The rate of the elementary reaction
`H_(2)(g) +I_(2)(g) hArr 2HI(g) ` at `25^(@)C` is given by `:`
Rate `=1.7xx10^(-18) [H_(2)][I_(2)]`
The rate of decomposition of gaseous `HI` to `H_(2)(g)` and `I_(2)(g)` at `25^(@)C` is Rate`=2.4xx10^(-21)[HI]^(2)`
Equilibrium constant for the formation of one mole of gaseous `HI` from the `H_(2)(g)` and `I_(2)(g)` is `:`

Options

A. 708
B. 354
C. 0.0014
D. 26.6

Answer

D

Explanation

`(1)/(2)H_(2)(g)+(1)/(2)I_(2)(g)hArr HI(g)`
`K_(c)=([HI])/([H_(2)]^((1)/(2))[I_(2)]^((1)/(2)))`
For the reaction
`H_(2)(g)+I_(2)(g)hArr2HI(g)`
`R_(f)=1.7xx10^(-18)[H_(2)][I_(2)]`
`R_(b)=2.4xx10^(-21)[HI]^(2)`
At eqm,
`R_(f)=R_(b)`
`1.7xx10^(-18)[H_(2)][I_(2)]=2.4xx10^(-2)[HI]^(2)`
`(1.7xx10^(-18))/(2.4xx10^(-21))=([HI]^(2))/([H_(2)][I_(2)])`
`(170)/(24)xx10^(2)=K_(c)^(2)`
`K_(c)=sqrt((170)/(24))xx10=sqrt(7.08)xx10`
`2.66xx10=26.6`