For the gaseous reaction, N_2 O_5 arrow 2 NO_2+1/2 O_2 the rate can be expressed as -(d [N_2 O_5 ])/dt=K_1 [~N_2 O_5 ] +(d [NO_2 ])/dt=K_2 [~N_2 O_5 ] +(d [O_2 ])/dt=K_3 [~N_2 O_5 ] The correct relation between K_1, ~K_2 and K_3 is

Correct answer: (B) 2 ~K_1=K_2=4 ~K_3. N_2 O_5 arrow 2 NO_2+1/2 O_2 Rate of reaction =-(d [N_2 O_5 ])/dt=1/2 (~d [NO_2 ])/dt=2 (~d [O_2 ])/dt ∴ K_1 [~N_2 O_5 ]=1/2 ~K_2 [~N_2 O_5 ]=2 ~K_3 [~N_2 O_5 ] ∴ 2 ~K_1=K_2=4 ~K_3

Q24 / 160 · TS EAMCET 2024 (11 May Shift 1) · Chemistry

For the gaseous reaction, $\mathrm{N}_2 \mathrm{O}_5 \rightarrow 2 \mathrm{NO}_2+\frac{1}{2} \mathrm{O}_2$ the rate can be expressed as $\begin{aligned} & -\frac{\mathrm{d}\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\mathrm{dt}}=\mathrm{K}_1\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\ & +\frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=\mathrm{K}_2\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\ & +\frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}}=\mathrm{K}_3\left[\mathrm{~N}_2 \mathrm{O}_5\right]\end{aligned}$ The correct relation between $\mathrm{K}_1, \mathrm{~K}_2$ and $\mathrm{K}_3$ is

A
$\mathrm{K}_1=2 \mathrm{~K}_2=4 \mathrm{~K}_3$
Correct answer
B
$2 \mathrm{~K}_1=\mathrm{K}_2=4 \mathrm{~K}_3$
C
$2 \mathrm{~K}_1=3 \mathrm{~K}_2=4 \mathrm{~K}_3$
D
$4 \mathrm{~K}_1=2 \mathrm{~K}_2=\mathrm{K}_3$

Solution

$\begin{aligned} & \text { } \mathrm{N}_2 \mathrm{O}_5 \rightarrow 2 \mathrm{NO}_2+\frac{1}{2} \mathrm{O}_2 \\ & \text { Rate of reaction }=-\frac{\mathrm{d}\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{~d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=2 \frac{\mathrm{~d}\left[\mathrm{O}_2\right]}{\mathrm{dt}} \\ & \therefore \quad \mathrm{K}_1\left[\mathrm{~N}_2 \mathrm{O}_5\right]=\frac{1}{2} \mathrm{~K}_2\left[\mathrm{~N}_2 \mathrm{O}_5\right]=2 \mathrm{~K}_3\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\ & \therefore 2 \mathrm{~K}_1=\mathrm{K}_2=4 \mathrm{~K}_3\end{aligned}$

Hence, the correct answer is option: 'B'.

Solution

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