To determine which statement about the given reaction is correct, let's analyze the reaction:
[tex]\[
CH _{4(g)} + 2 O _{2(g)} \rightarrow CO _{2(g)} + 2 H _2 O _{(l)}: \Delta H = -890 \, \text{kJ}
\][/tex]
This tells us that the enthalpy change [tex]\(\Delta H\)[/tex] for the reaction is [tex]\(-890 \, \text{kJ}\)[/tex], meaning the reaction releases 890 kJ of energy when one mole of methane reacts with two moles of oxygen.
Now, let's evaluate each statement one by one:
1. The reaction of one mole of oxygen [tex]\(\left( O _2\right)\)[/tex] absorbs 445 kJ of energy.
- Since [tex]\(\Delta H\)[/tex] is negative ([tex]\(-890 \, \text{kJ}\)[/tex]), the reaction releases energy, not absorbs it.
- For two moles of oxygen, the total energy released is 890 kJ.
- Therefore, for one mole of oxygen, the energy released would be:
[tex]\[
\frac{-890 \, \text{kJ}}{2} = -445 \, \text{kJ}
\][/tex]
The reaction of one mole of oxygen releases 445 kJ of energy, not absorbs. So, this statement is incorrect.
2. The reaction of one mole of oxygen [tex]\(\left( O _2\right)\)[/tex] releases 445 kJ of energy.
- As calculated above, for one mole of oxygen, the energy change is:
[tex]\[
\frac{-890 \, \text{kJ}}{2} = -445 \, \text{kJ}
\][/tex]
This means that the reaction of one mole of oxygen releases 445 kJ of energy. This statement is correct.
3. The reaction of one mole of methane [tex]\(\left( CH _4\right)\)[/tex] absorbs 890 kJ of energy.
- The given [tex]\(\Delta H = -890 \, \text{kJ}\)[/tex] indicates that the reaction releases 890 kJ of energy.
- Since the reaction releases energy (negative [tex]\(\Delta H\)[/tex]), it does not absorb energy. Thus, this statement is incorrect.
4. The reaction of two moles of methane [tex]\(\left( CH _4\right)\)[/tex] releases 890 kJ of energy.
- The reaction equation shows that one mole of methane releases 890 kJ of energy.
- If we had two moles of methane, the energy released would be [tex]\(2 \times (-890 \, \text{kJ}) = -1780 \, \text{kJ}\)[/tex].
- Therefore, saying that the reaction of two moles of methane releases 890 kJ of energy is incorrect, as it actually releases 1780 kJ.
After analyzing all the given statements, we find that the correct statement is:
The reaction of one mole of oxygen [tex]\(\left( O _2\right)\)[/tex] releases 445 kJ of energy.
Thus, the correct statement is the second one.
