The reaction $\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}$ is…

The reaction $\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}$ is first order in $\mathrm{N}_{2} \mathrm{O}_{5}$ having rate constant $6 \cdot 2 \times 10^{-4} \mathrm{~s}^{-1} .$ What is the value of rate of reaction when concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$ is $1 \cdot 25 \mathrm{~mol} \mathrm{~L}^{-1}$ ?
  1. $7 \cdot 75 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
  2. $8 \cdot 15 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
  3. $4 \cdot 96 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
  4. $2 \cdot 01 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$

Solution

$\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}$ For first order reaction, $\begin{aligned} \text { Rate } &=\mathrm{k}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] \\ &=6.2 \times 10^{-4} \mathrm{~s}^{-1} \times 1.25 \mathrm{~mol} \mathrm{~L} \end{aligned}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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