Question

The decomposition of dimethyl ether leads to the formation of CH₄, H₂ and CO and the reaction rate is given by 
\(Rate = k [CH_3OCH_3]^{\frac 32}\)
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., 
\(Rate = k(p_{CH_3OCH_3})^{\frac 32}\)
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

Answer 1

\(If\  pressure \ is \ measured \ in\  bar\  and\  time \ in\  minutes\, \ then\)

\(Unit \ of\  rate = bar \ min^{-1}\)

\(Rate = k(p_{CH_3OCH_3})^{\frac 32}\)

\(k = \frac {Rate}{(p_{CH_3OCH_3})^{\frac 32}}\)

\(Therefore, \ unit\  of \ rate\  constants = \frac {bar \ min^{-1}}{bar^{\frac 32}}\)

= \(bar^{-\frac 12} min^{-1}\)