Problem 87 - Chemistry: The Central Science

Question

The standard enthalpies of formation of \(\mathrm{ClO}\) and \(\mathrm{ClO}_{2}\) are 101 and \(102 \mathrm{~kJ} / \mathrm{mol}\), respectively. Using these data and the thermodynamic data in Appendix \(C\), calculate the overall enthalpy change for each step in the following catalytic cycle: $$ \begin{aligned} &\mathrm{ClO}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}_{2}(g)+\mathrm{O}_{2}(g) \\ &\mathrm{ClO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ What is the enthalpy change for the overall reaction that results from these two steps?

Step-by-Step Solution

Answer

The overall enthalpy change for the reaction can be calculated by first determining the enthalpy changes for each step in the catalytic cycle using Hess's Law: For Step 1: ∆H₁ = [∆Hf(ClO₂) + ∆Hf(O₂)] - [∆Hf(ClO) + ∆Hf(O₃)] For Step 2: ∆H₂ = [∆Hf(ClO) + ∆Hf(O₂)] - [∆Hf(ClO₂) + ∆Hf(O)] Then, the enthalpy change for the overall reaction (∆H_total) is calculated by summing the enthalpy changes of both steps: ∆H_total = ∆H₁ + ∆H₂

Step 1: Determine the enthalpies of formation for the other compounds

Use the thermodynamic data in Appendix C to find the standard enthalpies of formation for O₃, O₂, and O. These values are needed to apply Hess's Law in the following steps.

Step 2: Calculate the enthalpy change for the first step in the cycle

Using Hess's Law, calculate the enthalpy change for the first reaction: ClO(g) + O₃(g) → ClO₂(g) + O₂(g) The enthalpy change for this step (∆H₁) can be calculated using the formula: ∆H₁ = [∆Hf(ClO₂) + ∆Hf(O₂)] - [∆Hf(ClO) + ∆Hf(O₃)] Plug in the given values and the values obtained from Appendix C to find ∆H₁.

Step 3: Calculate the enthalpy change for the second step in the cycle

Using Hess's Law, calculate the enthalpy change for the second reaction: ClO₂(g) + O(g) → ClO(g) + O₂(g) The enthalpy change for this step (∆H₂) can be calculated using the formula: ∆H₂ = [∆Hf(ClO) + ∆Hf(O₂)] - [∆Hf(ClO₂) + ∆Hf(O)] Plug in the given values and the values obtained from Appendix C to find ∆H₂.

Step 4: Calculate the enthalpy change for the overall reaction

To find the enthalpy change for the overall reaction (∆H_total), add the enthalpy changes of both steps: ∆H_total = ∆H₁ + ∆H₂ Once you have found ∆H_total, the overall enthalpy change for the reaction is obtained.