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  • The decomposition of dimethyl ether is a fractional order reaction. The rate of reaction is given by: Rate <img alt="=\mathrm{k}\left(\mathrm{PCH}_3 \mathrm{OCH}_3\right)^{3 / 2}" src="https

The decomposition of dimethyl ether is a fractional order reaction. The rate of reaction is given by:
Rate =\mathrm{k}\left(\mathrm{PCH}_3 \mathrm{OCH}_3\right)^{3 / 2} . If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constant respectively?

Option: 1

\mathrm{bar ~\mathrm{min}^{-1}, bar ^2 \mathrm{~min}^{-1} }


Option: 2

\mathrm{bar ~\mathrm{min}^{-1}, bar ^{-1 / 2} \mathrm{~min}^{-1} }


Option: 3

\operatorname{bar}^{-1 / 2} \mathrm{~min}^{-1}, \operatorname{bar}^2 \mathrm{~min}^{-1}


Option: 4

\mathrm{bar~ min { }^{-1}, bar ^{1 / 2} \min ^{-1}}


Answers (1)

best_answer

For a reaction,
Rate  \mathrm{ =k(\text { concentration })^{\text {order }}}
where  \mathrm{ n}  is order of reaction
Unit of rate = Concentration. \mathrm{ time ^{-1}}
Unit of \mathrm{\mathrm{k}=(\text { Concentration })^{1-n} \cdot time ^{-1}}
Similarly in terms of pressure,
Rate \mathrm{ =k\left(\mathrm{P}_{\mathrm{CH}_3 \mathrm{OCH}_3}\right)^{3 / 2}}
Unit of rate = Pressure \mathrm{ time ^{-1}}
Unit of rate = bar \mathrm{ min ^{-1}}
Unit of   \mathrm{ \mathrm{k}=(\text { Pressure })^{1-n} \cdot time ^{-1}}
Unit of   \mathrm{ \mathrm{k}=(\text { bar })^{1-\frac{3}{2}} \cdot \min ^{-1}}
Unit of   \mathrm{ \mathrm{k}=b a r^{\frac{-1}{2}} \cdot \min ^{-1}}.

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