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Question

Acetic acid and propionic acid have Ka values 1.75×105 and 1.3×105 respectively at a certain temperature. An equimolar solution of a mixture of the two acids is partially neutralised by NaOH. How is the ratio of the contents of acetate and propionate ions related to the Ka values and the molarity?

A
(α1α)=1.751.3×(β1β), where α and β are ionized fractions of the acids
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B
The ratio is unrelated to the Ka values
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C
The ratio is unrelated to the molarity
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D
The ratio is unrelated to the pH of the solution
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Solution

The correct option is A (α1α)=1.751.3×(β1β), where α and β are ionized fractions of the acids
The equilibrium reaction for the ionization of acetic acid is as given below:
CH3COOH1αCH3COOα+H+α+β
The equilibrium reaction for the ionization of propanoic acid is given below:
C2H5COOH1βC2H5COOβ+H+α+β
Let, represent the degree of ionization at same concentrations of acetic acid and propanioc acid respectively.
The expression for the dissociation constant for acetic acid is as given below:
KAcetic acid=[α][α+β]c[1α]
The expression for the dissociation constant for propanoic acid is as given below:
KPropionic acid=[β][α+β]c[1β]
The ration of the acid dissociation constants is calculated as shown below:
KAcetic acidKPropionic acid=α1α×(1β)β
Hence, α1α=1.751.3×[β1β]

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