Calculate the enthalpy of formation of `Delta_(f)H` for `C_(2)H_(5)OH` from tabulated data and its heat of combustion as represented by the following equaitons:
i. `H_(2)(g) +(1)/(2)O_(2)(g) rarr H_(2)O(g), DeltaH^(Theta) =- 241.8 kJ mol^(-1)`
ii. `C(s) +O_(2)(g) rarr CO_(2)(g),DeltaH^(Theta) =- 393.5kJ mol^(-1)`
iii. `C_(2)H_(5)OH (l) +3O_(2)(g) rarr 3H_(2)O(g) + 2CO_(2)(g), DeltaH^(Theta) =- 1234.7kJ mol^(-1)`

Options

A. a. `-2747.1 kJ mol^(-1)`
B. b. `-277.7 kJ mol^(-1)`
C. c. `277.7 kJ mol^(-1)`
D. d. `2747.1 kJ mol^(-1)`

Explanation

To calculate the enthalpy of formation (Δ_fH) for ethanol (C₂H₅OH), we can use the provided combustion reaction and the enthalpy values from the given equations. Here's the step-by-step solution:

### Step 1: Write down the equations and their enthalpy changes

1. **Formation of water (H₂O)**:
\[ \text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2O(g), \quad \Delta H^{\Theta} = -241.8 \, \text{kJ/mol} \]
...