The rate constant is unmerically the same for three reactions of first, second and third order respectively, the unit of concentration being in moles per litre. If `R_(1), R_(2) and R_(3)` are the rates of three reactions of first, second and third order respectively aqnd K is the rate constant, which of the following relationships is valid for the three reactions.

Options

A. `R_(1)= R_(2) = R_(3)`
B. `R_(1)ltT_(2)ltR_(3)`
C. `R_(3)ltR_(2)ltR_(1)`
D. All of these

Answer

D

Explanation

Considring the rate law expressions (for a reation `ArarrB)` we have
`R_(1)=k[A]`
`R_(2)=k[A]^(2)`
`R_(3)=k[A]^(3)`
`K` is the rate constant, which is the same for the three reactions and `[A]` is the concentration of the reaction `A` in moles per litre.
`[A]=1,R_(1)=R_(2)=R_(3)`
`[A]= gt1,R_(3)gtR_(2)gtR_(1)`
`[A]= lt 1,R_(1)=R_(2)gtR_(3)`