Rate Constant

Q.

What is rate law?

Q. For the first order decomposition reaction of $N_2{O}_5$, it is observed that
$\left(i\right)N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right);\frac{-d\left[N_2{O}_5\right]}{dt}=k\left[N_2{O}_5\right]\left(ii\right)2N_2{O}_5\left(g\right)\to 4N{O}_2\left(g\right)+O_2\left(g\right);\frac{-d\left[N_2{O}_5\right]}{dt}=k^{\prime }\left[N_2{O}_5\right]$
Which of the following is true?

1. $k=k^{\prime }$
2. $k=2k^{\prime }$
3. $k=\frac{k^{\prime }}{2}$
4. $k=k^{\prime \frac{1}{2}}$

Q. The rate of a first order reaction is $1.8\times {10}^{-3}mol{L}^{-1}mi{n}^{-1},$ when the initial concentration is 0.3 mol $L^{-1}$ . The rate constant in the units of second is

1. ${10}^{-2}{s}^{-1}$
2. $6\times {10}^{-2}{s}^{-1}$
3. ${10}^{-4}{s}^{-1}$
4. $6\times {10}^2{s}^{-1}$

Q. 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 and the rate can 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 pressure is measured in bar and time in minutes, the units of rate constant are

1. $(bar{)}^{\frac{3}{2}}mi{n}^{-1}$
2. $(bar{)}^{-}\frac{3}{2}mi{n}^{-1}$
3. $(bar{)}^{-}\frac{1}{2}mi{n}^{-1}$
4. $(bar{)}^{-1}mi{n}^{-1}$