The decomposition of dimethyl ether leads to the formation of $CH _{4}, H _{2}$ and $CO$ and the reaction rate is given by

Rate $=k\left[ CH _{3} OCH _{3}\right]^{3 / 2}$

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 $=k\left(p_{ CH _{3} OCH _{3}}\right)^{3 / 2}$

If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

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If pressure is measured in bar and time in minutes, then

Unit of rate $=$ bar $\min ^{-1}$

Rate $ = k{\left( {{p_{C{H_3}OC{H_3}}}} \right)^{3/2}}$

$ \Rightarrow k = \frac{{{\rm{ Rate }}}}{{{{\left( {{p_{C{H_3}OC{H_3}}}} \right)}^{3/2}}}}$

Therefore, unit of rate constants $(k)=\frac{\text { bar min }^{-1}}{\operatorname{bar}^{3 / 2}}$

$ = ba{r^{ - 1/2}}{\min ^{ - 1}}$

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