Question

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 = \[\ce{k(P_{CH_3OCH_3})^{3/2}}\].

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 = \[\ce{\frac{Partial pressure}{time} = \frac{bar}{min}}\] = bar min⁻¹

Rate = \[\ce{k(P_{CH_3OCH_3})^{3/2}}\]

k = \[\ce{\frac{Rate}{(P_{CH_3OCH_3})^{3/2}}}\]

Therefore, unit of rate constants (k) = \[\ce{\frac{bar min ^{-1}}{bar^{3/2}}}\]

= bar^−1/2 min⁻¹