An acid-base indicator which is a weak acid has a `pK_(a)` value=5.45. At what concentration ratio of sodium acetate to acetic acid would the indicator show a colour half-way between those of its acid and conjugate base forms ? [`pK_(a)` of acetic acid =4.75]

Options

A. `4:1`
B. `7:1`
C. `5:1`
D. `2:1`

Answer

C

Explanation

Indicator is weak acid `HIN hArr H^+ + In^(-)`
given it shows colour at half way of ionisation
`K_a=([H^+][In^(-)])/([HIn])` so `pK_a=pH=5.35`
but for `CH_3COOH` and `CH_3COONa` buffer
`pH=pK_a+"log"(["Salt"])/(["Acid"])`
`5.35=4.75+"log"(["Salt"])/(["Acid"])implies (["Salt"])/(["Acid"])=5/1`