(C) The reaction is $2 \ A_{(g)} + B_{(g)} \longrightarrow C_{(g)}$.At $t = 0$,$P_A = 1.5 \ atm$ and $P_B = 0.7 \ atm$. The initial rate is $r_1 = K(P

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(C) The reaction is $2 \ A_{(g)} + B_{(g)} \longrightarrow C_{(g)}$.At $t = 0$,$P_A = 1.5 \ atm$ and $P_B = 0.7 \ atm$. The initial rate is $r_1 = K(P_A)^2(P_B) = K(1.5)^2(0.7)$.When $P_C = 0.5 \ atm$,the pressure of $A$ consumed is $2 \times 0.5 = 1.0 \ atm$ and $B$ consumed is $0.5 \ atm$.Remaining pressures are $P_A = 1.5 - 1.0 = 0.5 \ atm$ and $P_B = 0.7 - 0.5 = 0.2 \ atm$.The rate at this time is $r_2 = K(0.5)^2(0.2)$.Taking the ratio: $\frac{r_1}{r_2} = \frac{K(1.5)^2(0.7)}{K(0.5)^2(0.2)} = \frac{2.25 \times 0.7}{0.25 \times 0.2} = \frac{1.575}{0.05} = 31.5$.Since $31.5 = 315 \times 10^{-1}$,the value is $315$.

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

Medium

Consider the following single step reaction in gas phase at constant temperature.
$2 \ A_{(g)} + B_{(g)} \rightarrow C_{(g)}$
The initial rate of the reaction is recorded as $r_1$ when the reaction starts with $1.5 \ atm$ pressure of $A$ and $0.7 \ atm$ pressure of $B$. After some time,the rate $r_2$ is recorded when the pressure of $C$ becomes $0.5 \ atm$. The ratio $r_1 : r_2$ is $\qquad$ $\times 10^{-1}$.
(Nearest integer)

JEE MAIN 2024 All JEE MAIN

A
$318$
B
$317$
C
$315$
D
$319$

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Rate law , Rate constant , Order of Reaction and Molecularity

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Pressure $(mm \ Hg)$	$50, 100, 200$
Half-life period $(hrs)$	$3.52, 1.76, 0.88$

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