Question

The decomposition of dimethyl ether leads to the formation of CH4, H2 and CO and the reaction rate is given by
$Rate = k [CH_3OCH_3]^{\frac 32}$
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.,
$Rate = k(p_{CH_3OCH_3})^{\frac 32}$
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

Answer 1

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

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

$Rate = k(p_{CH_3OCH_3})^{\frac 32}$

$k = \frac {Rate}{(p_{CH_3OCH_3})^{\frac 32}}$

$Therefore, \ unit\ of \ rate\ constants = \frac {bar \ min^{-1}}{bar^{\frac 32}}$

= $bar^{-\frac 12} min^{-1}$