Question

\(2\mathrm{NO(g)} + \mathrm{Cl_2(g)} \rightleftharpoons 2\mathrm{NOCl(s)}\)
This reaction was studied at \(-10^\circ\) and the following data was obtained

Run	\([\mathrm{NO}]_0\)	\([\mathrm{Cl_2}]_0\)	\(r_0\)
1	0.10	0.10	0.18
2	0.10	0.20	0.35
3	0.20	0.20	1.40

\([\mathrm{NO}]_0\) and \([\mathrm{Cl_2}]_0\) are the initial concentrations and \(r_0\) is the initial reaction rate.
The overall order of the reaction is __________. (Round off to the Nearest Integer).

Hint:

Use the method of initial rates: vary one concentration at a time to find the order with respect to each reactant, then add them.

Answer 1

Correct Answer: 3

Let rate \(= k[\mathrm{NO}]^m[\mathrm{Cl_2}]^n\).
Runs 1 and 2: \([\mathrm{NO}]\) is constant and \([\mathrm{Cl_2}]\) doubles; \(\frac{r_2}{r_1} = \frac{0.35}{0.18} \approx 1.94 \approx 2 = 2^n\), so \(n = 1\).
Runs 2 and 3: \([\mathrm{Cl_2}]\) is constant and \([\mathrm{NO}]\) doubles; \(\frac{r_3}{r_2} = \frac{1.40}{0.35} = 4 = 2^m\), so \(m = 2\).
Overall order \(= m + n = 2 + 1 = 3\).
Answer: 3