Problem 20 - Chemical Reaction Engineering

Question

Experiment shows that the homogeneous decomposition of ozone proceeds with a rate $$-r_{\mathrm{O}_{3}}=k\left[\mathrm{O}_{3}\right]^{2}\left[\mathrm{O}_{2}\right]^{-1}$$ (a) What is the overall order of reaction? (b) Suggest a two-step mechanism to explain this rate and state how you would further test this mechanism.

Step-by-Step Solution

Answer

The overall order of reaction is 1. A possible two-step mechanism could be the formation of an intermediate from two ozone molecules and its subsequent breakdown. The mechanism can be tested by detecting intermediates, changing reactant concentrations, or introducing a third substance.

Step 1: Determine the Overall Order of Reaction

To find the overall order of the reaction, sum the powers of the concentration terms in the rate expression. The rate is given by the expression \[-r_{\mathrm{O}_{3}}=k\left[\mathrm{O}_{3}\right]^{2}\left[\mathrm{O}_{2}\right]^{-1}\]. Summing the exponents of the reactant concentrations gives the overall order: 2 - 1 = 1.

Step 2: Suggest a Two-Step Mechanism

The mechanism involves proposing two elementary steps that sum up to the overall reaction and produce a rate law consistent with the observed rate. Step 1 might involve the collision between two ozone molecules forming an intermediate species and oxygen: \[\mathrm{O}_3 + \mathrm{O}_3 \rightarrow \mathrm{O}_5 + \mathrm{O}_2 \]. Step 2 could involve the breakdown of the intermediate species into ozone and oxygen: \[\mathrm{O}_5 \rightarrow 2\mathrm{O}_3\].

Step 3: Test the Mechanism

To test this mechanism, conduct experiments to detect the presence of the intermediate species, change the concentrations of ozone or oxygen to see if the rate law changes accordingly, or introduce a third substance that could interact with the intermediate to see if it affects the rate.

Key Concepts

Rate Law Determination

Understanding the rate law determination is essential when studying chemical kinetics, especially in the context of reactions like ozone decomposition. To determine the rate law for a given reaction, one must identify the relationship between the concentration of the reactants and the rate of the reaction. This is expressed mathematically by the rate expression. In our example with ozone, \[ -r_{\mathrm{O}_{3}}=k\left[\mathrm{O}_{3}\right]^{2}\left[\mathrm{O}_{2}\right]^{-1} \], the overall order is calculated by summing the exponents of the concentrations in the rate expression.

For this particular case, the sum of the exponents is 2 (from \(\left[\mathrm{O}_{3}\right]^2\)) minus 1 (from \(\left[\mathrm{O}_{2}\right]^{-1}\)), equating to an overall reaction order of 1. It's fascinating to note that not all reactants need to have a positive exponent; in some cases, like ozone decomposition, a reactant can indeed decrease the reaction rate, represented by a negative exponent.

Reaction Mechanism

The reaction mechanism provides a microscopic view of the steps a chemical reaction undergoes from reactants to products. It consists of a sequence of elementary reactions, each with its own rate law, that make up the overall reaction. Creating a plausible reaction mechanism is akin to solving a puzzle; the pieces must fit together perfectly to match the experimental data, including the rate law.

To explain the rate expression for ozone decomposition, we suggest a two-step mechanism. The first step might involve two ozone molecules colliding and forming an intermediate complex plus the formation of oxygen. In the second step, this intermediate could decay back into ozone and oxygen. Verifying such mechanisms requires experimentation to detect intermediates or changes in reaction rates upon varying reactant concentrations or adding potential inhibitors.

Chemical Kinetics

Chemical kinetics is the study of reaction rates and the factors affecting them. It encompasses everything from rate laws to the mechanisms by which chemical reactions proceed. A cornerstone of this discipline is the understanding that reaction rates are influenced by various factors such as reactant concentrations, temperature, and the presence of a catalyst.

In educational settings, simplifying and breaking down these concepts into digestible pieces allows students to better grasp the idea that not all reactants will necessarily speed up a reaction, which is clearly shown in our ozone example where oxygen's increasing concentration appears to slow the reaction rate according to the negative exponent in the rate law.

Ozone Decomposition

Ozone, or O3, is an essential molecule in Earth's atmosphere that absorbs harmful ultraviolet radiation. The decomposition of ozone in the atmosphere is a natural process, but it's also one of significant environmental concern, especially when accelerated by pollutants.

The rate expression we've discussed illustrates a not-so-simple reaction, where the rate increases with the concentration of ozone squared but decreases with the concentration of oxygen. Enhanced understanding of such reactions can help in forming effective strategies for ozone layer conservation. Furthermore, it showcases how concepts from chemical kinetics interplay to govern real-world chemical processes of great importance.