(A) The initial rate of reaction is $r_1 = k[A]^{n}[B]^{m}$.When the concentration of $A$ is doubled $(2[A])$ and the concentration of $B$ is halved $

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(A) The initial rate of reaction is $r_1 = k[A]^{n}[B]^{m}$.When the concentration of $A$ is doubled $(2[A])$ and the concentration of $B$ is halved $(\frac{[B]}{2})$,the new rate $r_2$ is given by:$r_2 = k(2[A])^{n} \cdot \left(\frac{[B]}{2}\right)^{m}$$r_2 = k \cdot 2^{n} \cdot [A]^{n} \cdot \frac{[B]^{m}}{2^{m}}$$r_2 = 2^{(n-m)} \cdot k[A]^{n}[B]^{m}$Therefore,the ratio $\frac{r_2}{r_1} = \frac{2^{(n-m)} k[A]^{n}[B]^{m}}{k[A]^{n}[B]^{m}} = 2^{(n-m)}$.

Class 12 Chemistry Chemical Kinetics Rate law , Rate constant , Order of Reaction and Molecularity

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Rate law for a reaction between $A$ and $B$ is given by $R=k[A]^{n}[B]^{m}$. If concentration of $A$ is doubled and concentration of $B$ is halved from their initial value,the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{r_2}{r_1}\right)$ is

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A
$2^{(n-m)}$
B
$(n-m)$
C
$(m+n)$
D
$\frac{1}{2^{m+n}}$

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Chemical Kinetics

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Rate law , Rate constant , Order of Reaction and Molecularity

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The hypothetical reaction $A_2 + B_2 \rightarrow 2AB$ follows the mechanism given below. What is the overall order of the reaction?
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Rate law for a reaction between $A$ and $B$ is given by $R=k[A]^{n}[B]^{m}$. If concentration of $A$ is doubled and concentration of $B$ is halved from their initial value,the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{r_2}{r_1}\right)$ is

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The rate constant for the reaction $2N_2O_5 \to 4NO_2 + O_2$ is $3.0 \times 10^{-5} \, sec^{-1}$. If the rate is $2.40 \times 10^{-5} \, M \, sec^{-1}$,then the concentration of $N_2O_5$ (in $M$) is?

For the reaction: $2A + B \to A_2B$; the rate $= K[A][B]^2$ with $K = 2.0 \times 10^{-6} \ L^2 \ mol^{-2} \ s^{-1}$. Initial concentrations of $A$ and $B$ are $[A]_0 = 0.2 \ mol/L$ and $[B]_0 = 0.4 \ mol/L$ respectively. Calculate the rate of reaction after $[A]$ is reduced to $0.12 \ mol/L$.

The hypothetical reaction $A_2 + B_2 \rightarrow 2AB$ follows the mechanism given below. What is the overall order of the reaction?$A_2 \rightleftharpoons A + A$ ...... (fast);$A + B_2 \rightarrow AB + B$ ...... (slow);$A + B \rightarrow AB$ ...... (fast)

For the reaction $aA + bB \to$ product,the rate of reaction is given by $Rate = k[A]^3 [B]^0$. If the concentration of $A$ is doubled and the concentration of $B$ is halved,the rate of reaction will be: (in $\times$)

If $a$ is the initial concentration and $n$ is the order of the reaction and the half-life period is $T$,then:

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The hypothetical reaction $A_2 + B_2 \rightarrow 2AB$ follows the mechanism given below. What is the overall order of the reaction?
$A_2 \rightleftharpoons A + A$ ...... (fast);
$A + B_2 \rightarrow AB + B$ ...... (slow);
$A + B \rightarrow AB$ ...... (fast)