Question

The decomposition of dimethyl ether is a fractional order reaction. The rate of reaction is given by rate $=k{\left(p_{C{H}_{3}OC{H}_3}\right)}^{3/2}$. If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constant?

• A. bar $mi{n}^{-1}$, $ba{r}^{2}mi{n}^{-1}$
• B. bar $mi{n}^{-1}$, $ba{r}^{-1/2}mi{n}^{-1}$
• C. $ba{r}^{-1/2}mi{n}^{-1}$, $ba{r}^{2}mi{n}^{-1}$
• D. $barmi{n}^{-1}$, $ba{r}^{1/2}mi{n}^{-1}$

Answer 1

Answer: (B)

In terms of pressure,
Rate $=k{\left(p_{C{H}_{3}OC{H}_3}\right)}^{3/2}$
Unit of rate = bar $mi{n}^{-1}$
Unit of rate constant $=\frac{rate}{{\left(p_{C{H}_{3}OC{H}_3}\right)}^{3/2}}$
$=\frac{barmi{n}^{-1}}{ba{r}^{3/2}}$
$=ba{r}^{-1/2}mi{n}^{-1}$