Question

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

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

Answer 1

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

For a reaction,
$Rate=k(\text{concentration}{)}^{\text{order}}$

$k=\frac{\text{Rate}}{(\text{Concnetration}{)}^n}$
where n is order of reaction

$\text{Unit of rate}=\text{Concentration}.{\text{time}}^{-1}$
$\text{Unit of k}=(\text{Concentration}{)}^{1-n}.tim{e}^{-1}$

Similarly in terms of pressure,

$Rate=k(P_{C{H}_{3}OC{H}_3}{)}^{3/2}$
$\text{Unit of rate}=\text{Pressure}.{\text{time}}^{-1}$
$\text{Unit of rate}=barmi{n}^{-1}$

$\text{Unit of k}=(\text{Pressure}{)}^{1-n}.tim{e}^{-1}$
$\text{Unit of k}=(bar{)}^{1-\frac{3}{2}}.mi{n}^{-1}$
$\text{Unit of k}=ba{r}^{\frac{-1}{2}}.mi{n}^{-1}$