Assertion`:-` For the combustion of methane `DeltaHltDeltaU` at
`125^(@)C`
Reason`:-` For combustion `DeltaH` is always less than `DeltaU`

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Explanation

To solve the assertion and reason question regarding the combustion of methane, we will analyze the statements step by step.

### Step 1: Understand the Assertion
The assertion states that for the combustion of methane, ΔH (change in enthalpy) is less than ΔU (change in internal energy) at 125°C.

### Step 2: Write the Reaction
The balanced chemical equation for the combustion of methane (CH₄) is:
\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \]

### Step 3: Identify the Change in Moles of Gas (ΔNG)
To find ΔNG, we need to count the number of moles of gaseous products and reactants:
- **Reactants**: 1 mole of CH₄ (g) + 2 moles of O₂ (g) = 3 moles of gas
- **Products**: 1 mole of CO₂ (g) + 2 moles of H₂O (l) = 1 mole of gas (only CO₂ is gaseous)

Now, we can calculate ΔNG:
\[ \Delta N_G = \text{Moles of gaseous products} - \text{Moles of gaseous reactants} = 1 - 3 = -2 \]

### Step 4: Relate ΔH and ΔU
The relationship between ΔH and 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
- R = universal gas constant
- T = temperature in Kelvin

Since ΔNG is negative (-2), the term ΔN_G RT will also be negative. Therefore:
\[ \Delta H < \Delta U \]
This confirms that for the combustion of methane, ΔH is indeed less than ΔU.

### Step 5: Evaluate the Reason
The reason states that for combustion, ΔH is always less than ΔU. However, this is not universally true; it depends on the value of ΔNG. The condition that ΔH < ΔU holds true only when ΔNG is less than zero.

### Conclusion
- **Assertion**: True (ΔH < ΔU for the combustion of methane at 125°C)
- **Reason**: False (ΔH is not always less than ΔU; it depends on ΔNG)

### Final Answer
Assertion is true, but the reason is false.

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