The values of limiting ionic conductance of `H^(+)` and `HCOO^(-)` ions are respectively 347 and `53S cm^(2) mol^(-1)` the dissociation constant of methanoic acid at 298 K is

Options

A. a) `1 xx 10 ^(-5)`
B. b)`2 xx 10 ^(-5)`
C. c)`1.5 xx 10^(-4)`
D. d) `2.5 xx 10^(-4)`

Answer

D

Explanation

Given, `^^ _(H ^(+)) ^(0) = 347 S cm ^(2) mol ^(-1)`
`^^ _(HCOO ^(-)) ^(0) = 53 S cm ^(2) mol ^(-1)`
`^^ _(HCOOH)^(oo) = 347 + 53 = 400 S cm ^(2) mol ^(-1)`
Degree of dissociation.
`alpha = (^^_(C ) ^(@))/( ^^_( HCOOH) ^(@)) = (40)/(400) = (1)/(10) = 0.1 `
HCOOH ionises as
`{:(HCOOH to H ^(+) + HCOO^(-)), ( " "C " "0 " "0), ( C-Calpha " "Calpha " "Calpha):}`
`K _(a) = ([H ^(+)] [HCOO^(-)])/([HCOOH]) = (C ^(2) alpha ^(2))/( C - C alpha ) = (Calpha ^(2))/( (1- alpha ))`
`because alpha lt lt lt 1 so 1 - alpha ~~ 1`
` K _(a) C alpha ^(2)`
`= 0.025 xx (0.1) ^(2)`
`= 2. 5 xx 10 ^(-4)`