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_3OCH_3))^(3/2)`

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

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#### Solution

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

Unit of rate = bar min^{−1}

`Rate = k(p_(CH_3OCH_3))^(3/2)`

`=>k = "Rate"/(P_(CH_3OCH_3))^(3/2)`

Therefore, unit of rate constants (k) = `("bar " min^(-1))/"bar"^(3/2)`

`= "bar"^(-1/2) "min"^(-1)`

Concept: Rate of a Chemical Reaction

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