Consider the following thermochemical equations: C(graphite) + O, (g) → co, (g) AH° = -393.5 kJ H2 (9) + % 0, (g) → H,0 (I) AH°n = -285.8 kJ 2 C2H6 (g) + 7 O2 (g) → 4 CO2 (g) + 6 H;O (1) AHm = -3119.6 kJ a. Derive the thermochemical equation describing the combustion of two moles of C(graphite). b. Derive the thermochemical equation describing the combustion of three moles of H2 (g). c. Derive the thermochemical equation describing the synthesis of one mole of C,H6 (g) from carbon dioxide and water.

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### Thermochemical Equations and Hess's Law

Consider the following thermochemical equations:

1. \( \text{C(graphite)} + \text{O}_2 \, (g) \rightarrow \text{CO}_2 \, (g) \)
   - \( \Delta H^\circ_{\text{rxn}} = -393.5 \, \text{kJ} \)

2. \( \text{H}_2 \, (g) + \frac{1}{2} \text{O}_2 \, (g) \rightarrow \text{H}_2\text{O} \, (l) \)
   - \( \Delta H^\circ_{\text{rxn}} = -285.8 \, \text{kJ} \)

3. \( 2 \, \text{C}_2\text{H}_6 \, (g) + 7 \, \text{O}_2 \, (g) \rightarrow 4 \, \text{CO}_2 \, (g) + 6 \, \text{H}_2\text{O} \, (l) \)
   - \( \Delta H^\circ_{\text{rxn}} = -3119.6 \, \text{kJ} \)

#### Tasks:

a. **Derive the thermochemical equation for the combustion of two moles of C(graphite).**

b. **Derive the thermochemical equation for the combustion of three moles of H\(_2\) (g).**

c. **Derive the thermochemical equation for the synthesis of one mole of C\(_2\)H\(_6\) (g) from carbon dioxide and water.**

d. **Use Hess’s Law and the equations derived in parts a-c to determine the \( \Delta H^\circ_{\text{rxn}} \) for the following reaction:**

   - \( 2 \, \text{C(graphite)} + 3 \, \text{H}_2 \, (g) \rightarrow \text{C}_2\text{H}_6 \, (g) \)

### Explanation of Graphs or Diagrams

- **No graphs or diagrams** are present in this task. The focus is purely on deriving thermochemical equations and applying Hess's Law to find the enthalpy of reaction for the synthesis of eth
Transcribed Image Text:### Thermochemical Equations and Hess's Law Consider the following thermochemical equations: 1. \( \text{C(graphite)} + \text{O}_2 \, (g) \rightarrow \text{CO}_2 \, (g) \) - \( \Delta H^\circ_{\text{rxn}} = -393.5 \, \text{kJ} \) 2. \( \text{H}_2 \, (g) + \frac{1}{2} \text{O}_2 \, (g) \rightarrow \text{H}_2\text{O} \, (l) \) - \( \Delta H^\circ_{\text{rxn}} = -285.8 \, \text{kJ} \) 3. \( 2 \, \text{C}_2\text{H}_6 \, (g) + 7 \, \text{O}_2 \, (g) \rightarrow 4 \, \text{CO}_2 \, (g) + 6 \, \text{H}_2\text{O} \, (l) \) - \( \Delta H^\circ_{\text{rxn}} = -3119.6 \, \text{kJ} \) #### Tasks: a. **Derive the thermochemical equation for the combustion of two moles of C(graphite).** b. **Derive the thermochemical equation for the combustion of three moles of H\(_2\) (g).** c. **Derive the thermochemical equation for the synthesis of one mole of C\(_2\)H\(_6\) (g) from carbon dioxide and water.** d. **Use Hess’s Law and the equations derived in parts a-c to determine the \( \Delta H^\circ_{\text{rxn}} \) for the following reaction:** - \( 2 \, \text{C(graphite)} + 3 \, \text{H}_2 \, (g) \rightarrow \text{C}_2\text{H}_6 \, (g) \) ### Explanation of Graphs or Diagrams - **No graphs or diagrams** are present in this task. The focus is purely on deriving thermochemical equations and applying Hess's Law to find the enthalpy of reaction for the synthesis of eth
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