Let's analyze the reaction step by step to determine which statement is correct.
### The Reaction
The given reaction is:
[tex]\[ \text{CH}_4(\text{g}) + 2 \text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g}) + 2 \text{H}_2\text{O}(\text{l}); \Delta H = -890 \text{kJ} \][/tex]
Here, \(\Delta H = -890 \text{kJ}\) indicates that 890 kJ of energy is released when one mole of methane (\(\text{CH}_4\)) reacts with oxygen (\(\text{O}_2\)). This release of energy signifies that it is an exothermic reaction.
### Interpretation of \(\Delta H\)
- If \(\Delta H\) is negative, the reaction releases energy.
- If \(\Delta H\) is positive, the reaction absorbs energy.
For our reaction:
- \(\Delta H = -890 \text{kJ}\) means 890 kJ of energy is released for the combustion of one mole of \(\text{CH}_4\).
### Moles of Reactants
From the reaction equation:
- One mole of \(\text{CH}_4\) reacts with 2 moles of \(\text{O}_2\).
### Energy Released per Mole of \(\text{O}_2\)
Since 890 kJ is released for 2 moles of \(\text{O}_2\):
Energy released per mole of \(\text{O}_2\) is:
[tex]\[ \frac{-890 \text{kJ}}{2} = -445 \text{kJ} \][/tex]
### Analyzing the Statements
1. The reaction of one mole of oxygen (\(\text{O}_2\)) absorbs 445 kJ of energy.
- Incorrect. The negative \(\Delta H\) denotes release of energy, not absorption.
2. The reaction of one mole of oxygen (\(\text{O}_2\)) releases 445 kJ of energy.
- Correct. Each mole of \(\text{O}_2\) releases 445 kJ of energy.
3. The reaction of one mole of methane (\(\text{CH}_4\)) absorbs 890 kJ of energy.
- Incorrect. The reaction releases 890 kJ of energy, not absorbs.
4. The reaction of two moles of methane (\(\text{CH}_4\)) releases 890 kJ of energy.
- Incorrect. The reaction specifies that one mole of \(\text{CH}_4\) releases 890 kJ of energy.
Thus, the correct statement is:
2. The reaction of one mole of oxygen ([tex]\(\text{O}_2\)[/tex]) releases 445 kJ of energy.
