Question

The decomposition of dimethyl ether leads to the formation of $CH_{4},H_{2}$ and $CO$ and the reaction rate is given by
Rate $=k\left[C H_{3} O C H_{3}\right]^{\frac{3}{2}}$
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 $=k\left(P_{C H_{3} O C H_{3}}\right)^{\frac{3}{2}}$
If the pressure is measured in bar and time in minutes, then the unit of rate constants is

• A. $bar^{1 / 2} \, min$
• B. $bar^{3 / 2} \, min^{- 1}$
• C. $bar^{- 1 / 2} \, min^{- 1}$
• D. $barmin^{- 1}$

Answer 1

Answer: (C)

As $rate=k\left[C H_{3} O C H_{3}\right]^{\frac{3}{2}}$
bar/min $=k\left(b a r\right)^{\frac{3}{2}}$
Unit of $k=bar^{- \frac{1}{2}} \, m i n^{- 1}$