Problem 35 - Chemistry The Science in Context

Question

Stratospheric Ozone Depletion Chlorine monoxide (C1O) plays a major role in the creation of the ozone holes in the stratosphere over Earth's polar regions. a. If \(\Delta[\mathrm{ClO}] / \Delta t\) at \(298 \mathrm{K}\) is \(-2.3 \times 10^{7} M / \mathrm{s},\) what is the rate of change in \(\left[\mathrm{Cl}_{2}\right]\) and \(\left[\mathrm{O}_{2}\right]\) in the following reaction? $$ 2 \mathrm{ClO}(g) \rightarrow \mathrm{Cl}_{2}(g)+\mathrm{O}_{2}(g) $$ b. If \(\Delta[\mathrm{ClO}] / \Delta t\) is \(-2.9 \times 10^{4} M / s,\) what is the rate of formation of oxygen and \(\mathrm{ClO}_{2}\) in the following reaction? $$ \mathrm{ClO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{ClO}_{2}(g) $$

Step-by-Step Solution

Answer

Question: Determine the rate of change of Cl2 and O2 in the first reaction, and the rate of formation of O2 and ClO2 in the second reaction, given that the rate of change of ClO is -2.3 x 10^7 M/s in the first reaction and -2.9 x 10^4 M/s in the second reaction. Answer: The rate of change of Cl2 and O2 in the first reaction is 1.15 x 10^7 M/s, and the rate of formation of O2 and ClO2 in the second reaction is 2.9 x 10^4 M/s.

Step 1: Identify the balanced chemical equation.

In the first reaction, the balanced chemical equation is: $$ 2 \mathrm{ClO}(g) \rightarrow \mathrm{Cl}_{2}(g)+\mathrm{O}_{2}(g) $$ and for the second reaction, the balanced chemical equation is: $$ \mathrm{ClO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{O}_{2}(g)+\mathrm{ClO}_{2}(g) $$

Step 2: Find rate of change of Cl2 and O2 (#first_react#).

In the first reaction, given the rate of change of ClO: \(\Delta \left[\mathrm{ClO}\right] / \Delta t = -2.3 \times 10^{7} M/s\). Using stoichiometry, we can determine the rate of change of Cl2 and O2: $$ -2\frac{\Delta[\mathrm{ClO}]}{\Delta t} = \frac{\Delta[\mathrm{Cl}_{2}]}{\Delta t} = \frac{\Delta[\mathrm{O}_{2}]}{\Delta t} $$ Now, plug in the given rate of change for ClO and solve for the rate of change of Cl2 and O2: $$ -2\frac{-2.3 \times 10^{7} M/s}{\Delta t} = \frac{\Delta[\mathrm{Cl}_{2}]}{\Delta t} = \frac{\Delta[\mathrm{O}_{2}]}{\Delta t} \rightarrow \frac{\Delta[\mathrm{Cl}_{2}]}{\Delta t} = \frac{\Delta[\mathrm{O}_{2}]}{\Delta t} = 1.15 \times 10^{7} M/s $$ So the rate of change of Cl2 and O2 is \(1.15 \times 10^{7} M/s\).

Step 3: Find the rate of formation of O2 and ClO2 (#second_react#).

In the second reaction, we are given the rate of change of ClO: \(\Delta \left[\mathrm{ClO}\right] / \Delta t = -2.9 \times 10^{4} M/s\). Using stoichiometry, we can determine the rate of formation of O2 and ClO2: $$ -\frac{\Delta[\mathrm{ClO}]}{\Delta t} = \frac{\Delta[\mathrm{O}_{2}]}{\Delta t} = \frac{\Delta[\mathrm{ClO}_{2}]}{\Delta t} $$ Now, plug in the given rate of change for ClO and solve for the rate of formation of O2 and ClO2: $$ -\frac{-2.9 \times 10^{4} M/s}{\Delta t} = \frac{\Delta[\mathrm{O}_{2}]}{\Delta t} = \frac{\Delta[\mathrm{ClO}_{2}]}{\Delta t} \rightarrow \frac{\Delta[\mathrm{O}_{2}]}{\Delta t} = \frac{\Delta[\mathrm{ClO}_{2}]}{\Delta t} = 2.9 \times 10^{4} M/s $$ So the rate of formation of O2 and ClO2 is \(2.9 \times 10^{4} M/s\).

Key Concepts

Understanding Chemical Kinetics

Chemical kinetics is the study of rates at which chemical processes occur, focusing on the factors that influence these rates and how they can be controlled. The degradation of stratospheric ozone involves a series of chemical reactions, where kinetics play a pivotal role.

An integral aspect of chemical kinetics is the reaction rate, which refers to the speed at which reactants are converted into products. For example, in the context of stratospheric ozone depletion, chlorine monoxide (ClO) reacts to form chlorine (Cl₂) and oxygen (O₂), each with its own reaction rate that can be measured and quantified. Understanding how these rates are determined and altered by the concentration of reactants, temperature, and presence of catalysts, allows scientists to predict and mitigate ozone depletion.

Examining Reaction Rate

Reaction rate is a measure of the change in concentration of reactants or products over time in a chemical reaction. In the given example of stratospheric ozone depletion, we measure the rate at which chlorine monoxide (ClO) is reacting. A negative rate of change, as seen with \( -2.3 \times 10^{7} M/s \), indicates that ClO is being consumed in the reaction.

Understanding the reaction rate is critical in environmental chemistry for predicting how quickly harmful reactions occur. Reaction rates are influenced by various factors, such as temperature, which in the case of ozone depletion, varies with altitude and latitude, further affecting the rate at which ozone holes expand.

Applying Stoichiometry to Reaction Rates

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using the coefficients of a balanced equation to connect the rates at which substances react. In the stratospheric ozone depletion scenario, the stoichiometry of the balanced chemical equations allows us to determine the rate of change or formation of other substances based on the rate of change of ClO.

For the reaction \(2 \mathrm{ClO} \rightarrow \mathrm{Cl}_{2} + \mathrm{O}_{2}\), stoichiometry tells us that two moles of ClO produce one mole each of Cl₂ and O₂. By applying the stoichiometric ratios and the given rate of ClO, we can calculate the corresponding rates for Cl₂ and O₂, exemplifying how stoichiometry is crucial for understanding chemical kinetics and reaction rates in real-world problems like ozone layer protection.