For the following rate law determine the unit of rate constant. Rate $=-\frac{d[ R ]}{d t}=k[ A ]^{\frac{1}{2}}[ B ]^{2}$
For the following rate law determine the unit of rate constant. Rate $=-\frac{d[ R ]}{d t}=k[ A ]^{\frac{1}{2}}[ B ]^{2}$
The total order of reaction $n=\frac{1}{2}+2=\frac{5}{2}=2.5$ Rate $k[\mathrm{~A}]^{\frac{1}{2}}[\mathrm{~B}]^{2}=[\mathrm{R}]^{\frac{5}{2}}$
$\therefore k=\frac{\text { Rate }}{[\mathrm{R}]^{5 / 2}}$
$\therefore$ unit of $k=\frac{\text { unit of rate }}{\text { (unit of concentration) }^{5 / 2}}$
$=\frac{\left(\mathrm{mol} \mathrm{L}^{-1}\right)^{1} \mathrm{~s}^{-1}}{\left(\mathrm{~mol} \mathrm{~L}^{-1}\right)^{\frac{5}{2}}}$
$=\left(\mathrm{mol} \mathrm{L}^{-1}\right)^{1-\frac{5}{2}} \mathrm{~s}^{-1}$
$=\left(\mathrm{mol} \mathrm{L}^{-1}\right)^{-\frac{3}{2}} \mathrm{~s}^{-1}$
$=(\mathrm{mol})^{\frac{-3}{2}}\left(\mathrm{~L}^{-1}\right)^{\frac{-3}{2}} \mathrm{~s}^{-1}$
$=\mathrm{mol}^{\frac{-3}{2}} \mathrm{~L}^{\frac{+3}{2}} \mathrm{~s}^{-1}$
If the order of reaction $=\frac{5}{2}$ then unit of rate constant $k$ is $\mathrm{L}^{\frac{+3}{2}} \mathrm{~mol}^{\frac{-3}{2}} \mathrm{~s}^{-1}$.
Similar Questions
The rate of the reaction becomes twice when the concentration of reactant becomes $8$ times then the order of the reaction is
The rate of the reaction becomes twice when the concentration of reactant becomes $8$ times then the order of the reaction is
The rate constant k, for the reaction ${N_2}{O_5}(g) \to $ $2N{O_2}(g) + \frac{1}{2}{0_2}(g)$ is $2.3 \times {10^{ - 2}}\,{s^{ - 1}}$. Which equation given below describes the change of $[{N_2}{O_5}]$ with time? ${[{N_2}{O_5}]_0}$ and ${[{N_2}{O_5}]_t}$ correspond to concentration of ${N_2}{O_5}$ initially and at time $t$.
The rate constant k, for the reaction ${N_2}{O_5}(g) \to $ $2N{O_2}(g) + \frac{1}{2}{0_2}(g)$ is $2.3 \times {10^{ - 2}}\,{s^{ - 1}}$. Which equation given below describes the change of $[{N_2}{O_5}]$ with time? ${[{N_2}{O_5}]_0}$ and ${[{N_2}{O_5}]_t}$ correspond to concentration of ${N_2}{O_5}$ initially and at time $t$.
- [AIIMS 2004]
For a chemical reaction, $A + 2B \to C + D$, the rate of reaction increases three times, when concentration of $A$ only is increased nine times. While when concentration of $B$ only is increased $2\, times$, then rate of reaction also increases $2\, times$. The order of this reaction is
For a chemical reaction, $A + 2B \to C + D$, the rate of reaction increases three times, when concentration of $A$ only is increased nine times. While when concentration of $B$ only is increased $2\, times$, then rate of reaction also increases $2\, times$. The order of this reaction is
For a reaction taking place in three steps at same temperature, overall rate constant $\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3}$. If $\mathrm{Ea}_1, \mathrm{Ea}_2$ and $\mathrm{Ea}_3$ are $40$,$50$ and $60 \mathrm{~kJ} / \mathrm{mol}$ respectively, the overall $\mathrm{Ea}$ is ________ $\mathrm{kJ} / \mathrm{mol}$.
For a reaction taking place in three steps at same temperature, overall rate constant $\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3}$. If $\mathrm{Ea}_1, \mathrm{Ea}_2$ and $\mathrm{Ea}_3$ are $40$,$50$ and $60 \mathrm{~kJ} / \mathrm{mol}$ respectively, the overall $\mathrm{Ea}$ is ________ $\mathrm{kJ} / \mathrm{mol}$.
- [JEE MAIN 2024]
The following data was obtained for chemical reaction given below at $975\, \mathrm{~K}$.
$2 \mathrm{NO}_{(\mathrm{g})}+2 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{N}_{2(\mathrm{~g})}+2 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})}$
$[NO]$
$\mathrm{mol} \mathrm{L}^{-1}$
${H}_{2}$
$\mathrm{mol} \mathrm{L}^{-1}$
Rate
$\mathrm{mol}L^{-1}$ $s^{-1}$
$(A)$
$8 \times 10^{-5}$
$8 \times 10^{-5}$
$7 \times 10^{-9}$
$(B)$
$24 \times 10^{-5}$
$8 \times 10^{-5}$
$2.1 \times 10^{-8}$
$(C)$
$24 \times 10^{-5}$
$32 \times 10^{-5}$
$8.4 \times 10^{-8}$
The order of the reaction with respect to $\mathrm{NO}$ is ..... .
The following data was obtained for chemical reaction given below at $975\, \mathrm{~K}$.
$2 \mathrm{NO}_{(\mathrm{g})}+2 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{N}_{2(\mathrm{~g})}+2 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})}$
|
$[NO]$ $\mathrm{mol} \mathrm{L}^{-1}$ |
${H}_{2}$ $\mathrm{mol} \mathrm{L}^{-1}$ |
Rate $\mathrm{mol}L^{-1}$ $s^{-1}$ |
|
| $(A)$ | $8 \times 10^{-5}$ | $8 \times 10^{-5}$ | $7 \times 10^{-9}$ |
| $(B)$ | $24 \times 10^{-5}$ | $8 \times 10^{-5}$ | $2.1 \times 10^{-8}$ |
| $(C)$ | $24 \times 10^{-5}$ | $32 \times 10^{-5}$ | $8.4 \times 10^{-8}$ |
The order of the reaction with respect to $\mathrm{NO}$ is ..... .
- [JEE MAIN 2021]