5. Write a balanced thermochemical equation for the heat of combustion of gaseous ethylene, C2H4, given the following enthalpies of formation (kJ/mol): C2H4 (g), 52.3; H20 (I), -285.8; and CO2 (g), -393.5.

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**Problem 5:**

Write a balanced thermochemical equation for the heat of combustion of gaseous ethylene, \( \text{C}_2\text{H}_4 \), given the following enthalpies of formation (kJ/mol):

- \(\text{C}_2\text{H}_4 (g)\): 52.3
- \(\text{H}_2\text{O} (l)\): -285.8
- \(\text{CO}_2 (g)\): -393.5

**Solution:**

To address this problem, you need to write a balanced chemical equation for the combustion of ethylene, then calculate the heat of the reaction using the provided enthalpies of formation.

**Step 1: Write the balanced chemical equation:**

The combustion of ethylene involves its reaction with oxygen to produce carbon dioxide and water. The balanced equation is:

\[ \text{C}_2\text{H}_4 (g) + 3\text{O}_2 (g) \rightarrow 2\text{CO}_2 (g) + 2\text{H}_2\text{O} (l) \]

**Step 2: Calculate the heat of combustion:**

The heat of the reaction (\(\Delta H_{rxn}\)) can be calculated using the enthalpies of formation (\(\Delta H_f^\circ\)):

\[
\Delta H_{rxn} = \left[ 2 \times \Delta H_f^\circ (\text{CO}_2) + 2 \times \Delta H_f^\circ (\text{H}_2\text{O}) \right] - \left[ \Delta H_f^\circ (\text{C}_2\text{H}_4) \right]
\]

Substituting the given values:

\[
\Delta H_{rxn} = \left[ 2 \times (-393.5) + 2 \times (-285.8) \right] - [52.3]
\]

\[
\Delta H_{rxn} = \left[ -787.0 - 571.6 \right] - 52.3
\]

\[
\Delta H_{rxn} = -1358.6 - 52.3
\]

\[
\Delta H_{rxn} = -1410.9 \, \
Transcribed Image Text:**Problem 5:** Write a balanced thermochemical equation for the heat of combustion of gaseous ethylene, \( \text{C}_2\text{H}_4 \), given the following enthalpies of formation (kJ/mol): - \(\text{C}_2\text{H}_4 (g)\): 52.3 - \(\text{H}_2\text{O} (l)\): -285.8 - \(\text{CO}_2 (g)\): -393.5 **Solution:** To address this problem, you need to write a balanced chemical equation for the combustion of ethylene, then calculate the heat of the reaction using the provided enthalpies of formation. **Step 1: Write the balanced chemical equation:** The combustion of ethylene involves its reaction with oxygen to produce carbon dioxide and water. The balanced equation is: \[ \text{C}_2\text{H}_4 (g) + 3\text{O}_2 (g) \rightarrow 2\text{CO}_2 (g) + 2\text{H}_2\text{O} (l) \] **Step 2: Calculate the heat of combustion:** The heat of the reaction (\(\Delta H_{rxn}\)) can be calculated using the enthalpies of formation (\(\Delta H_f^\circ\)): \[ \Delta H_{rxn} = \left[ 2 \times \Delta H_f^\circ (\text{CO}_2) + 2 \times \Delta H_f^\circ (\text{H}_2\text{O}) \right] - \left[ \Delta H_f^\circ (\text{C}_2\text{H}_4) \right] \] Substituting the given values: \[ \Delta H_{rxn} = \left[ 2 \times (-393.5) + 2 \times (-285.8) \right] - [52.3] \] \[ \Delta H_{rxn} = \left[ -787.0 - 571.6 \right] - 52.3 \] \[ \Delta H_{rxn} = -1358.6 - 52.3 \] \[ \Delta H_{rxn} = -1410.9 \, \
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