$\begin{array}{1 1} 1.73 \times 10^{-5} s^{-1} \\ 3.46 \times 10^{-5} s^{-1} \\ 0.865 \times 10^{-5} s^{-1} \\ 5.12 \times 10^{-5} s^{-1} \end{array}$

Answer: $1.73 \times 10^{-5} s^{-1}$

Given $2\; N_2O_5\; (g) \rightarrow 4 NO_2\;(g) + O_2\;(g)$

We can equate a dimensionless ratio of two rates to a rate law with an as yet an undetermined order, as follows:

$\Rightarrow \large\frac{5.45 \times 10^{-5}} { 1.35 \times 10%{-5}}$$ = \large\frac{3.15^a}{0.78^a}$

$\Rightarrow 4.037 = 4.039^a \rightarrow a \approx 1$

Now that the order is found to be $ = 1$, we can find the rate constant as $\large\frac{5.45\times10^{-5}}{3.15} $$ =1.73 \times 10^{-5} s^{-1}$

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