The decomposition of dimethyl ether leads to the formation of CH4, H2 and CO and the reaction rate is given by If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

The decomposition of dimethyl ether leads to the formation of CH₄, H₂ and CO and the reaction rate is given by
Rate = k [CH₃OCH₃]^3/2
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
Rate = k [CH₃OCH₃]^3/2
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
Answer
Given that
Rate = k [CH₃OCH₃]^3/2
In this problem pressure is in bar and time in minutes so that Unit of rate = bar min⁻¹
Given that Rate = k [CH₃OCH₃]^3/2
unit of k = unit of rate / unit of [CH₃OCH₃]^3/2
Hence unit of K = bar min ^-1/ bar^3/2
= bar^-1/2 min^-1