Which of the following statement(s) is/are true?

Options

A. `DeltaU = 0` for combustion of `C_(2)H_(6)`(g) in a sealed rigid adiabatic container
B. `Delta_(f)H^(@)` (S, monoclinic) `ne 0`
C. If dissociation energy of `CH_(4)(g)` is `1656 kJ//"mol"` and `C_(2)H_(6)` (g) is 2812 kJ/mol, then value of C-C bond energy will be 328 kJ/mol
D. If `DeltaH_(f)(H_(2)O,g)=-242 " kJ"//"mol", DeltaH_("vap")(H_(2)O,l)=44 " kJ"//"mol"`
then, `Delta_(f)H^(@)(OH^(-),aq.)` will be -142 kJ/mol

Explanation

To determine which of the statements are true, we will analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** ΔU = 0 for the combustion of C2H6 in a sealed rigid adiabatic container.

- **Explanation:**
- In a sealed rigid container, there is no volume change, which means no work is done (W = 0).
- Since the container is adiabatic, there is no heat exchange with the surroundings (Q = 0).
- Therefore, using the first law of thermodynamics: ΔU = Q + W = 0 + 0 = 0.

- **Conclusion:** Statement A is **true**.

### Step 2: Analyze Statement B
**Statement B:** ΔH⁰ of formation of sulfur monochloride is not equal to zero.

- **Explanation:**
- The standard enthalpy of formation (ΔH⁰) of a compound is defined as the change in enthalpy when one mole of the compound is formed from its elements in their standard states.
- For elements in their standard states, ΔH⁰ = 0. Sulfur monochloride (SCl) is a compound, and its formation from elemental sulfur and chlorine would have a non-zero enthalpy change.

- **Conclusion:** Statement B is **false**.

### Step 3: Analyze Statement C
**Statement C:** If the dissociation energy of CH4 is 1656 kJ/mol and C2H6 is 2812 kJ/mol, then the value of C-C bond energy will be 328 kJ/mol.

- **Explanation:**
- The dissociation energy of C2H6 can be expressed as the sum of the bond energies of the C-H bonds and the C-C bond.
- For C2H6 (which has 6 C-H bonds), the energy can be calculated as:
\[ \text{C-C bond energy} = \text{Dissociation energy of C2H6} - \text{(number of C-H bonds)} \times \text{Dissociation energy of CH4} \]
\[ \text{C-C bond energy} = 2812 \text{ kJ/mol} - 6 \times \left(\frac{1656 \text{ kJ/mol}}{4}\right) \]
\[ \text{C-C bond energy} = 2812 - 6 \times 414 = 328 \text{ kJ/mol} \]

- **Conclusion:** Statement C is **true**.

### Step 4: Analyze Statement D
**Statement D:** The formation enthalpy for H2O in gaseous state is -242 kJ/mol and ΔH vaporization is 44 kJ/mol, then the formation enthalpy of OH⁻ will be -142 kJ/mol.

- **Explanation:**
- The enthalpy of vaporization (ΔH vaporization) is the energy required to convert water from liquid to gas.
- The relationship can be expressed as follows:
\[ \Delta H_{\text{vaporization}} = \Delta H_{\text{formation, gas}} - \Delta H_{\text{formation, liquid}} \]
\[ 44 = (-242) - \Delta H_{\text{formation, liquid}} \]
\[ \Delta H_{\text{formation, liquid}} = -286 \text{ kJ/mol} \]
- For the formation of OH⁻:
\[ -57.3 = -286 - 4 \times \Delta H_{\text{formation, OH}^-} \]
\[ \Delta H_{\text{formation, OH}^-} = -228.7 \text{ kJ/mol} \]

- **Conclusion:** Statement D is **false**.

### Final Conclusion
The true statements are **A and C**.

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