Question

Be sure to answer all parts A 10.0-mL solution of 0.390 M NH, is titrated with a 0.130 M HCl solution. Calculate the pH after the following additions of the HCl solution: (a) 0.00 mL (b) 10.0 mL (c) 30.0 mL (d) 40.0 mL

Answer 1

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