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 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[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 constants ?

Explanation

Given , unit of pressure = bar and units of time = minute
`therefore" Unit of rate = bar . min"^(-1)`
The rate law of the given reaction , rate `=k[P_(CH_(3)COCH_(3))]^(3//2)`
`therefore" Unit of k"=("Rate")/ (P_(CH_(3)COCH_(3)))^(3//2)=("bar.min"^(-1))/("bar"^(3//2))`
`"bar"^(-1//2)."min"^(-1)`