Problem 36 - Chemistry: An Atoms-Focused Approach

Question

The chemistry of smog formation includes \(\mathrm{NO}_{3}\) as an intermediate in several reactions. a. If \(\Delta\left[\mathrm{NO}_{3}\right] / \Delta t=-2.2 \times 10^{5} \mathrm{m} M / \mathrm{min}\) in the following reaction, what is the rate of formation of \(\mathrm{NO}_{2} ?\) $$\mathrm{NO}_{3}(g)+\mathrm{NO}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ b. What is the rate of change of \(\left[\mathrm{NO}_{2}\right]\) in the following$$ \begin{array}{l} \text { reaction if } \Delta\left[\mathrm{NO}_{3}\right] / \Delta t=-2.3 \mathrm{mM} / \mathrm{min} \text { ? } \\ \qquad 2 \mathrm{NO}_{3}(g) \rightarrow 2 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \end{array}$$

Step-by-Step Solution

Answer

Answer: The rate of formation of NO₂ for reaction 1 is 1.1 x 10^5 mM/min, and the rate of formation of NO₂ for reaction 2 is 1.15 mM/min.

Step 1: a. Rate of formation of \(\mathrm{NO}_{2}\) for reaction 1

For reaction 1, the stoichiometry is as follows: $$\mathrm{NO}_{3}(g)+\mathrm{NO}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ The relationship between the rate of change of \(\mathrm{NO}_{3}\) and the rate of change of \(\mathrm{NO}_{2}\) is: $$\frac{-\Delta\left[\mathrm{NO}_{3}\right]}{\Delta t} = 2 \frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t}$$We are given that \(\Delta\left[\mathrm{NO}_{3}\right]/\Delta t=-2.2\times 10^{5}mM/min\). Plug this into the equation and solve for \(\Delta\left[\mathrm{NO}_{2}\right] / \Delta t\): $$2\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t} = -\left(-2.2\times 10^{5} \mathrm{mM} / \mathrm{min}\right)$$ $$\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t} = \frac{2.2\times 10^{5}\mathrm{mM} / \mathrm{min}}{2}$$

Step 2: a. Solution for reaction 1

Divide by 2 to get the rate of formation of \(\mathrm{NO}_{2}\): $$\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t} = 1.1\times 10^{5} \mathrm{mM} / \mathrm{min}$$

Step 3: b. Rate of change of \(\mathrm{NO}_{2}\) for reaction 2

For reaction 2, the stoichiometry is as follows: $$2 \mathrm{NO}_{3}(g) \rightarrow 2 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ The relationship between the rate of change of \(\mathrm{NO}_{3}\) and the rate of change of \(\mathrm{NO}_{2}\) is: $$\frac{-\Delta\left[\mathrm{NO}_{3}\right]}{2\Delta t} = \frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t}$$We are given that \(\Delta\left[\mathrm{NO}_{3}\right]/\Delta t=-2.3mM/min\). Plug this into the equation and solve for \(\Delta\left[\mathrm{NO}_{2}\right] / \Delta t\): $$\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t} = -\frac{1}{2}\left(-2.3 \mathrm{mM} / \mathrm{min}\right)$$

Step 4: b. Solution for reaction 2

Multiply -2.3 by -1/2 to get the rate of change of \(\mathrm{NO}_{2}\): $$\frac{\Delta\left[\mathrm{NO}_{2}\right]}{\Delta t} = 1.15 \mathrm{mM} / \mathrm{min}$$ In summary, the rate of formation of \(\mathrm{NO}_{2}\) for reaction 1 is \(1.1\times 10^{5} \mathrm{mM} / \mathrm{min}\), and the rate of change of \(\left[\mathrm{NO}_{2}\right]\) for reaction 2 is \(1.15 \mathrm{mM} / \mathrm{min}\).

Key Concepts

Smog Formation

Smog is an air pollution phenomenon that results in a captivating yet detrimental haze, often seen in urban environments. Its formation involves complex chemical reactions. One of the key players in smog chemistry is nitrogen dioxide ( NO_2 ), which forms part of the nitrogen oxides family. In the atmosphere, sunlight interacts with nitrogen oxides and volatile organic compounds (VOCs), leading to smog. Nitrogen dioxide reacts with other chemicals in the atmosphere, largely contributing to the formation of secondary pollutants, including ozone. The increased concentration of ozone is harmful, affecting respiratory health and the environment.

• Smog is primarily photochemical, requiring sunlight to catalyze reactions.
• Major components: Nitrogen oxides ( NO_x ), VOCs, and secondary pollutants like ozone.
• Impacts: Health issues, environmental damage, and reduced visibility.

Understanding the kinetics of reactions that form smog helps to develop strategies for pollution control and prevention.

Rate of Reaction

Rate of reaction is a vital concept in chemistry, which describes how fast or slow a reaction proceeds. It is quantified by the change in concentration of reactants or products over time. In smog formation chemistry, the rate of formation of nitrogen dioxide (NO_2) is particularly interesting because it is a precursor to photochemical smog. Several factors, such as temperature, concentration, and the presence of catalysts, can influence the reaction rate.

• Expressed as \(\frac{\Delta \text{[Product]}}{\Delta t}\) or \(\frac{-\Delta \text{[Reactant]}}{\Delta t}\).
• Can be controlled for pollution management by reducing reactant availability (e.g., reducing NO_x emissions).

In the exercise, the rate of reaction is calculated using changes in concentration over a given time frame, highlighting the dynamic aspects of atmospheric reactions.

Stoichiometry

Stoichiometry in reactions, like those involved in smog formation, is crucial for understanding the relationship between reactants and products. It involves using coefficients in chemical equations to predict the amounts of substances consumed or produced. In the given reactions:1. \(\text{NO}_3 (g) + \text{NO} (g) \rightarrow 2 \text{NO}_2 (g)\)2. \(2 \text{NO}_3 (g) \rightarrow 2 \text{NO}_2 (g) + \text{O}_2 (g)\)The coefficients tell us how much NO_2 is produced from the reaction of NO_3 .

• The first reaction has a 1:2 ratio of NO_3 to NO_2.
• The second reaction emphasizes a stoichiometric balance with equal parts of NO_3 and NO_2produced.

By using stoichiometry, one can determine the expected concentration of products, which is crucial for predicting and controlling atmospheric chemistry outcomes.

Nitrogen Oxides

Nitrogen oxides ( NO_x ) are significant compounds in atmospheric chemistry. They primarily consist of nitric oxide ( NO ) and nitrogen dioxide ( NO_2 ). These gases play a critical role in environmental and health issues as they are involved in processes leading to smog and acid rain.

• Natural sources include soil emissions, lightning, and biological decay.
• Major anthropogenic sources include vehicle exhausts and industrial emissions.
• React to form secondary pollutants such as ozone ( O_3 ) and nitric acid ( HNO_3 ).

Nitrogen oxides catalyze reactions that degrade air quality. By understanding their role in the atmosphere, regulations can be designed to limit emissions, improving both environmental and public health. Effective strategies include promoting cleaner fuel alternatives and advancing vehicle emission technologies.