Which among the following represents standard enthalpy of formation?

Options

A. `2C(s)_("graphite")+3H_(2)(g)+(1)/(2)O_(2)(g) rarr C_(2)H_(5)OH(l)`
B. `CaO(s)+CO_(2)(g) rarr CaCO_(3)`
C. `C_(6)H_(6)(l)+(15)/(2)O_(2)(g) rarr 6CO_(2)(g)+3H_(2)O(l)`
D. `Fe_(2)O_(3)(s) + 3H_(2)(g) rarr 2Fe(s) + 3H_(2)O(l)`

Answer

To determine which option represents the standard enthalpy of formation, we need to understand the definition of standard enthalpy of formation. It is defined as the enthalpy change that occurs when one mole of a compound is formed from its elements in their standard states.

### Step-by-Step Solution:

1. **Understanding Standard Enthalpy of Formation**:
- The standard enthalpy of formation (ΔH_f°) is the heat change when one mole of a compound is formed from its elements in their standard states.

2. **Identify the Standard States of Elements**:
- The standard state of an element is its most stable form at 1 atm pressure and a specified temperature (usually 25°C).
- For example:
- Carbon (C) in its standard state is graphite.
- Hydrogen (H) in its standard state is H₂ gas.
- Oxygen (O) in its standard state is O₂ gas.

3. **Analyzing Each Option**:
- **Option 1: Ethanol Formation**:
- The formation of ethanol (C₂H₅OH) from its elements:
\[ 2C_{(s)} + 3H_{2(g)} + \frac{1}{2}O_{2(g)} \rightarrow C_{2}H_{5}OH_{(l)} \]
- This reaction shows that one mole of ethanol is formed from its elements in their standard states. Thus, this option represents the standard enthalpy of formation.

- **Option 2: Calcium Carbonate Formation**:
- The formation of calcium carbonate (CaCO₃) from its elements:
\[ Ca_{(s)} + C_{(s)} + \frac{3}{2}O_{2(g)} \rightarrow CaCO_{3(s)} \]
- This reaction does represent the formation from elements in their standard states, but it is not the correct option because we need to form one mole of the compound.

- **Option 3: Formation of Carbon Dioxide**:
- The formation of carbon dioxide (CO₂) typically involves the combustion of carbon:
\[ C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} \]
- However, this option does not represent the formation of one mole of a compound from its elements, as it mentions 6 moles of CO₂.

- **Option 4: Another Compound Formation**:
- Without specific details, we can assume this option does not meet the criteria for standard enthalpy of formation.

4. **Conclusion**:
- The only option that correctly represents the standard enthalpy of formation is **Option 1**, which is the formation of ethanol from its elements in their standard states.

### Final Answer:
**Option 1 represents the standard enthalpy of formation.**

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