For a reaction Rate `= "k [acetone]"^((3)/(2))` then unit of rate constant and rate of reaction respectively is

Options

A. `("mol "L^(-1)s^(-1)), ("mol"^(-1//2)L^(1//2)s^(-1))`
B. `("mol"^(-1//2)L^(1//2)s^(-1)), ("mol "L^(-1)s^(-1))`
C. `("mol"^(1//2)L^(1//2)s^(-1)), ("mol "L^(-1)s^(-1))`
D. `("mol "Ls^(-1)), ("mol"^(1//2)L^(1//2)s)`

Explanation

Rate `=K[A]^(n)`
Rate `=(-d[A])/(dt), " unit of rate"=("mol "L^(-1))/(s)="mol "L^(-1)s^(-1)`
unit of rate constant `=(("mol "L^(-1)s^(-1)))/(("mol "L^(-1))^(n))="mol"^(1-n)L^(n-1)s^(-1)`
In this case, rate `=k["Acetone"]^(3//2)`
`n=3//2`
`"mol"^(1-(3//2))L^((3//2)-1)s^(-1) rArr "mol"^(-(1//2))L^((1//2))s^(-1)`