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QJEEM24Chaa01: JEE Main 2024 Chemistry - Class 12 JEEM24Chaa01 Solution: Consider the following single step reaction in gas phase at…

Consider the following single step reaction in gas phase at constant temperature.

2 A(g)+B(g)→C(g)2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}

The initial rate of the reaction is recorded as r1\mathrm{r}_1 when the reaction starts with 1.5 atm1.5 \mathrm{~atm} pressure of A\mathrm{A} and 0.7 atm0.7 \mathrm{~atm} pressure of B. After some time, the rate r2r_2 is recorded when the pressure of C becomes 0.5 atm0.5 \mathrm{~atm} . The ratio r1:r2\mathrm{r}_1: \mathrm{r}_2 is _________ ×10−1\times 10^{-1} . (Nearest integer)

Step-by-Step Verified Solution

2 A( g)+B(g)→C(g)2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})

As this is single step reaction,

r=kf[A]2[ B]2\mathrm{r}=\mathrm{k}_{\mathrm{f}}[\mathrm{A}]^2[\mathrm{~B}]^2

amp;2 A( g)+amp;B(g)→amp;C(g)t=0amp;1.5amp;0.7amp;0t=t′amp;1.5−2xamp;0.7−xamp;x\begin{array}{lllll} & 2 \mathrm{~A}(\mathrm{~g})+ & \mathrm{B}(\mathrm{g}) \rightarrow & \mathrm{C}(\mathrm{g}) \\\mathrm{t}=0 & 1.5 & 0.7 & 0 \\\mathrm{t}=\mathrm{t}^{\prime} & 1.5-2 \mathrm{x} \quad & 0.7-\mathrm{x} & \mathrm{x}\end{array}

amp;⇒x=0.5 atmamp;r1=kf(1.5)2(0.7)amp;r2=kf(0.5)2(0.2)amp;r1r2=9×72=31.5amp;=315×10−1\begin{aligned}& \Rightarrow x=0.5 \mathrm{~atm} \\& \mathrm{r}_1=\mathrm{k}_{\mathrm{f}}(1.5)^2(0.7) \\& \mathrm{r}_2=\mathrm{k}_{\mathrm{f}}(0.5)^2(0.2) \\& \frac{r_1}{r_2}=\frac{9 \times 7}{2}=31.5 \\& =315 \times 10^{-1}\end{aligned}

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