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
For the first order decompsition reaction of $N_2O_5$, it is found that -
$(a)$ $2N_2O_5\rightarrow\,\,4NO_2(g)+O_2(g)-\frac{d[N_2O_5]}{dt}=k[N_2O_5]$
$(a)$ $N_2O_5\rightarrow\,\,2NO_2(g)+1/2\,\,O_2(g)-\frac{d[N_2O_5]}{dt}=k'[N_2O_5]$
which of the following is true ?
For the first order decompsition reaction of $N_2O_5$, it is found that -
$(a)$ $2N_2O_5\rightarrow\,\,4NO_2(g)+O_2(g)-\frac{d[N_2O_5]}{dt}=k[N_2O_5]$
$(a)$ $N_2O_5\rightarrow\,\,2NO_2(g)+1/2\,\,O_2(g)-\frac{d[N_2O_5]}{dt}=k'[N_2O_5]$
which of the following is true ?
The rates of a certain reaction $(dc/dt)$ at different times are as follows
Time Rate (mole $litre^{-1}\,sec^{ -1}$ )
$0$ $2.8 \times {10^{ - 2}}$
$10$ $2.78 \times {10^{ - 2}}$
$20 $ $2.81 \times {10^{ - 2}}$
$30$ $2.79 \times {10^{ - 2}}$
The reaction is
The rates of a certain reaction $(dc/dt)$ at different times are as follows
Time Rate (mole $litre^{-1}\,sec^{ -1}$ )
$0$ $2.8 \times {10^{ - 2}}$
$10$ $2.78 \times {10^{ - 2}}$
$20 $ $2.81 \times {10^{ - 2}}$
$30$ $2.79 \times {10^{ - 2}}$
The reaction is
For the reaction $A + B \to $ products, what will be the order of reaction with respect to $A$ and $B$ ?
Exp.
$[A]\,(mol\,L^{-1})$
$[B]\,(mol\,L^{-1})$
Initial rate $(mol\,L^{-1}\,s^{-1})$
$1.$
$2.5\times 10^{-4}$
$3\times 10^{-5}$
$5\times 10^{-4}$
$2.$
$5\times 10^{-4}$
$6\times 10^{-5}$
$4\times 10^{-3}$
$3.$
$1\times 10^{-3}$
$6\times 10^{-5}$
$1.6\times 10^{-2}$
For the reaction $A + B \to $ products, what will be the order of reaction with respect to $A$ and $B$ ?
| Exp. | $[A]\,(mol\,L^{-1})$ | $[B]\,(mol\,L^{-1})$ | Initial rate $(mol\,L^{-1}\,s^{-1})$ |
| $1.$ | $2.5\times 10^{-4}$ | $3\times 10^{-5}$ | $5\times 10^{-4}$ |
| $2.$ | $5\times 10^{-4}$ | $6\times 10^{-5}$ | $4\times 10^{-3}$ |
| $3.$ | $1\times 10^{-3}$ | $6\times 10^{-5}$ | $1.6\times 10^{-2}$ |
Define following term / Give definition :
$(1)$ Elementary reaction
$(2)$ Complex reaction
Define following term / Give definition :
$(1)$ Elementary reaction
$(2)$ Complex reaction
For a reaction $\mathrm{A} \xrightarrow{\mathrm{K}_4} \mathrm{~B} \xrightarrow{\mathrm{K}_2} \mathrm{C}$
If the rate of formation of $B$ is set to be zero then the concentration of $B$ is given by :
For a reaction $\mathrm{A} \xrightarrow{\mathrm{K}_4} \mathrm{~B} \xrightarrow{\mathrm{K}_2} \mathrm{C}$
If the rate of formation of $B$ is set to be zero then the concentration of $B$ is given by :
- [JEE MAIN 2024]