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?

Answer

Unit of rate `=` bar `mi n^(-1)`
Unit of `k= ba r^(1//2)mi n^(-1)`

Explanation

`CH_(3)OCH_(3)rarrCH_(4)+CO+H_(2)`
Rate `=k[CH_(3)OCH_(3)]^(3//2)`
Units of rate `=(DeltaP)/(Deltat)=` bar `mi n^(-1)`
Units of `k=["Conc"]^(1-n) "time"^(-1)`
`=[ba r]^(1-3//2) mi n^(-1)`
`= ba r^(-1//2)mi n^(-1)`