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
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
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