Given that : `C(s)+O_(2)(g)to CO_(2)(g) , Delta H = -394 kJ` and `2H_(2)(g)+O_(2)(g)to 2H_(2)O(l) , Delta H =- 568 kJ` and `C_(2)H_(5)OH(l)+3O_(2)(g)to 2CO_(2)(g)+3H_(2)O(l) , Delta H =- 1058` kJ/mole. Using the data, the heat of formation of ethanol is

Options

A. `-582 kJ`
B. 71.8 kJ
C. `-244 kJ`
D. `+782 kJ`

Answer

To find the heat of formation of ethanol (C₂H₅OH) using the given thermodynamic data, we can apply Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

### Step-by-Step Solution:

1. **Write down the given reactions and their ΔH values:**
- Reaction 1: \( C(s) + O_2(g) \rightarrow CO_2(g) \), ΔH = -394 kJ
- Reaction 2: \( 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \), ΔH = -568 kJ
- Reaction 3: \( C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l) \), ΔH = -1058 kJ

2. **Identify the heat of formation equation:**
The heat of reaction can be expressed in terms of the heat of formation:
\[ \Delta H_{reaction} = \Delta H_{f, products} - \Delta H_{f, reactants} \]

3. **Set up the equation for Reaction 3:**
For Reaction 3, we can express the heat of formation of ethanol (C₂H₅OH) as follows:
\[ -1058 = [2 \Delta H_f(CO_2) + 3 \Delta H_f(H_2O)] - \Delta H_f(C_2H_5OH) - 3 \Delta H_f(O_2) \]

4. **Substitute known values:**
- The heat of formation of \( CO_2 \) is -394 kJ/mol.
- The heat of formation of \( H_2O \) can be calculated from Reaction 2. Since the ΔH for 2 moles of water is -568 kJ, for 1 mole:
\[ \Delta H_f(H_2O) = \frac{-568}{2} = -284 \text{ kJ/mol} \]
- The heat of formation of \( O_2 \) in its elemental form is 0 kJ/mol.

5. **Substitute these values into the equation:**
\[ -1058 = [2(-394) + 3(-284)] - \Delta H_f(C_2H_5OH) - 3(0) \]
\[ -1058 = [-788 - 852] - \Delta H_f(C_2H_5OH) \]
\[ -1058 = -1640 - \Delta H_f(C_2H_5OH) \]

6. **Rearranging the equation to solve for ΔH_f(C₂H₅OH):**
\[ \Delta H_f(C_2H_5OH) = -1640 + 1058 \]
\[ \Delta H_f(C_2H_5OH) = -582 \text{ kJ/mol} \]

### Final Answer:
The heat of formation of ethanol (C₂H₅OH) is **-582 kJ/mol**.