Question

Consider the reaction: \[ 4\,\text{NO}_2(g) + \text{O}_2(g) \rightarrow 2\,\text{N}_2\text{O}_5(g) \] In an experiment, the rate of disappearance of O\(_2\) is \(0.24\,\text{mol L}^{-1}\text{s}^{-1}\). Calculate: (i) the rate of disappearance of NO\(_2\) and (ii) the rate of formation of N\(_2\)O\(_5\).

Hint:

Rates of reactions are related to stoichiometric coefficients. Multiply the given rate by the ratio of coefficients to find rates of other species.

Answer 1

Step 1: Write the stoichiometric rate relation for the reaction: \[ -\frac{1}{4}\frac{d[\text{NO}_2]}{dt} = -\frac{1}{1}\frac{d[\text{O}_2]}{dt} = \frac{1}{2}\frac{d[\text{N}_2\text{O}_5]}{dt} \]
Step 2: Given rate of disappearance of oxygen: \[ -\frac{d[\text{O}_2]}{dt} = 0.24\,\text{mol L}^{-1}\text{s}^{-1} \]
Step 3: Calculate rate of disappearance of NO\(_2\): \[ -\frac{d[\text{NO}_2]}{dt} = 4 \times 0.24 = 0.96\,\text{mol L}^{-1}\text{s}^{-1} \]
Step 4: Calculate rate of formation of N\(_2\)O\(_5\): \[ \frac{d[\text{N}_2\text{O}_5]}{dt} = 2 \times 0.24 = 0.48\,\text{mol L}^{-1}\text{s}^{-1} \]