If the rate constant for a reaction repreasented by `2HI rarr H_(2)+I_(2)` is denoted by k then for the same reaction if represented by
`HI rarr (1)/(2) H_(2)+(1)/(2)I_(2)`, the rate constant shall be equal to

Options

A. `k+2`
B. `k`
C. `k//2`
D. `2 k`

Answer

C

Explanation

Fro the chemical equation
`2HIrarrH_(2)+I_(2)`
the differential rate law is
Rate `=-(1)/(2)(d[HI])/(dt)=k[HI]^(x)`
where `x` is the order of the reaction which does not depend upon how do we write the equation
For the chemical equation
`HIrarr(1)/(2)H_(2)+(1)/(2)1_(2)`
the differential rate law is
Rate `=(-d[HI])/(dt)=k'[HI]^(x)`
According to Eq. `(1)` , we have
`(d[HI])/(dt)=-2k[HI]^(x)`
Substituting this result into Eq. `(2)` , we get
`-(-2k[HI]^(x))=k'[HI]^(x)`
Or `k'=2k`