Answered

```markdown
[tex]$
CH _{4(g)} + 2 O _{2(g)} \rightarrow CO _{2(g)} + 2 H _2 O _{(l)}: \Delta H = -890 \text{ kJ}
$[/tex]

Which statement about this reaction is correct?

A. The reaction of one mole of oxygen [tex]$\left( O_2 \right)$[/tex] absorbs 445 kJ of energy.
B. The reaction of one mole of oxygen [tex]$\left( O_2 \right)$[/tex] releases 445 kJ of energy.
C. The reaction of one mole of methane [tex]$\left( CH_4 \right)$[/tex] absorbs 890 kJ of energy.
D. The reaction of one mole of methane [tex]$\left( CH_4 \right)$[/tex] releases 890 kJ of energy.
```



Answer :

GinnyAnswer
Sure, let's analyze the reaction step-by-step and focus on the enthalpy change to determine the correct statement.

The given reaction is:

[tex]\[ CH_4 (g) + 2 O_2 (g) \rightarrow CO_2 (g) + 2 H_2O (l) \][/tex]

And the enthalpy change for this reaction is given as [tex]\(\Delta H = -890 \, \text{kJ}\)[/tex].

This means that when 1 mole of methane [tex]\( CH_4 \)[/tex] reacts with 2 moles of oxygen [tex]\( O_2 \)[/tex], 890 kJ of energy is released (since [tex]\(\Delta H\)[/tex] is negative, indicating an exothermic reaction).

Now, let's break this down:

1. Energy Change for One Mole of Methane:
[tex]\[ \Delta H = -890 \, \text{kJ} \][/tex]
This implies that the complete reaction involving one mole of methane releases 890 kJ of energy. Hence, the statement "The reaction of one mole of methane [tex]\( CH_4 \)[/tex] releases 890 kJ of energy" is correct.

2. Energy Change for One Mole of Oxygen:
Since the reaction involves 2 moles of [tex]\( O_2 \)[/tex] releasing 890 kJ of energy, we can find the energy change for just 1 mole of [tex]\( O_2 \)[/tex].

[tex]\[ \text{Energy released per mole of } O_2 = \frac{-890 \, \text{kJ}}{2} = -445 \, \text{kJ} \][/tex]

This means that the reaction of one mole of oxygen [tex]\( O_2 \)[/tex] releases 445 kJ of energy. Therefore, the statement "The reaction of one mole of oxygen [tex]\( O_2 \)[/tex] releases 445 kJ of energy" is correct.

3. Other Statements:
- "The reaction of one mole of oxygen [tex]\( O_2 \)[/tex] absorbs 445 kJ of energy": This is incorrect because we have established that energy is released, not absorbed.
- "The reaction of one mole of methane [tex]\( CH_4 \)[/tex] absorbs 890 kJ of energy": This is incorrect because the reaction releases energy, it does not absorb it.

Thus, the correct statements about the reaction are:

- The reaction of one mole of oxygen [tex]\( O_2 \)[/tex] releases 445 kJ of energy.
- The reaction of one mole of methane [tex]\( CH_4 \)[/tex] releases 890 kJ of energy.

To summarize, the correct statement in the context of the energy change for one mole of oxygen is:

"The reaction of one mole of oxygen [tex]\( O_2 \)[/tex] releases 445 kJ of energy."