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Consider the reaction between chlorine and nitric oxide ${Cl}_{2} (g) + 2 NO (g) \to 2 NOCl (g)$
On doubling the concentration of both reactants, the rate of the reaction increases by a factor of 8 however, if only the concentration of $C l_{2}$ is doubled, the rate increases by a factor of 2. The order of this reaction with respect to NO is :

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answer is C.

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Detailed Solution

Order w.r.t $C l_{2}$

$\begin{array}{l} C^{n} \propto rate \\ 2^{x} = 2 \\ x = 1 \end{array}$

Order W.r.t $N O$ and $C l_{2}$

$\begin{array}{l} C^{n} \propto rate \\ 2^{x} . 2^{y} = 8 \\ 2^{x} . 2^{y} = 2^{3} \\ x + y = 3 \\ but x = 1 \\ ∴ y = 2 \end{array}$

Order W.r.t. NO = 2

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