To determine which of the statements are correct, we will analyze each statement step by step.
### Step 1: Analyze the first statement
**Statement**: In a cyclic process, work done is zero.
**Explanation**: In a cyclic process, the system returns to its initial state after completing a cycle. Since the initial and final states are the same, there is no net change in internal energy (ΔU = 0). According to the first law of thermodynamics, the work done (W) is related to the change in internal energy (ΔU) and heat exchanged (Q) by the equation:
\[ \Delta U = Q - W \]
Since ΔU = 0, it implies that:
\[ W = Q \]
However, if the system returns to its initial state, the work done over one complete cycle is zero. Therefore, this statement is correct.
### Step 2: Analyze the second statement
**Statement**: The dissociation energy of methane is 1656 kJ/mol.
**Explanation**: Methane (CH₄) has four C-H bonds. The total dissociation energy for breaking all four bonds is given as 1656 kJ/mol. To find the average bond dissociation energy for one C-H bond, we divide the total by the number of bonds:
\[ \text{C-H bond energy} = \frac{1656 \text{ kJ/mol}}{4} = 414 \text{ kJ/mol} \]
This calculation confirms that the dissociation energy of methane is indeed 1656 kJ/mol, making this statement correct.
### Step 3: Analyze the third statement
**Statement**: The dissociation energy of ethane (C₂H₆) is 2812 kJ/mol.
**Explanation**: Ethane has one C-C bond and six C-H bonds. The total dissociation energy is given as 2812 kJ/mol. We can calculate the C-C bond dissociation energy by using the previously calculated C-H bond energy:
1. Total energy for six C-H bonds:
\[ 6 \times 414 \text{ kJ/mol} = 2484 \text{ kJ/mol} \]
2. Now, subtract the total C-H bond energy from the total dissociation energy to find the C-C bond energy:
\[ \text{C-C bond energy} = 2812 \text{ kJ/mol} - 2484 \text{ kJ/mol} = 328 \text{ kJ/mol} \]
This calculation shows that the dissociation energy of ethane is indeed 2812 kJ/mol, making this statement correct.
### Step 4: Analyze the fourth statement
**Statement**: ΔH for the reaction N₂ + O₂ → 2 NO is negative.
**Explanation**: The formation of nitrogen monoxide (NO) from nitrogen (N₂) and oxygen (O₂) is an endothermic reaction, meaning it requires energy input (often from heat or lightning) to occur. Therefore, the enthalpy change (ΔH) for this reaction is positive, not negative. Thus, this statement is incorrect.
### Conclusion
Based on the analysis:
1. The first statement is correct.
2. The second statement is correct.
3. The third statement is correct.
4. The fourth statement is incorrect.
Thus, the correct statements are 1, 2, and 3.
