Which of the following equations correctly represents the standard heat of formation`(Delta H_f^@)` of methane?

Options

A. `C("diamond") + 4H(g) rarr CH_(4)(g)`
B. `C("diamond") + 2H_2(g) rarr CH_(4)(g)`
C. `C("graphite") + 2H_2(g) rarr CH_(4)(g)`
D. `C("graphite") + 4H(g) rarr CH_(4)(g)`

Explanation

To determine the correct equation that represents the standard heat of formation (ΔH_f°) of methane (CH₄), we need to understand the definition of standard heat of formation and how it relates to the formation of a compound from its elements.

### Step-by-Step Solution:

1. **Understanding Standard Heat of Formation**:
- The standard heat of formation (ΔH_f°) of a compound is defined as the heat change that occurs when one mole of the compound is formed from its elements in their standard states at a specified temperature (usually 25°C or 298 K) and pressure (1 atm).

2. **Identifying the Elements of Methane**:
- Methane (CH₄) is composed of carbon (C) and hydrogen (H).
- In its standard state, carbon is typically found as graphite, and hydrogen is found as diatomic hydrogen gas (H₂).

3. **Writing the Formation Reaction**:
- The formation of one mole of methane from its elements can be represented as:
\[ \text{C (s, graphite)} + 2 \text{H}_2 \text{(g)} \rightarrow \text{CH}_4 \text{(g)} \]
- This equation shows that one mole of methane is formed from one mole of solid carbon (in the form of graphite) and two moles of diatomic hydrogen gas.

4. **Selecting the Correct Option**:
- Based on the above reaction, the correct equation that represents the standard heat of formation of methane is:
\[ \Delta H_f° = \text{C (s, graphite)} + 2 \text{H}_2 \text{(g)} \rightarrow \text{CH}_4 \text{(g)} \]
- Therefore, the correct option is the one that matches this equation.

### Conclusion:
The correct representation of the standard heat of formation of methane is:
\[ \text{C (s, graphite)} + 2 \text{H}_2 \text{(g)} \rightarrow \text{CH}_4 \text{(g)} \]