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(A) The rate of reaction is defined as the rate of disappearance of reactant divided by its stoichiometric coefficient.For reaction $(a)$: $2N_2O_5 \r

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$k = 2k'$

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(A) The rate of reaction is defined as the rate of disappearance of reactant divided by its stoichiometric coefficient.For reaction $(a)$: $2N_2O_5 \rightarrow 4NO_{2(g)} + O_{2(g)}$Rate $= -\frac{1}{2} \frac{d[N_2O_5]}{dt} = k_{rate}[N_2O_5]$Given $-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$,so Rate $= \frac{k}{2} [N_2O_5]$.For reaction $(b)$: $N_2O_5 \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$Rate $= -\frac{d[N_2O_5]}{dt} = k'_{rate}[N_2O_5]$Given $-\frac{d[N_2O_5]}{dt} = k'[N_2O_5]$,so Rate $= k' [N_2O_5]$.Since the rate of the reaction is the same regardless of how the stoichiometry is written,we equate the rates:$\frac{k}{2} [N_2O_5] = k' [N_2O_5]$$k = 2k'$

For the first order decomposition reaction of $N_2O_5$,it is found that -
$(a)$ $2N_2O_5 \rightarrow 4NO_{2(g)} + O_{2(g)}$ ; $-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$(b)$ $N_2O_5 \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$ ; $-\frac{d[N_2O_5]}{dt} = k'[N_2O_5]$
Which of the following is true?

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For the first order decomposition reaction of $N_2O_5$,it is found that -$(a)$ $2N_2O_5 \rightarrow 4NO_{2(g)} + O_{2(g)}$ ; $-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$$(b)$ $N_2O_5 \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$ ; $-\frac{d[N_2O_5]}{dt} = k'[N_2O_5]$Which of the following is true?