(B) Let the rate law be $r = k[A]^x[B]^y$. According to the problem,when the concentration of $B$ is doubled,the rate doubles: $2r = k[A]^x(2[B])^y$.

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(B) Let the rate law be $r = k[A]^x[B]^y$. According to the problem,when the concentration of $B$ is doubled,the rate doubles: $2r = k[A]^x(2[B])^y$. This implies $2^y = 2$,so $y = 1$. When the concentration of both $A$ and $B$ is doubled,the rate increases by a factor of $8$: $8r = k(2[A])^x(2[B])^y$. Substituting $y = 1$,we get $8r = k(2^x[A]^x)(2[B]) = 2^{x+1}k[A]^x[B]$. Since $r = k[A]^x[B]$,we have $8 = 2^{x+1}$,which means $2^3 = 2^{x+1}$. Therefore,$x + 1 = 3$,so $x = 2$. The rate law is $r = k[A]^2[B]$.

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

Medium

For a reaction $2A + B \to \text{Products}$,doubling the initial concentration of both the reactants increases the rate by a factor of $8$,and doubling the concentration of $B$ alone doubles the rate. The rate law for the reaction is

A
$r = k[A][B]^2$
B
$r = k[A]^2[B]$
C
$r = k[A][B]$
D
$r = k[A]^2[B]^2$

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Class 12

Chemistry Questions

Chapter

Chemical Kinetics

Subtopic

Rate law , Rate constant , Order of Reaction and Molecularity

Write the unit of the rate constant for the following reactions:
$1.$ $\frac{1}{2}$ order
$2.$ $\frac{3}{2}$ order

Easy

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The hydrolysis of an ester is catalyzed by dilute acids $A$ and $B$. The rate constants for the two processes are $K_A$ and $K_B$ respectively. If $K_A > K_B$,which of the following statements is correct?

Medium

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During the kinetic study of the reaction,$2A + B \rightarrow C + D,$ the following results were obtained:

$Run$ $[A] / mol \ L^{-1}$ $[B] / mol \ L^{-1}$ Initial rate of formation of $D / mol \ L^{-1} \ min^{-1}$

$I.$ $0.1$ $0.1$ $6.0 \times 10^{-3}$

$II.$ $0.3$ $0.2$ $7.2 \times 10^{-2}$

$III.$ $0.3$ $0.4$ $2.88 \times 10^{-1}$

$IV.$ $0.4$ $0.1$ $2.40 \times 10^{-2}$

Based on the above data,which one of the following is correct?

AIPMT 2010

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What is the order of reaction $A + B \to C$?

Observation $[A] \ (mol \ L^{-1})$ $[B] \ (mol \ L^{-1})$ Rate $(mol \ L^{-1} \ sec^{-1})$

$1$ $0.1$ $0.1$ $2 \times 10^{-3}$

$2$ $0.4$ $0.1$ $3.2 \times 10^{-3}$

$3$ $0.1$ $0.2$ $8 \times 10^{-3}$

Observation	$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	Rate $(mol \ L^{-1} \ sec^{-1})$
$1$	$0.1$	$0.1$	$2 \times 10^{-3}$
$2$	$0.4$	$0.1$	$3.2 \times 10^{-3}$
$3$	$0.1$	$0.2$	$8 \times 10^{-3}$

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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 $0.12 \ mol/L$.

Medium

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$Run$	$[A] / mol \ L^{-1}$	$[B] / mol \ L^{-1}$	Initial rate of formation of $D / mol \ L^{-1} \ min^{-1}$
$I.$	$0.1$	$0.1$	$6.0 \times 10^{-3}$
$II.$	$0.3$	$0.2$	$7.2 \times 10^{-2}$
$III.$	$0.3$	$0.4$	$2.88 \times 10^{-1}$
$IV.$	$0.4$	$0.1$	$2.40 \times 10^{-2}$

For a reaction $2A + B \to \text{Products}$,doubling the initial concentration of both the reactants increases the rate by a factor of $8$,and doubling the concentration of $B$ alone doubles the rate. The rate law for the reaction is

Similar Questions

Write the unit of the rate constant for the following reactions:$1.$ $\frac{1}{2}$ order$2.$ $\frac{3}{2}$ order

The hydrolysis of an ester is catalyzed by dilute acids $A$ and $B$. The rate constants for the two processes are $K_A$ and $K_B$ respectively. If $K_A > K_B$,which of the following statements is correct?

What is the order of reaction $A + B \to C$? Observation $[A] \ (mol \ L^{-1})$ $[B] \ (mol \ L^{-1})$ Rate $(mol \ L^{-1} \ sec^{-1})$ $1$ $0.1$ $0.1$ $2 \times 10^{-3}$ $2$ $0.4$ $0.1$ $3.2 \times 10^{-3}$ $3$ $0.1$ $0.2$ $8 \times 10^{-3}$

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 $0.12 \ mol/L$.

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Write the unit of the rate constant for the following reactions:
$1.$ $\frac{1}{2}$ order
$2.$ $\frac{3}{2}$ order

What is the order of reaction $A + B \to C$?

Observation $[A] \ (mol \ L^{-1})$ $[B] \ (mol \ L^{-1})$ Rate $(mol \ L^{-1} \ sec^{-1})$

$1$ $0.1$ $0.1$ $2 \times 10^{-3}$

$2$ $0.4$ $0.1$ $3.2 \times 10^{-3}$

$3$ $0.1$ $0.2$ $8 \times 10^{-3}$