Acetic acid and propionic acid have `K_(a)` values `1.75xx10^(-5)` and `1.3xx10^(-5)` respectively at a cetrain 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 `K_(a)` values and the molarity ?

Options

A. `((alpha)/(1-alpha))=(1.75)/(1.3)xx((beta)/(1-beta))`, where `alpha` and `beta` are ionised fractions of these acids
B. The ratio is unrelated to the `K_(a)` values
C. The ratio is unrelated to the molarity
D. The ratio is unrelated to the pH of the solution

Answer

A

Explanation

In a given mixture, the ionisatikon of two acids can be written as: Let `alpha, beta` be degree of ionisation at same concentration.
`{:(CH_(3)COOHhArr,CH_(3)COO^(-)+,H^(+)),(1-alpha,alpha,alpha+beta):}`
`{:(C_(2)H_(5)COOHhArr, C_(2)H_(5)COO^(-)+, H^(+)),(1-beta,beta,alpha+beta):}`
`:. K_(A.A)= ([alpha][alpha+beta].c)/([1-alpha])`
`K_(P.A)= ([beta][alpha+beta].c)/([1-beta])`
`(K_(A.A))/(K_(P.A))=(alpha)/(1-alpha)xx(1-beta)/(beta)`
or `(alpha)/(1-alpha)=(1.75)/(1.3)xx[(beta)/(1-beta)]`