The decomposition of dimethyl ether leads to the formation of $C H_{4}, H_{2}$ and $C O$ and the reaction rate is given by:
$R a t e = k [C H_{3} O C H_{3}]^{3 / 2}$

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., $R a t e = k [P_{C H_{3} O C H_{3}}]^{3 / 2}$

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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Solution

Rate $= \frac{b a r}{m i n} = u n i t o f r a t e = b a r m i n^{- 1}$

$R a t e = k (P_{C H_{3} O C H_{3}})^{3 / 2} = k (b a r)^{3 / 2}$

$k = \frac{b a r m i n^{- 1}}{(b a r)^{3 / 2}} = b a r^{- 1 / 2} m i n^{- 1}$

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