One mole of methanol when burnt in `O_(2)`, gives out 723 kJ `mol^(-1)` of heat. If one mole of `O_(2)` is used, what will be the amount of heat evovled?

Options

A. 723 kJ
B. 964 kJ
C. 482 kJ
D. 241 kJ

Answer

To solve the problem, we need to analyze the combustion of methanol (CH₃OH) in the presence of oxygen (O₂) and determine how much heat is evolved when only one mole of O₂ is used.

### Step-by-Step Solution:

1. **Write the balanced chemical equation for the combustion of methanol:**
\[ \text{CH}_3\text{OH} + \frac{3}{2} \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} \]
This equation shows that one mole of methanol reacts with 1.5 moles of oxygen.

2. **Identify the heat evolved for the complete combustion of methanol:**
According to the problem, the combustion of one mole of methanol releases 723 kJ of heat. This value corresponds to the complete reaction with 1.5 moles of O₂.

3. **Determine the heat evolved per mole of O₂:**
Since 723 kJ of heat is released when 1.5 moles of O₂ are consumed, we can find the heat released per mole of O₂ by dividing the total heat by the number of moles of O₂ used:
\[ \text{Heat evolved per mole of O}_2 = \frac{723 \text{ kJ}}{1.5} = 482 \text{ kJ} \]

4. **Conclusion:**
Therefore, when one mole of O₂ is used, the amount of heat evolved is 482 kJ.

### Final Answer:
The amount of heat evolved when one mole of O₂ is used is **482 kJ**.

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