Question

$2NO\left(g\right)+C{l}_2\left(g\right)\rightleftharpoons 2NOCl\left(s\right)$

This reaction was studied at $-{10}^{\circ }C$ and the following data was obtained

$\begin{array}{cccc}run& [NO{]}_0& [C{l}_2{]}_0& r_0\\ 1& 0.10& 0.10& 0.18\\ 2& 0.10& 0.20& 0.35\\ 3& 0.20& 0.20& 1.40\end{array}$

$\left[NO{]}_{0}and\right[C{l}_2{]}_0$ are the initial concentration and $r_0$ is the initial reaction rate.

The overall order of the reaction is _______.

(Round off to the Nearest Integer)

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Answer 1

$Rate\left(r\right)=k\left[NO{]}^x\right[C{I}_2{]}^y$

From run (2) and (3)

$\frac{(r_0{)}_3}{(r_0{)}_2}=\frac{\left(0.20{)}^x\right(0.20{)}^y}{\left(0.10{)}^x\right(0.20{)}^y}$

$\Rightarrow 2^x=\frac{1.40}{0.35}=2^2$

$\therefore x=2$

From run (1) and (2)

$\frac{(r_0{)}_2}{(r_0{)}_1}=\frac{\left(0.10{)}^x\right(0.20{)}^y}{\left(0.10{)}^x\right(0.10{)}^y}$

$\frac{0.35}{0.18}=2^y$
$2=2^y$
$\Rightarrow y=1$

$\therefore r=k\left[NO{]}^2\right[C{l}_2{]}^1$

$\therefore \text{Overall order of reaction}=2+1=3$