Question

The decomposition of dimethyl ether leads to the formation of $C{H}_4,H_2$ and CO and the reaction rate is given by $Rate=k[C{H}_{3}OC{H}_3{]}^{\frac{3}{2}}$
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., $Rate=k(P_{C{H}_{3}OC{H}_3}{)}^{\frac{3}{2}}$
If the pressure is measured in bar and time in minutes, then the unit of rate constants is:

• A. $ba{r}^{\frac{1}{2}}min$
• B. $ba{r}^{\frac{3}{2}}mi{n}^{-1}$
• C. $ba{r}^{-\frac{1}{2}}mi{n}^{-1}$
• D. $barmi{n}^{-1}$

Answer 1

The correct option is C $ba{r}^{-\frac{1}{2}}mi{n}^{-1}$

As $Rate=k(P_{C{H}_{3}OC{H}_3}{)}^{\frac{3}{2}}$
$bar/min=k(bar{)}^{\frac{3}{2}}$
$\therefore$ unit of k$=ba{r}^{-\frac{1}{2}}mi{n}^{-1}$