Problem 76 - 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 (second-order) reactions of Cl atoms with ozone and organic compounds; each is given with its rate constant. $$\begin{array}{ll}\hline & \text { Rate Constant } \\\\\text { Reaction } & \left(298 \mathrm{K}, \mathrm{cm}^{3} / \mathrm{molecule} \cdot \mathrm{s}\right) \\\\\hline \text { (a) } \mathrm{Cl}+0_{3} \longrightarrow \mathrm{Cl} 0+0_{2} & 1.2 \times 10^{-11} \\\\\text {(b) } \mathrm{Cl}+\mathrm{CH}_{4} \longrightarrow\mathrm{HCl}+\mathrm{CH}_{3} & 1.0 \times 10^{-13} \\\\\text {(c) } \mathrm{Cl}+\mathrm{C}_{3} \mathrm{H}_{8} \longrightarrow\mathrm{HCl}+\mathrm{C}_{3} \mathrm{H}_{7} & 1.4 \times 10^{-10} \\\\\text {(d) } \mathrm{Cl}+\mathrm{CH}_{2} \mathrm{FCl} \longrightarrow\mathrm{HCl}+\mathrm{CHFCl} & 3.0 \times 10^{-18} \\\\\hline\end{array}$$ For equal concentrations of Cl and the other reactant, which is the slowest reaction? Which is the fastest reaction?

Step-by-Step Solution

Answer

The slowest reaction is (d), and the fastest reaction is (c).

Step 1: Identify the Rate Constant for Each Reaction

We are given the rate constants for each of the reactions in the table. They are:(a) \(1.2 \times 10^{-11}\)(b) \(1.0 \times 10^{-13}\)(c) \(1.4 \times 10^{-10}\)(d) \(3.0 \times 10^{-18}\)We need to compare these rate constants to determine which reaction is the slowest and which is the fastest.

Step 2: Determine the Slowest Reaction

The slowest reaction will have the smallest rate constant. Comparing the rate constants, Reaction (d) with a rate constant of \(3.0 \times 10^{-18}\) has the smallest value, indicating it is the slowest reaction.

Step 3: Determine the Fastest Reaction

The fastest reaction will have the largest rate constant. Reaction (c) has a rate constant of \(1.4 \times 10^{-10}\), which is the largest among the given reactions, making it the fastest reaction.

Key Concepts

Rate Constant

The rate constant is a crucial factor in chemical reactions. It's essentially a number that quantifies how fast a reaction proceeds. The rate constant depends on various factors such as temperature and the nature of the reactants. For a given reaction at a specific temperature, the rate constant remains unchanged.

• The unit for the rate constant of a second-order reaction is \( \mathrm{cm}^3 / \mathrm{molecule} \cdot \mathrm{s} \).
• A larger rate constant implies a faster reaction.
• A smaller rate constant indicates a slower reaction.

When analyzing rate constants, it's important to compare them directly to understand reaction speeds. This allows us to predict which reactions contribute more significantly to phenomena like ozone depletion.

Second-Order Reactions

Second-order reactions are a type of chemical reaction where the rate depends on the concentration of two reactants. In other words, the rate is proportional to the product of the concentrations of two reacting species. The rate equation for a second-order reaction is:\[ \text{Rate} = k[A][B] \]Where:

• \(k\) is the rate constant.
• \([A]\) and \([B]\) are the concentrations of the two reactants.

Understanding second-order reactions helps in studying ozone depletion because these reactions often involve molecular collisions, such as between chlorine atoms and ozone. The reaction rate will increase if the concentration of either reactant increases, leading to more rapid ozone layer depletion if the concentrations of destructive agents like chlorine are high.

Chlorine Atom Reactions

Chlorine atom reactions are primarily responsible for ozone layer depletion. These reactions often occur in the stratosphere, where chlorine atoms react with ozone (\(O_3\)) and other organic compounds. The main concern is the ability of chlorine to continuously participate in reactions that destroy ozone molecules, leading to a thinning ozone layer.The notable reaction is the one involving chlorine atoms with ozone:\[ \mathrm{Cl} + \mathrm{O_3} \longrightarrow \mathrm{ClO} + \mathrm{O_2} \]Key points to understand about these reactions include:

• Chlorine atoms are highly reactive and capable of interacting with various organic compounds.
• The rate constants for these reactions vary significantly, indicating different speeds of reaction.
• Continual exposure to chlorine can result in substantial ozone depletion over time.

Gaining insight into chlorine atom reactions helps us devise strategies to mitigate the detrimental effects on the ozone layer, such as reducing chlorine-containing pollutants.