Enthalpy of `CH_(4)+(1)/(2)O_(2)rarrCH_(3)OH` is
negative. If enthalpy of combustion of `CH_(4)` and `CH_(4)OH` are `x` and `y` respectively, then which relation is correct?

Options

A. `xgt y`
B. `xlt y`
C. `x=y`
D. `xgey`

Explanation

To solve the problem, we need to analyze the enthalpy changes associated with the combustion of methane (CH₄) and methanol (CH₃OH) and how they relate to the given reaction.

### Step-by-Step Solution:

1. **Write the Combustion Reactions**:
- The combustion of methane (CH₄):
\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
Let the enthalpy change for this reaction be \( x \).

- The combustion of methanol (CH₃OH):
\[ \text{CH}_3\text{OH} + 1.5\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
Let the enthalpy change for this reaction be \( y \).

2. **Identify the Given Reaction**:
- The reaction given in the problem is:
\[ \text{CH}_4 + \frac{1}{2}\text{O}_2 \rightarrow \text{CH}_3\text{OH} \]
It is stated that the enthalpy change for this reaction is negative.

3. **Relate the Reactions**:
- We can express the enthalpy change for the reaction of interest in terms of the enthalpy changes of the combustion reactions.
- By subtracting the combustion reaction of methanol from that of methane, we can derive the relationship:
\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \quad (x) \]
\[ \text{CH}_3\text{OH} + 1.5\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \quad (y) \]

4. **Subtract the Two Reactions**:
- When we subtract the second equation from the first, we get:
\[ \text{CH}_4 + 2\text{O}_2 - (\text{CH}_3\text{OH} + 1.5\text{O}_2) \rightarrow 0 \]
- This simplifies to:
\[ \text{CH}_4 + 0.5\text{O}_2 \rightarrow \text{CH}_3\text{OH} \]
- The enthalpy change for this reaction can be expressed as:
\[ \Delta H = x - y \]

5. **Analyze the Sign of Enthalpy Change**:
- Since the enthalpy change for the reaction \(\text{CH}_4 + 0.5\text{O}_2 \rightarrow \text{CH}_3\text{OH}\) is negative, we have:
\[ x - y < 0 \]
- This implies:
\[ y > x \]

### Conclusion:
Therefore, the correct relation is:
\[ y > x \]