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Question: The decomposition of dimethyl ether is a fractional order reaction. The rate of reaction is given by...

The decomposition of dimethyl ether is a fractional order reaction. The rate of reaction is given by rate = k(pCH3OCH3)3/2k(p_{CH_{3}OCH_{3}})^{3/2} if the pressure is measure in bar and time in minutes then what are the unit of rate and rate constant?

A

barmin⁡−1,bar2min⁡−1bar\min^{- 1},bar^{2}\min^{- 1}{}

B

barmin⁡−1,bar−1/2min⁡−1bar\min^{- 1},bar^{- 1/2}\min^{- 1}{}

C

bar−1/2min⁡−1,bar2min⁡−1bar^{- 1/2}\min^{- 1},bar^{2}\min^{- 1}{}

D

barmin⁡−1,bar1/2min⁡−1bar\min^{- 1},bar^{1/2}\min^{- 1}{}

Answer

barmin⁡−1,bar−1/2min⁡−1bar\min^{- 1},bar^{- 1/2}\min^{- 1}{}

Explanation

Solution

In terms of pressure,

Rate =k(pCH3OCH3)3/2= {k_{(p_{CH_{3}OCH_{3}})}}^{3/2}

Unit of rate = bar min⁡−1\min^{- 1}{}

Unit of rate constant =rate(PCH3OCH3)3/2= \frac{rate}{(P_{CH_{3}OCH_{3}})^{3/2}}

=barmin⁡−1bar3/2=bar−1/2min⁡−1= \frac{bar\min^{- 1}}{bar^{3/2}} = bar^{- 1/2}\min^{- 1}{}