The decomposition of dimethyl ether leads to the formation of `CH_(4),H_(2),` and `CO` and the reaction rate is given by
Rate `=k[CH_(3)OCH_(3)]^(3//2)`
The rate of reaction is followed by increase in the pressure in a closed vessel , so the rate can also be expressed in terms of the partial pressure of dimethyl either, `i.e., `
Rate `=k[p_(CH_(3)OCH_(3))]^(3//2)`
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constant ?

Options

A. `"bar min"^(-1), "bar"^(2)"min"^(-1)`
B. `"bar min"^(-1), "bar"^(-1//2)"min"^(-1)`
C. `"bar"^(-1//2)"min"^(-1),"bar"^(2)"min"^(-1)`
D. `"bar min"^(-1),"bar"^(-1//2)"min"^(-1)`

Answer

B

Explanation

Unit of rate : `"bar min"^(-1)`
Unit of rate constant : `"bar"^(-1//2)"min"^(-1)`