Question

Consider a 1.0-L solution that is 0.480 M C5H5N and 0.17 M C5H5NHCl at 25 °C. What is the pH of this solution before and after 0.012 moles of HI have been added? Kb of C5H5N is 1.7E-9

a-initial pH: 4.78, final pH: 5.72

.b- initial pH: 5.68, final pH: 5.64

.c- initial pH: 5.68, final pH: 5.74.

d-initial pH: 5.23, final pH: 4.82.

e-initial pH: 5.68, final pH: 4.82

Answer 1

Here the given C5H5N is a weak base and C5H5NHCl is the salt of the conjugate acid of the weak base. Now the solution where both a weak acid and its salt are present is called a buffer and the pH of a basic buffer is calculated by using Henderson Hasslblach equation-

pOH = pKb + log [salt]/[base]

Where pKb = -log Kb

And pH = 14 - pOH

Now applying the above concept-

1- Given [base] = [C5H5N] = 0.480 M

And [salt] = [C5H5NHCl] = 0.17 M

Kb for C5H5N = 1.7* 10^-9   

Thus pKb = -log Kb = -log (1.7* 10^-9)

= 9 - log 1.7

= 9 - 0.23

= 8.77‬

a-Before adding HI

Thus putting the values-

pOH = pKb + log [salt]/[base]

pOH = 8.77‬ + log [0.17]/[0.48]

= 8.77‬ + log [0.354]

= 8.77‬ + (-0.450)

= 8.32

Thus pH = 14 - pOH = pH = 14 - 8.32 = 5.68‬

b- After addition of HI

Now when we add HI (a strong acid), the H+ of the acid react with C5H5N to form C5H5NH+ i.e

H+ + C5H5N -----------> C5H5NH+

That means due to addition of HI, the amount of C5H5N from the solution will decrease and the amount of C5H5NH+ (conjugate acid) will increase.

Now given HI added = 0.012 moles

Thus concentration of HI added = moles/ volume

=  0.012 moles/ 1 L

= 0.012 M

So the final concentrations of the weak base and its conjugate acid can e found from the ICE table i.e

Reaction	H+	C5H5N	C5H5NH+
Initial	0.012 M	0.480 M	0.17 M
Change	-0.012 M	-0.012 M	+0.012 M
Equilibrium	0	0.468‬ M	0.182 M

Thus after addition of acid, new [C5H5N] = 0.468 M

and new [C5H5NH+] = 0.182 M

So the changed

pOH = pKb + log [salt]/[base]

pOH = 8.77‬ + log [0.182]/[0.468]

= 8.77‬ + log [0.388]

= 8.77‬ + (-0.41)

= 8.36

Thus pH = 14 - pOH = pH = 14 - 8.36 = 5.64

Thus before and after 0.012 moles of HI have been added, .b- initial pH: 5.68, final pH: 5.64