Statement -1 in the following reaction :
`C(s)+O_(2)(g)to CO_(2) (g), DeltaH=DeltaU-RT`
Statement -2: `DeltaH` Is related to `DeltaU ` by the equation ,
`DeltaH=DeltaU+Deltan_(g)RT`

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem, we need to analyze the two statements provided regarding the relationship between enthalpy change (ΔH) and internal energy change (ΔU) for the reaction:

**Reaction:**
\[ C(s) + O_2(g) \rightarrow CO_2(g) \]

### Step 1: Understand the Relationship Between ΔH and ΔU
The relationship between enthalpy change (ΔH) and internal energy change (ΔU) is given by the equation:
\[ \Delta H = \Delta U + \Delta n_g RT \]
where:
- Δn_g = change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants)
- R = universal gas constant
- T = temperature in Kelvin

### Step 2: Calculate Δn_g for the Given Reaction
In the reaction:
- Products: 1 mole of CO₂ (g)
- Reactants: 1 mole of O₂ (g) and 0 moles of C (s) since it is a solid and does not contribute to Δn_g.

Now, we calculate Δn_g:
\[ \Delta n_g = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]
\[ \Delta n_g = 1 - 1 = 0 \]

### Step 3: Substitute Δn_g into the Equation
Now that we have Δn_g = 0, we can substitute this value into the relationship:
\[ \Delta H = \Delta U + 0 \cdot RT \]
This simplifies to:
\[ \Delta H = \Delta U \]

### Step 4: Evaluate the Statements
- **Statement 1:** \( \Delta H = \Delta U - RT \) is **false** because we derived that \( \Delta H = \Delta U \).
- **Statement 2:** \( \Delta H = \Delta U + \Delta n_g RT \) is **true** since we confirmed that \( \Delta H = \Delta U \) when Δn_g = 0.

### Conclusion
Thus, we conclude that:
- Statement 1 is false.
- Statement 2 is true.

The correct answer is **D** (Statement 1 is false, Statement 2 is true).

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