Question

Calculate the pH at the equivalence point in the titration of 60.0 mL of 0.160 M methylamine ( Kb = 4.4 × 10−4 ) with 0.275 M HCl. pH =

Answer 1

find the volume of HCl used to reach equivalence point

M(CH3NH2)*V(CH3NH2) =M(HCl)*V(HCl)

0.16 M *60.0 mL = 0.275M *V(HCl)

V(HCl) = 34.9091 mL

Given:

M(HCl) = 0.275 M

V(HCl) = 34.9091 mL

M(CH3NH2) = 0.16 M

V(CH3NH2) = 60 mL

mol(HCl) = M(HCl) * V(HCl)

mol(HCl) = 0.275 M * 34.9091 mL = 9.6 mmol

mol(CH3NH2) = M(CH3NH2) * V(CH3NH2)

mol(CH3NH2) = 0.16 M * 60 mL = 9.6 mmol

We have:

mol(HCl) = 9.6 mmol

mol(CH3NH2) = 9.6 mmol

9.6 mmol of both will react to form CH3NH3+ and H2O

CH3NH3+ here is strong acid

CH3NH3+ formed = 9.6 mmol

Volume of Solution = 34.9091 + 60 = 94.9091 mL

Ka of CH3NH3+ = Kw/Kb = 1.0E-14/4.4E-4 = 2.273*10^-11

concentration ofCH3NH3+,c = 9.6 mmol/94.9091 mL = 0.1011 M

CH3NH3+ + H2O -----> CH3NH2 + H+

0.1011 0 0

0.1011-x x x

Ka = [H+][CH3NH2]/[CH3NH3+]

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 ((2.273*10^-11)*0.1011) = 1.516*10^-6

since c is much greater than x, our assumption is correct

so, x = 1.516*10^-6 M

[H+] = x = 1.516*10^-6 M

use:

pH = -log [H+]

= -log (1.516*10^-6)

= 5.8192

Answer: 5.82