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The rate of the reaction \( 2 \mathrm{~N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2} \) can be written in three ways :
\( \frac{-\mathrm{d}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]}{\mathrm{dt}}=\mathrm{k}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] \)
\( \frac{\mathrm{d}\left[\mathrm{NO}_{2}\right]}{\mathrm{dt}}=\mathrm{k}^{\prime}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] \)
\( \frac{\mathrm{d}\left[\mathrm{O}_{2}\right]}{\mathrm{dt}}=\mathrm{k}^{\prime \prime}\left[\mathrm{N}_{2} \mathrm{O}_{5}\right] \)
The relationship between \( \mathrm{k} \) and \( \mathrm{k}^{\prime} \) and between \( \mathrm{k} \) and \( \mathrm{k}^{\prime \prime} \) are:
(a) \( \mathrm{k}^{\prime}=2 \mathrm{k} ; \mathrm{k}^{\prime}=\mathrm{k} \)
(b) \( \mathrm{k}^{\prime}=2 \mathrm{k} ; \mathrm{k}^{\prime \prime}=\mathrm{k} / 2 \)
(c) \( \mathrm{k}^{\prime}=2 \mathrm{k} ; \mathrm{k}^{\prime \prime}=2 \mathrm{k} \)
(d) \( \mathrm{k}^{\prime}=\mathrm{k} ; \mathrm{k}^{\prime \prime}=\mathrm{k} \)
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