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 data for the reaction $A + B \to C$ isThe rate law corresponds to the above data is
Exp.
$[A]_0$
$[B]_0$
Initial rate
$(1)$
$0.012$
$0.035$
$0.10$
$(2)$
$0.024$
$0.070$
$0.80$
$(3)$
$0.024$
$0.035$
$0.10$
$(4)$
$0.012$
$0.070$
$0.80$
The data for the reaction $A + B \to C$ isThe rate law corresponds to the above data is
|
Exp. |
$[A]_0$ |
$[B]_0$ |
Initial rate |
|
$(1)$ |
$0.012$ |
$0.035$ |
$0.10$ |
|
$(2)$ |
$0.024$ |
$0.070$ |
$0.80$ |
|
$(3)$ |
$0.024$ |
$0.035$ |
$0.10$ |
|
$(4)$ |
$0.012$ |
$0.070$ |
$0.80$ |
- [AIPMT 1994]
For a reaction $A \to B$, the rate of reaction quadrupled when the concentration of $A$ is doubled. The rate expression of the reaction is $r = K{(A)^n}$. when the value of $n$ is
For a reaction $A \to B$, the rate of reaction quadrupled when the concentration of $A$ is doubled. The rate expression of the reaction is $r = K{(A)^n}$. when the value of $n$ is
For the reaction:
$2 A + B \rightarrow A _{2} B $
the rate $=k[ A ][ B ]^{2}$ with $k =2.0 \times 10^{-6} \,mol ^{-2}\, L ^{2} \,s ^{-1}$. Calculate the initial rate of the reaction when $[ A ]=0.1 \,mol \,L ^{-1},[ B ]=0.2\, mol \,L ^{-1}$. Calculate the rate of reaction after $[A] $ is reduced to $0.06 \,mol\, L ^{-1}$
For the reaction:
$2 A + B \rightarrow A _{2} B $
the rate $=k[ A ][ B ]^{2}$ with $k =2.0 \times 10^{-6} \,mol ^{-2}\, L ^{2} \,s ^{-1}$. Calculate the initial rate of the reaction when $[ A ]=0.1 \,mol \,L ^{-1},[ B ]=0.2\, mol \,L ^{-1}$. Calculate the rate of reaction after $[A] $ is reduced to $0.06 \,mol\, L ^{-1}$
For a certain reaction : $(A)(g) \to B(g)$ Half life for different initial pressures of $A$ is given below
$\begin{array}{|l|l|l|} \hline {P_{{A_0}}}(atm) & 0.1 & 0.025 \\ \hline {t_{1/2}}(\sec\,\,) & 100 & 50 \\ \hline \end{array}$
The correct statement about order of reaction is
For a certain reaction : $(A)(g) \to B(g)$ Half life for different initial pressures of $A$ is given below
$\begin{array}{|l|l|l|} \hline {P_{{A_0}}}(atm) & 0.1 & 0.025 \\ \hline {t_{1/2}}(\sec\,\,) & 100 & 50 \\ \hline \end{array}$
The correct statement about order of reaction is
Consider following two reaction,
$A \to {\text{Product ;}}\,\, - \frac{{d[A]}}{{dt}} = {k_1}{[A]^o}$
$B \to {\text{Product ;}}\,\, - \frac{{d[B]}}{{dt}} = {k_2}{[B]}$
Units of $k_1$ and $k_2$ are expressed in terms of molarity $(M)$ and time $(sec^{-1})$ as
Consider following two reaction,
$A \to {\text{Product ;}}\,\, - \frac{{d[A]}}{{dt}} = {k_1}{[A]^o}$
$B \to {\text{Product ;}}\,\, - \frac{{d[B]}}{{dt}} = {k_2}{[B]}$
Units of $k_1$ and $k_2$ are expressed in terms of molarity $(M)$ and time $(sec^{-1})$ as