Problem 22 - Chemistry: An Atoms-Focused Approach

Question

Write expressions for \(K_{c}\) and \(K_{p}\) for the following reactions, which contribute to the destruction of stratospheric ozone. a. \(\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{ClO}(g)+\mathrm{O}_{2}(g)\) b. \(2 \mathrm{ClO}(g) \rightleftharpoons 2 \mathrm{Cl}(g)+\mathrm{O}_{2}(g)\) c. \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

Question: Write the expressions for the equilibrium constants, both in terms of concentrations (Kc) and pressures (Kp), for the following chemical reaction involving stratospheric ozone destruction: Reaction: 2 ClO → 2 Cl + O2 Answer: For this reaction, the expression for the equilibrium constant in terms of concentrations is: Kc = ([Cl]^2[O2])/([ClO]^2) And the expression for the equilibrium constant in terms of pressures is: Kp = (P_{Cl}^2P_{O2})/(P_{ClO}^2)

Step 1: Reaction a: Identify Reactants and Products

In reaction a, the reactants are chlorine gas (Cl) and ozone (O3), while the products are chlorine monoxide (ClO) and dioxygen (O2).

Step 2: Reaction a: Expression for \(K_c\)

For reaction a, the expression for the equilibrium constant in terms of concentrations is: \(K_c = \dfrac{[\mathrm{ClO}][\mathrm{O_2}]}{[\mathrm{Cl}][\mathrm{O_3}]}\)

Step 3: Reaction a: Expression for \(K_p\)

For reaction a, the expression for the equilibrium constant in terms of pressures is: \(K_p = \dfrac{P_{\mathrm{ClO}}P_{\mathrm{O_2}}}{P_{\mathrm{Cl}}P_{\mathrm{O_3}}}\)

Step 4: Reaction b: Identify Reactants and Products

In reaction b, the reactants are two chlorine monoxide (ClO) molecules and the products are two chlorine gas (Cl) molecules and a dioxygen (O2) molecule.

Step 5: Reaction b: Expression for \(K_c\)

For reaction b, the expression for the equilibrium constant in terms of concentrations is: \(K_c = \dfrac{[\mathrm{Cl}]^2[\mathrm{O_2}]}{[\mathrm{ClO}]^2}\)

Step 6: Reaction b: Expression for \(K_p\)

For reaction b, the expression for the equilibrium constant in terms of pressures is: \(K_p = \dfrac{P_{\mathrm{Cl}}^2P_{\mathrm{O_2}}}{P_{\mathrm{ClO}}^2}\)

Step 7: Reaction c: Identify Reactants and Products

In reaction c, the reactants are two ozone (O3) molecules and the products are three dioxygen (O2) molecules.

Step 8: Reaction c: Expression for \(K_c\)

For reaction c, the expression for the equilibrium constant in terms of concentrations is: \(K_c = \dfrac{[\mathrm{O_2}]^3}{[\mathrm{O_3}]^2}\)

Step 9: Reaction c: Expression for \(K_p\)

For reaction c, the expression for the equilibrium constant in terms of pressures is: \(K_p = \dfrac{P_{\mathrm{O_2}}^3}{P_{\mathrm{O_3}}^2}\)

Key Concepts

Equilibrium Constants

In chemical equilibrium, the reaction has reached a state where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant. The equilibrium constant, denoted as either \(K_c\) for concentration or \(K_p\) for pressure, provides a snapshot of the ratio of product concentrations to reactant concentrations at equilibrium.

For the reactions contributing to the destruction of stratospheric ozone, the equilibrium constant expression is derived from the balanced chemical equations. For example, for the reaction \(\text{Cl}(g) + \text{O}_3(g) \rightleftharpoons \text{ClO}(g) + \text{O}_2(g)\), we write:

• \(K_c = \dfrac{[\text{ClO}][\text{O}_2]}{[\text{Cl}][\text{O}_3]}\)
• \(K_p = \dfrac{P_{\text{ClO}} P_{\text{O}_2}}{P_{\text{Cl}} P_{\text{O}_3}}\)

These constants tell us whether a system favors products or reactants at equilibrium. A larger \(K_c\) or \(K_p\) indicates a higher concentration of products compared to reactants. Understanding these constants is important for predicting how changes in conditions can shift the equilibrium of a reaction.

Pressure and Concentration

Pressure and concentration play crucial roles in chemical reactions, especially for gases. In gaseous equilibria, pressure changes can significantly affect reaction dynamics. Le Chatelier's principle highlights how systems at equilibrium respond to changes in pressure or concentration to counteract the change and restore equilibrium.

For example, increasing the pressure of a system shifts the equilibrium towards the side with fewer gas molecules, minimizing pressure changes. This is because the system attempts to reduce the overall pressure, acting as a buffer. The expression \(K_p = \dfrac{P_{products}}{P_{reactants}}\) allows us to consider the partial pressures of gases, while \(K_c\) uses molar concentrations: \(K_c = \dfrac{[products]}{[reactants]}\).

In the stratospheric ozone reactions:

• Increasing concentrations of \(\text{Cl}\), \(\text{O}_2\), or \(\text{O}_3\) can shift the equilibrium.
• Overall, it reflects how external conditions influence reaction balances.

Understanding these concepts is key in manipulating reaction conditions for desired outcomes.

Stratospheric Ozone Chemistry

Stratospheric ozone chemistry involves complex reactions that play a crucial role in protecting life on Earth from harmful ultraviolet (UV) radiation. In the stratosphere, ozone (\(\text{O}_3\)) is continually formed and destroyed by natural chemical processes.

Chlorine compounds, such as \(\text{ClO}\), and ozone react, contributing significantly to ozone layer depletion. The reaction \(\text{Cl}(g) + \text{O}_3(g) \rightleftharpoons \text{ClO}(g) + \text{O}_2(g)\) represents ozone destruction. Here, chlorine acts as a catalyst. A single chlorine atom can destroy thousands of ozone molecules, disrupting the delicate balance in stratospheric chemistry.

Equations in the form of \(K_c\) and \(K_p\) help understand the concentrations and pressures of those involved in these reactions. The reactions:

• Show the conversion between chlorine monoxide and ozone.
• Demonstrate the ongoing challenge in maintaining stratospheric ozone levels.

This chemical understanding helps in studying impacts on the ozone layer, driving strategies for reducing harmful emissions and protecting this vital atmospheric component.