The decomposition of dimethyl ether leads to formation of \(CH_4\), \(H_2\) and \(CO\). The reaction rate is given by Rate \(= k[PCH_3OCH_3]^{3/2}\). If pressure is measured in bar and time in minutes, what is the unit of rate constant?

\(bar^{–1/2} min^{–1}\)

The correct answer is option 1.\(bar^{–1/2} min^{–1}\).

The rate equation given is:
\[ \text{Rate} = k[P_{\text{CH}_3\text{OCH}_3}]^{3/2} \]
To determine the units of the rate constant (\(k\)), we can substitute the units of rate and concentration into the equation and solve for the units of \(k\).
\[ \text{Rate} = k[P_{\text{CH}_3\text{OCH}_3}]^{3/2} \]
Units of rate = \([P_{\text{CH}_3\text{OCH}_3}]^{3/2}\) divided by the units of time.
\[ \text{Units of Rate} = \frac{[P_{\text{CH}_3\text{OCH}_3}]^{3/2}}{\text{Time}} \]
Since the concentration term is raised to the power of \(3/2\), and the time is in the denominator, the units of \(k\) would be the reciprocal of the square root of concentration and time.
Therefore, the correct unit of the rate constant (\(k\)) is: (1) \(bar^{-1/2} \, min^{-1}\)