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Chemistry · 2023 · 2 marks
CBSE 2023 · Region 4 · Set 1 · Q22
The rate constant for the first order decomposition of N_2 O_5 is given by the following equation: log k =23 · 6-(2 × 10^4 K)/T Calculate E_a for…
The rate constant for the first order decomposition of $\displaystyle \mathrm{N}_{2} \mathrm{O}_{5}$ is given by the following equation : \[\log \mathrm{k}=23 \cdot 6-\frac{2 \times 10^{4} \mathrm{~K}}{\mathrm{~T}} \] Calculate $\displaystyle \mathrm{E}_{\mathrm{a}}$ for this reaction. \[\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right] \]
Marking-scheme solution
$$\log k = \log A - \frac{E_a}{2\cdot303\ RT}$$$$-\frac{E_a}{2\cdot303\ R} = -2 \times 10^{4}\ \mathrm{K}$$$$E_a = 2\cdot303 \times 8\cdot314\ \mathrm{J\ K^{-1}\ mol^{-1}} \times 2 \times 10^{4}\ \mathrm{K}$$$$E_a = 3.830 \times 10^{5}\ \mathrm{J\ mol^{-1}}$$
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