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To calculate the enthalpy change (ΔH) for the vaporization of ethanol, \( \text{C}_2\text{H}_5\text{OH} \), from liquid to gas, we will apply Hess's Law using the provided reactions:

### Given Data:
1. **Reaction for gaseous ethanol**:
   \[
   2\text{C}(s) + 3\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{C}_2\text{H}_5\text{OH}(g); \quad \Delta H = -235.1 \, \text{kJ}
   \]

2. **Reaction for liquid ethanol**:
   \[
   2\text{C}(s) + 3\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{C}_2\text{H}_5\text{OH}(l); \quad \Delta H = -277.7 \, \text{kJ}
   \]

### Target Reaction:
We want to find \( \Delta H \) for the vaporization reaction:
\[
\text{C}_2\text{H}_5\text{OH}(l) \rightarrow \text{C}_2\text{H}_5\text{OH}(g)
\]

### Solution Using Hess's Law:
Hess's Law states that the enthalpy change of the overall reaction is the sum of the enthalpy changes of individual steps.

The vaporization reaction can be derived by subtracting the enthalpy of formation of liquid ethanol from the enthalpy of formation of gaseous ethanol:
\[
\Delta H = \Delta H_{\text{gaseous}} - \Delta H_{\text{liquid}}
\]

Substituting the values:
\[
\Delta H = (-235.1) - (-277.7)
\]

Calculating this:
\[
\Delta H = -235.1 + 277.7 = 42.6 \, \text{kJ}
\]

### Answer:
The enthalpy change \( \Delta H \) for the vaporization of ethanol is:
\[
\Delta H = 42.6 \, \text{kJ}
\]

This result should be reported with three significant figures, as specified.

Would you like further details or have any questions about the calculation steps?

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Here are 5 additional related questions for practice:
1. How would you calculate \( \Delta H \) if only the combustion values of ethanol were given?
2. How does Hess’s Law apply in calculating enthalpy changes in multi-step reactions?
3. What is the significance of enthalpy of vaporization in thermodynamics?
4. Can Hess’s Law be applied to reactions in non-standard conditions?
5. How do bond enthalpies relate to calculating reaction enthalpies?

**Tip:** When using Hess’s Law, ensure that you align each reaction with the target reaction’s requirements (e.g., correct phases, products, and reactants).

Calculate ΔH for the vaporization of ethanol: C2H5OH(g) → C2H5OH(l), given:

1. 2C(s) + 3H2(g) + 1/2O2(g) → C2H5OH(g); ΔH = -235.1 kJ
2. 2C(s) + 3H2(g) + 1/2O2(g) → C2H5OH(l); ΔH = -277.7 kJ

Learn how to calculate the enthalpy change (ΔH) for the vaporization of ethanol from liquid to gas. Using Hess's Law, this solution applies thermodynamic principles and enthalpy of formation values. Includes step-by-step guidance suitable for college-level students.

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