Problem 139 - Introductory Chemistry Atoms First

Question

Consider the decomposition of ozone \(\left(\mathrm{O}_{3}\right)\) to oxygen \(\left(\mathrm{O}_{2}\right)\) \(2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)\) The rate law for this reaction is: Rate \(=k\left[\mathrm{O}_{3}\right]^{2} /\left[\mathrm{O}_{2}\right] .\) How is the rate of this reaction affected by the concentration of oxygen?

Step-by-Step Solution

Answer

The rate of the decomposition of ozone to oxygen is affected by the concentration of oxygen according to the rate law: \( Rate = k[\mathrm{O}_3]^2 / [\mathrm{O}_2] \). An increase in oxygen concentration will lead to a decrease in the reaction rate, while a decrease in oxygen concentration will result in an increase in the rate of the reaction.

Step 1: 1. Understand the rate law equation

The rate law equation for this reaction is given as: Rate \(= k\left[\mathrm{O}_{3}\right]^2/\left[\mathrm{O}_{2}\right] .\) where \(k\) is the rate constant, \([\mathrm{O}_{3}]\) is the concentration of ozone and \([\mathrm{O}_{2}]\) is the concentration of oxygen.

Step 2: 2. Analyze the effect of increasing oxygen concentration

According to the rate law, the rate of the reaction depends inversely on the concentration of oxygen. This means that as the concentration of oxygen increases, the rate of the reaction decreases.

Step 3: 3. Analyze the effect of decreasing oxygen concentration

Similarly, if the concentration of oxygen decreases, the denominator in the rate law equation becomes smaller, resulting in an increased rate of the reaction.

Step 4: 4. Conclusion

The rate of the decomposition of ozone to oxygen is affected by the concentration of oxygen. An increase in oxygen concentration will lead to a decrease in the reaction rate, while a decrease in oxygen concentration will result in an increase in the rate of the reaction.

Key Concepts

Chemical Kinetics

Chemical kinetics is a study that focuses on the speed or rate at which chemical reactions occur and the factors that influence this rate. Understanding chemical kinetics is essential for controlling reactions in various industries and laboratory settings. The rate of a chemical reaction can depend on various factors such as temperature, pressure, and the presence of catalysts. However, one critical aspect that plays a significant role in chemical kinetics is the concentration of reactants. According to the law of mass action, the rate of a reaction is proportional to the product of the concentrations of the reactants, each raised to a power that is equal to the stoichiometric coefficient in the balanced chemical equation.

Ozone Decomposition

The decomposition of ozone into oxygen is a fundamental reaction in the study of environmental chemistry, particularly in understanding the ozone layer's behavior and the implications of ozone-depleting substances. Ozone (O3) is an allotrope of oxygen and plays a vital role in blocking harmful ultraviolet radiation from the sun. Its decomposition is an example of a chemical reaction that can be studied using the concepts of kinetics. By understanding the decomposition reaction's rate law, it is possible to draw conclusions about how different conditions, such as the concentration of reactants and products, affect the reaction rate.

Rate Constant

The rate constant, denoted by the symbol 'k', is a proportionality constant in the rate law expression of a chemical reaction. It is a quantitative measure of the speed of the reaction and is influenced by the temperature and presence of catalysts, though it is independent of the concentrations of reactants and products. In the context of ozone decomposition, the rate constant connects the rate of the reaction with the concentrations of ozone and oxygen. This constant can only be determined experimentally and remains consistent for a particular reaction at a constant temperature.

Concentration Effects

Concentration effects are a critical part of chemical kinetics, as they directly impact reaction rates. For any given chemical reaction, the rate law expression indicates how the rate of reaction is affected by the concentration of reactants and products. In the case of ozone decomposition, as the exercise suggests, the rate law formula shows an inverse relationship between the reaction rate and the concentration of oxygen. This means that higher oxygen levels will cause the reaction rate to decrease, and vice versa. It is essential to understand that the concentration of reactants and products can have significantly different effects on the reaction rate depending on the overall kinetics and rate law of the specific chemical process.