Solution:
According to Hendersen -Hasselbalch equation for propionic acid buffer solution,
pH = pka + log [Sodium propionate] / [Propionic acid]
pka of propionic acid is calculated as,
pka = - log ka = - log 1.34 x 10^-5
pka = 5 - log 1.34 = 5 - 0.13 = 4.87
The addition of HCl decreases the moles of conjugate base (sodium propionate) while it increases the moles of propionic acid.
Number of moles of propionic acid = Molarity x Volume
= 0.329 M x 1.47 L = 0.484 mol
Number of moles of sodium propionate = Molarity x Volume
= 0.188 M x 1.47 L = 0.276 mol
Thus,
After addition of 0.073 mol HCl,
Moles of propionic acid = 0.484 + 0.073 = 0.557 mol
Moles of sodium propionate = 0.276 - 0.073 = 0.203 mol
Therefore, pH can be calculated as,
pH = pka + log (0.203 /0.557)
pH = 4.87 + log 0.364
pH = 4.87 - 0.44
pH = 4.43
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