What should the molar concentrations of benzoic acid and sodium benzoate be in a

Question

What should the molar concentrations of benzoic acid and sodium benzoate be in a solution that is buffered at a pH of 4.95 and has a freezing point of -2.0 ? C ? (Assume complete dissociation of sodium benzoate and a density of 1.01 g/mL for the solution.)

Express your answers using two significant figures separated by a comma.

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Note: (0.92, 0.16) is not the correct answer.

This is how the answer is expected.

Explanation / Answer

from freezing point

Van't Hoff factor (i) = 3 (benzoic acid, Na+, benzoate)

Kf water = 1.86 oC/m

So,

molality of solution = -dTf/Kf x i

                              = 2.0/1.86 x 3

                              = 0.36 M

Using Hendersen-Hasselbalck equation,

pH = pKa + log(base/acid)

4.95 = 4.20 + log(benzoate/benzoic acid)

(benzoate) = 5.62(benzoic acid)

(benzoic acid) + (benzoate) = 0.36 M

(benzoic acid) + 5.62(benzoic acid) = 0.36

benzoic acid = 0.36/6.62 = 0.05 M

benzoate = 0.36 - 0.05 = 0.31 M

So,

answer = 0.05 M, 0.31 M

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