Question

$2\mathrm{NO}\left(\mathrm{g}\right)+\mathrm{Cl}\left(\mathrm{g}\right)\to 2\mathrm{NOCl}\left(\mathrm{s}\right):$ This reaction was studied at$–10°\mathrm{C}$ and the following data was obtained.

${\left[\mathrm{NO}\right]}_0$ and ${\left[{\mathrm{Cl}}_2\right]}_0$ are the initial concentrations and ${\mathrm{r}}_0$ is the initial reaction rate. The overall order of the reaction is _________. (Round off to the Nearest Integer).

Answer 1

The above question can be solved as:

Step 1:

$$\begin{gathered} \mathrm{Exp}.\left(\mathrm{I}\right)0.18=\mathrm{K}(0.1)\mathrm{x}(0.1)+\mathrm{y}\dots .\left(1\right) \\ \mathrm{Exp}.\left(\mathrm{II}\right)0.35=\mathrm{K}(0.1)\mathrm{x}(0.2)\mathrm{y}\dots .\left(2\right) \\ \mathrm{Exp}.\left(\mathrm{III}\right)1.40=\mathrm{K}(0.2)\mathrm{x}(0.2)\mathrm{y}\dots .\left(3\right) \end{gathered}$$

Step 2:

$$\begin{gathered} \left(2\right)÷\left(3\right) \\ \frac{0.35}{1.40}=\frac{\mathrm{K}\times {(0.1)}^{\mathrm{x}}{(0.2)}^{\mathrm{y}}}{\mathrm{K}{(0.2)}^{\mathrm{x}}{(0.2)}^{\mathrm{y}}} \\ 0.25={(0.5)}^{\mathrm{x}} \\ {(0.5)}^2={(0.5)}^{\mathrm{x}} \\ \mathrm{x}=2 \end{gathered}$$

Step 3: Similarly,

$$\begin{gathered} \left(1\right)÷\left(2\right) \\ \frac{1}{2}={\left(\frac{1}{2}\right)}^{\mathrm{y}} \\ \Rightarrow \mathrm{y}=1 \end{gathered}$$

Step 4: Order of the reaction $$\begin{gathered} =2+1 \\ =3 \end{gathered}$$

Therefore, the overall order of reaction is $3$.