*10^-4) / 0.00197
= 0.090
Answer: 0.090
2)
a)
use:
pKa = -log Ka
4.756 = -log Ka
Ka = 1.754*10^-5
CH3COOH dissociates as:
CH3COOH -----> H+ + CH3COO-
1.27*10^-12 0 0
1.27*10^-12-x x x
Ka = [H+][CH3COO-]/[CH3COOH]
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 ((1.754*10^-5)*1.27*10^-12) = 4.72*10^-9
since x is comparable c, our assumption is not correct
we need to solve this using Quadratic equation
Ka = x*x/(c-x)
1.754*10^-5 = x^2/(1.27*10^-12-x)
2.227*10^-17 - 1.754*10^-5 *x = x^2
x^2 + 1.754*10^-5 *x-2.227*10^-17 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 1.754*10^-5
c = -2.227*10^-17
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 = 3.076*10^-10
roots are :
x = 1.27*10^-12 and x = -1.754*10^-5
since x can't be negative, the possible value of x is
x = 1.27*10^-12
So, [H+] = x = 1.27*10^-12 M
use:
pH = -log [H+]
= -log (1.27*10^-12)
= 11.8962
Answer: 11.90
b)
Alpha = x / initial concentration
= (1.27*10^-12)/(1.27*10^-12)
= 1.0
Answer: 1.0
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