a)when 0.0 mL of HCl is added
NH3 dissociates as:
NH3 +H2O -----> NH4+ + OH-
0.39 0 0
0.39-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)*0.39) = 2.65*10^-3
since c is much greater than x, our assumption is correct
so, x = 2.65*10^-3 M
So, [OH-] = x = 2.65*10^-3 M
use:
pOH = -log [OH-]
= -log (2.65*10^-3)
= 2.5768
use:
PH = 14 - pOH
= 14 - 2.5768
= 11.4232
Answer: 11.42
b)when 10.0 mL of HCl is added
Given:
M(HCl) = 0.13 M
V(HCl) = 10 mL
M(NH3) = 0.39 M
V(NH3) = 10 mL
mol(HCl) = M(HCl) * V(HCl)
mol(HCl) = 0.13 M * 10 mL = 1.3 mmol
mol(NH3) = M(NH3) * V(NH3)
mol(NH3) = 0.39 M * 10 mL = 3.9 mmol
We have:
mol(HCl) = 1.3 mmol
mol(NH3) = 3.9 mmol
1.3 mmol of both will react
excess NH3 remaining = 2.6 mmol
Volume of Solution = 10 + 10 = 20 mL
[NH3] = 2.6 mmol/20 mL = 0.13 M
[NH4+] = 1.3 mmol/20 mL = 0.065 M
They form basic buffer
base is NH3
conjugate acid is NH4+
Kb = 1.8*10^-5
pKb = - log (Kb)
= - log(1.8*10^-5)
= 4.745
use:
pOH = pKb + log {[conjugate acid]/[base]}
= 4.745+ log {6.5*10^-2/0.13}
= 4.444
use:
PH = 14 - pOH
= 14 - 4.4437
= 9.5563
Answer: 9.56
c)when 30.0 mL of HCl is added
Given:
M(HCl) = 0.13 M
V(HCl) = 30 mL
M(NH3) = 0.39 M
V(NH3) = 10 mL
mol(HCl) = M(HCl) * V(HCl)
mol(HCl) = 0.13 M * 30 mL = 3.9 mmol
mol(NH3) = M(NH3) * V(NH3)
mol(NH3) = 0.39 M * 10 mL = 3.9 mmol
We have:
mol(HCl) = 3.9 mmol
mol(NH3) = 3.9 mmol
3.9 mmol of both will react to form NH4+ and H2O
NH4+ here is strong acid
NH4+ formed = 3.9 mmol
Volume of Solution = 30 + 10 = 40 mL
Ka of NH4+ = Kw/Kb = 1.0E-14/1.8E-5 = 5.556*10^-10
concentration ofNH4+,c = 3.9 mmol/40 mL = 0.0975 M
NH4+ + H2O -----> NH3 + H+
9.75*10^-2 0 0
9.75*10^-2-x x x
Ka = [H+][NH3]/[NH4+]
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 ((5.556*10^-10)*9.75*10^-2) = 7.36*10^-6
since c is much greater than x, our assumption is correct
so, x = 7.36*10^-6 M
[H+] = x = 7.36*10^-6 M
use:
pH = -log [H+]
= -log (7.36*10^-6)
= 5.1331
Answer: 5.13
d)when 40.0 mL of HCl is added
Given:
M(HCl) = 0.13 M
V(HCl) = 40 mL
M(NH3) = 0.39 M
V(NH3) = 10 mL
mol(HCl) = M(HCl) * V(HCl)
mol(HCl) = 0.13 M * 40 mL = 5.2 mmol
mol(NH3) = M(NH3) * V(NH3)
mol(NH3) = 0.39 M * 10 mL = 3.9 mmol
We have:
mol(HCl) = 5.2 mmol
mol(NH3) = 3.9 mmol
3.9 mmol of both will react
excess HCl remaining = 1.3 mmol
Volume of Solution = 40 + 10 = 50 mL
[H+] = 1.3 mmol/50 mL = 0.026 M
use:
pH = -log [H+]
= -log (2.6*10^-2)
= 1.585
Answer: 1.58
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