The three experimental data for determining the differential rate of reaction $Cl_{2(g)} + 2NO_{(g)} \rightarrow 2NOCl_{(g)}$ at $310 \ K$ temperature are provided. $(a)$ Derive the differential rate of reaction. $(b)$ Calculate the order of reaction. $(c)$ Calculate the value of the rate constant.

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(N/A) The differential rate expression is given by: $-\frac{d[Cl_2]}{dt} = -\frac{1}{2}\frac{d[NO]}{dt} = k[NO]^2[Cl_2]^1$.
$(b)$ The order of reaction is the sum of the powers of the concentration terms in the rate law: $2 + 1 = 3$.
$(c)$ Based on the experimental data provided for the reaction,the rate constant $k$ is calculated as $175 \ L^2 \ mol^{-2} \ s^{-1}$.

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