Problem 66 - Chemistry and Chemical Reactivity

Question

Hundreds of different reactions can occur in the stratosphere, among them reactions that destroy the earth's ozone layer. The table below lists several (secondorder) reactions of Cl atoms with ozone and organic compounds; each is given with its rate constant. $$\begin{array}{ll}\text { Reaction } & \left(298 \mathrm{K}, \mathrm{cm}^{3} / \mathrm{molecule} \cdot \mathrm{s}\right) \\\\\hline \text { (a) } \mathrm{Cl}+\mathrm{O}_{3} \rightarrow \mathrm{ClO}+\mathrm{O}_{2} & 1.2 \times 10^{-11} \\\\\text {(b) } \mathrm{Cl}+\mathrm{CH}_{4} \rightarrow \mathrm{HCl}+\mathrm{CH}_{3} & 1.0 \times 10^{-13} \\\\\text {(c) } \mathrm{Cl}+\mathrm{C}_{3} \mathrm{H}_{8} \rightarrow \mathrm{HCl}+\mathrm{C}_{3} \mathrm{H}_{7} & 1.4 \times 10^{-10} \\\\\text {(d) } \mathrm{Cl}+\mathrm{CH}_{2} \mathrm{FCl} \rightarrow \mathrm{HCl}+\mathrm{CHFCl} &3.0 \times 10^{-18} \\\\\hline\end{array}$$ For equal concentrations of Cl and the other reactant, which is the slowest reaction? Which is the fastest reaction?

Step-by-Step Solution

Answer

Slowest: Reaction d; Fastest: Reaction c.

Step 1: Understanding Rate Constants

Rate constants are measures of how quickly a reaction proceeds. A larger rate constant indicates a faster reaction, while a smaller rate constant indicates a slower reaction.

Step 2: Identifying Reactions and Rate Constants

We have four reactions listed with their rate constants:- Reaction (a): \( k = 1.2 \times 10^{-11} \)- Reaction (b): \( k = 1.0 \times 10^{-13} \)- Reaction (c): \( k = 1.4 \times 10^{-10} \)- Reaction (d): \( k = 3.0 \times 10^{-18} \)

Step 3: Comparing Rate Constants

To identify the slowest reaction, we find the reaction with the smallest rate constant. Conversely, the fastest reaction will have the largest rate constant.

Step 4: Determining the Slowest Reaction

By comparing the rate constants, the slowest reaction is reaction (d) since \(3.0 \times 10^{-18}\) is the smallest value.

Step 5: Determining the Fastest Reaction

By comparing the rate constants, the fastest reaction is reaction (c) since \(1.4 \times 10^{-10}\) is the largest value.

Key Concepts

Ozone Layer Destruction

The ozone layer is a crucial shield in Earth's stratosphere, protecting life by absorbing the majority of the sun's ultraviolet radiation. However, certain chemical reactions, especially involving chlorine (Cl) atoms, can lead to the destruction of ozone molecules (O extsubscript{3}). This destruction process is primarily driven by reactions where Cl atoms act as catalysts, breaking down ozone into molecular oxygen, leading to less protection against UV radiation.
These destructive reactions occur in various steps and often involve intermediate species like chlorine monoxide (ClO). Keeping the ozone layer intact is vital because increased UV exposure can lead to health issues like skin cancer and cataracts and affect ecosystems negatively.
Addressing the chemical reactions responsible for ozone depletion is key to ensuring the longevity of this protective layer.

Rate Constants

Rate constants are integral in understanding how fast a chemical reaction occurs. They are unique for each reaction, dependent on factors such as temperature and the nature of the reactants. In chemical kinetics, a large rate constant indicates that the reaction occurs quickly, while a small rate constant means the reaction proceeds more slowly.
The units of rate constants vary based on the order of the reaction. For the second-order reactions discussed here, the units are typically cm extsuperscript{3}/molecule·s. This unit signifies that the rate of reaction depends on the concentration of two reactant molecules interacting with each other.

• Reaction (a): Cl + O extsubscript{3} with a rate constant of 1.2 × 10 extsuperscript{-11}
• Reaction (b): Cl + CH extsubscript{4} with a rate constant of 1.0 × 10 extsuperscript{-13}
• Reaction (c): Cl + C extsubscript{3}H extsubscript{8} with a rate constant of 1.4 × 10 extsuperscript{-10}
• Reaction (d): Cl + CH extsubscript{2}FCl with a rate constant of 3.0 × 10 extsuperscript{-18}

By comparing these values, we can quickly understand which reactions in the stratosphere are more likely to proceed faster than others.

Stratosphere Reactions

The stratosphere is a layer of Earth's atmosphere situated above the troposphere and characterized by its relative stability and higher concentration of ozone compared to other atmospheric layers. Chemical reactions occurring here are crucial as they can have significant impacts on the climate and air quality.
Among these reactions, those involving chlorine atoms are particularly concerning due to their role in ozone depletion. Chlorine can originate from man-made compounds like Chlorofluorocarbons (CFCs), which release chlorine atoms when broken down by UV light.
Once introduced into the stratosphere, chlorine engages in reactions with ozone and other molecules, leading to ozone layer thinning. Due to the stable conditions in the stratosphere, chemical species can persist for longer periods, allowing these reactions to impact ozone concentrations significantly.

Second-Order Reactions

Second-order reactions are chemical processes where the rate of reaction depends on the concentration of two reactants. The general form of the rate law for such reactions is expressed as:\[ \text{Rate} = k [A][B] \]Here, \(A\) and \(B\) represent the concentrations of the two reactants, and \(k\) is the second-order rate constant.

• If the concentrations of these reactants increase, the rate of the reaction also increases. This direct relationship is due to the increased probability of collision between the reactant molecules.
• In the context of the ozone layer, second-order reactions involving chlorine and ozone are pivotal. These reactions convert ozone to molecular oxygen, exacerbating ozone layer depletion.
• Understanding these reactions' order helps scientists predict how changes in atmospheric conditions might alter reaction rates, impacting the atmosphere's chemical balance.

Recognizing the order of reaction is also crucial in developing strategies to mitigate their environmental impacts.