Study the following two reactions:
(i) `CH_(4(g))+2 O_(2(g))to CO_(2(g))+2 H_2 O_((g)),
Delta H=-890.4 k J`
(ii) `2 Hg O_((s))to 2 Hg_((l))+O_(2(g)),
Delta H=+181.6 k J`
Which of the following statements is CORRECT?

Options

A. Both of them are exothermic
B. Both of them are endothermic
C. I is exothermic and II is endothermic
D. I is endothermic and II is exothermic

Explanation

To solve the question regarding the two reactions provided, we need to analyze each reaction in terms of whether they are exothermic or endothermic based on the given enthalpy changes (ΔH).

### Step-by-Step Solution:

1. **Identify the Reactions:**
- Reaction (i): \( CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) \) with \( \Delta H = -890.4 \, \text{kJ} \)
- Reaction (ii): \( 2 HgO(s) \rightarrow 2 Hg(l) + O_2(g) \) with \( \Delta H = +181.6 \, \text{kJ} \)

2. **Determine the Nature of Each Reaction:**
- **For Reaction (i):**
- The negative sign of \( \Delta H \) indicates that energy is released during the reaction. This means that the reaction is exothermic.
- **For Reaction (ii):**
- The positive sign of \( \Delta H \) indicates that energy is absorbed during the reaction. This means that the reaction is endothermic.

3. **Summarize the Findings:**
- Reaction (i) is exothermic because it releases heat.
- Reaction (ii) is endothermic because it absorbs heat.

4. **Conclusion:**
- Based on the analysis, we can conclude that the correct statement is that the first reaction is exothermic and the second reaction is endothermic.

### Final Answer:
The correct statement is that the first reaction is exothermic and the second reaction is endothermic.

---