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 $=k\left(p_{\mathrm{CH}_{3} \mathrm{OCH}_{3}}\right)^{3 / 2}$
If the pressure is measured in bar andtime in minutes, then what are the units of rate and rate constants?
If pressure is measured in bar and time in minutes, then
Unit of rate = bar min−1
Rate $=k\left(p_{\mathrm{CH}_{3} \mathrm{OCH}_{3}}\right)^{3 / 2}$
$\Rightarrow k=\frac{\text { Rate }}{\left(p_{\mathrm{CH}_{3} \mathrm{OCH}_{3}}\right)^{3 / 2}}$
Therefore, unit of rate constants $(k)=\frac{\operatorname{bar} \min ^{-1}}{\operatorname{bar}^{3 / 2}}$
$=b a r^{-1 / 2} \min ^{-1}$
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