Question

The standard enthalpies of formation of 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: $$\begin{array}{l}\mathrm{ClO}(g)+{\mathrm{O}}_3(g)⟶{\mathrm{ClO}}_2(g)+{\mathrm{O}}_2(g)\\ {\mathrm{ClO}}_2(g)+\mathrm{O}(g)⟶\mathrm{ClO}(g)+{\mathrm{O}}_2(g)\end{array}$$ What is the enthalpy change for the overall reaction that results from these two steps?

Short answer

The overall enthalpy change for the reaction in the catalytic cycle is -391.3 kJ/mol.

Step-by-step solution

Use the standard enthalpies of formation

: Recall the given standard enthalpies of formation for the ClO and ClO₂ molecules: $\mathrm{\Delta }{H}_{\text{f}}(C{l}_{2}O)=101\text{kJ/mol}$ $\mathrm{\Delta }{H}_{\text{f}}(C{l}_2{O}_2)=102\text{kJ/mol}$

Determine the enthalpy change for each step in the catalytic cycle

: Use the information given in Appendix C to find the standard enthalpies of formation for other species involved in the reaction: $\mathrm{\Delta }{H}_{\text{f}}(O_3)=142.2\text{kJ/mol}$ $\mathrm{\Delta }{H}_{\text{f}}(O_2)=0\text{kJ/mol}$ $\mathrm{\Delta }{H}_{\text{f}}(O)=249.1\text{kJ/mol}$ Now, use the standard enthalpies of formation for each species to find the enthalpy change for each step in the catalytic cycle using the following formula: $\mathrm{\Delta }{H}_{\text{rxn}}=\sum \mathrm{\Delta }{H}_{\text{f}}(\text{products})-\sum \mathrm{\Delta }{H}_{\text{f}}(\text{reactants})$ For Step 1: $$\mathrm{\Delta }{H}_1=[\mathrm{\Delta }{H}_{\text{f}}(Cl{O}_2)+\mathrm{\Delta }{H}_{\text{f}}(O_2)]-[\mathrm{\Delta }{H}_{\text{f}}(ClO)+\mathrm{\Delta }{H}_{\text{f}}(O_3)]$$ $$\mathrm{\Delta }{H}_1=[(102)+(0)]-[(101)+(142.2)]$$ $$\mathrm{\Delta }{H}_1=-141.2\text{kJ/mol}$$ For Step 2: $$\mathrm{\Delta }{H}_2=[\mathrm{\Delta }{H}_{\text{f}}(ClO)+\mathrm{\Delta }{H}_{\text{f}}(O_2)]-[\mathrm{\Delta }{H}_{\text{f}}(Cl{O}_2)+\mathrm{\Delta }{H}_{\text{f}}(O)]$$ $$\mathrm{\Delta }{H}_2=[(101)+(0)]-[(102)+(249.1)]$$ $$\mathrm{\Delta }{H}_2=-250.1\text{kJ/mol}$$

Calculate the overall enthalpy change for the reaction

: Now, add the enthalpy changes of the two individual steps to find the overall enthalpy change for the reaction: $$\mathrm{\Delta }{H}_{\text{overall}}=\mathrm{\Delta }{H}_1+\mathrm{\Delta }{H}_2$$ $$\mathrm{\Delta }{H}_{\text{overall}}=(-141.2)+(-250.1)$$ $$\mathrm{\Delta }{H}_{\text{overall}}=-391.3\text{kJ/mol}$$ The overall enthalpy change for the reaction in the catalytic cycle is -391.3 kJ/mol.

Key concepts

Standard Enthalpy of Formation

Understanding the standard enthalpy of formation ($\text{Δ}{H}_{\text{f}}^{\text{o}}$ ) is crucial for calculating the enthalpy change in chemical reactions. It defines the heat change that results when one mole of a compound is formed from its elements in their standard states. The standard state is the form in which the element or compound is most stable under conditions of 1 bar of pressure and a specified temperature, usually 298.15 K (25°C).

For example, the standard enthalpy of formation of a compound like water ($H_{2}O$ ) involves breaking bonds in the hydrogen and oxygen molecules, followed by the formation of new H-O bonds to create water. The standard state would mean the formation of liquid water under these conditions.

In a solved exercise, we observed the enthalpy changes for the reactions involving ClO and ClO₂. The provided standard enthalpies of formation for these substances, along with other reactants and products, allowed us to calculate the individual steps of a catalytic cycle. These values tell us how much energy is released or absorbed during the formation of one mole of a substance from its elements.

Catalytic Cycle Chemistry

Catalytic cycle chemistry involves the steps a catalyst goes through during a reaction, without being consumed in the process. A catalyst provides an alternative pathway for a reaction with a lower activation energy. Each step in the catalytic cycle has associated thermodynamic properties like enthalpy change that can be studied to understand the cycle's efficiency.

In our exercise, we calculated the enthalpy changes for two steps within a catalytic cycle involving the reactions of ClO, ClO₂, O₃, and O to ultimately produce O₂. The catalyst here facilitates these reactions, reducing the overall energy required. When we calculated the enthalpy changes for each reaction step, we gained insight into the energy profile of each stage of the catalyst's functioning. In real-world scenarios, improving these cycles means enhancing the overall energy efficiency of the processes, which can lead to significant industrial and environmental benefits.

Thermodynamic Data Usage

Thermodynamic data, such as standard enthalpies of formation, allow chemists to predict whether reactions will release or absorb energy. This data is harvested from meticulous experimentation and compiled in resources like appendices and chemical databases. When we use this data in a calculation, we're applying empirical knowledge to understand new or theoretical reactions.

In the given exercise, Appendix C provided the necessary thermodynamic data to calculate the enthalpy changes of the reactions within a catalytic cycle. We used the formula $\text{Δ}H=\text{ΣΔ}{H}_{\text{f}}^{\text{o}}(\text{products})-\text{ΣΔ}{H}_{\text{f}}^{\text{o}}(\text{reactants})$, which shows how enthalpy change for a reaction can be determined by subtracting the sum of the standard enthalpies of formation of the reactants from that of the products. Such calculations are crucial in sciences and engineering disciplines, aiding in the design of energy-efficient processes and the development of new materials.