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NEET 2011
Exam
NEET
Year
2011
Subject
Chemistry
Chapter
Chemical Kinetics

NEET 2011 · Chemistry · Chemical Kinetics

The rate of reaction 2 ~N_2 O_5 4 NO_2+O_2 can be written in three...

The rate of reaction 2 N2O5⟶4NO2+O22 \mathrm{~N}_2 \mathrm{O}_5 \longrightarrow 4 \mathrm{NO}_2+\mathrm{O}_2 can be written in three ways −d[ N2O5]dt=k[ N2O5]d[NO2]dt=k′[N2O5]d[O2]dt=k′′[N2O5]\begin{aligned} \frac{-d\left[\mathrm{~N}_2 \mathrm{O}_5\right]}{d t} & =k\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\ \frac{d\left[\mathrm{NO}_2\right]}{d t} & =k^{\prime}\left[\mathrm{N}_2 \mathrm{O}_5\right] \\ \frac{d\left[\mathrm{O}_2\right]}{d t} & =k^{\prime \prime}\left[\mathrm{N}_2 \mathrm{O}_5\right] \end{aligned} The relationship between kandk′k and k^{\prime} and between kandk′′k and k^{\prime \prime} are

Options

  1. Ak′=2k;k′=kk^{\prime}=2 k ; k^{\prime}=k
  2. Bk′=2k;k′′=k/2k^{\prime}=2 k ; k^{\prime \prime}=k / 2
  3. Ck′=2k;k′′=2kk^{\prime}=2 k ; k^{\prime \prime}=2 k
  4. Dk′=k;k′′=kk^{\prime}=k ; k^{\prime \prime}=k

Correct answer

B. k′=2k;k′′=k/2k^{\prime}=2 k ; k^{\prime \prime}=k / 2

Step-by-step solution

\begin{aligned}& \text{ Rate }=-\frac{1}{2} \frac{d\left[\mathrm{~N}_2 \mathrm{O}_5\right]}{d t}=\frac{1}{4} \frac{d\left[\mathrm{NO}_2\right]}{d t}=\frac{d\left[\mathrm{O}_2\right]}{d t}\\ & \Rightarrow \frac{1}{2}k\left[\mathrm{~N}}_{2} \mathrm{O}}_{5}\right]=\frac{1}{4}k^{\prime}\left[\mathrm{N}}_{2} \mathrm{O}}_{5}\right]=k^{\prime \prime}\left[\mathrm{N}}_{2} \mathrm{O}}_{5}\right] \end{aligned} ⇒k2=k′4=k′′∴k′=2k;k′′=k2\begin{array}{llrl} \Rightarrow& \frac{k}{2}& =\frac{k^{\prime}}{4}=k^{\prime \prime} \\ & \therefore & k^{\prime} & =2 k ; k^{\prime \prime}=\frac{k}{2} \end{array}
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