In a hypothetical reaction `X to Y`, the activation energy for the forward backward reactions are 15 and 9 kJ `mol^(-1)` respectively. The potential energy of X is 10 kJ `mol^(-1)`. Which of the following statement is/are correct?
(i) The threshold energy of the reaction is 25 kJ `mol^(-1)`
(ii) The potential energy of Y is 16 kJ `mol^(-1)`
(iii) Heat of reaction is 6 kJ `mol^(-1)`
The reaction is endothermic.

Options

A. Only (i)
B. Only (i) and (ii)
C. Only (ii) and (iii)
D. All are correct

Explanation

To solve the problem, we need to analyze the given data and calculate the required values step by step.

### Step 1: Understanding Activation Energy
The activation energy for the forward reaction (Ea_f) is given as 15 kJ/mol, and for the backward reaction (Ea_b), it is 9 kJ/mol.

### Step 2: Calculate the Heat of Reaction (ΔH)
The heat of reaction (ΔH) can be calculated using the formula:
\[ \Delta H = E_a^f - E_a^b \]
Substituting the values:
\[ \Delta H = 15 \, \text{kJ/mol} - 9 \, \text{kJ/mol} = 6 \, \text{kJ/mol} \]

### Step 3: Determine the Potential Energy of Y
The potential energy of Y can be calculated using the potential energy of X and the heat of reaction:
\[ \text{Potential energy of Y} = \text{Potential energy of X} + \Delta H \]
Given that the potential energy of X is 10 kJ/mol:
\[ \text{Potential energy of Y} = 10 \, \text{kJ/mol} + 6 \, \text{kJ/mol} = 16 \, \text{kJ/mol} \]

### Step 4: Calculate the Threshold Energy
The threshold energy (which is the energy required to start the reaction) is the potential energy of X plus the activation energy for the forward reaction:
\[ \text{Threshold energy} = \text{Potential energy of X} + E_a^f \]
Substituting the values:
\[ \text{Threshold energy} = 10 \, \text{kJ/mol} + 15 \, \text{kJ/mol} = 25 \, \text{kJ/mol} \]

### Step 5: Determine if the Reaction is Endothermic
Since the heat of reaction (ΔH) is positive (6 kJ/mol), the reaction is endothermic.

### Summary of Results
- (i) The threshold energy of the reaction is 25 kJ/mol. **(Correct)**
- (ii) The potential energy of Y is 16 kJ/mol. **(Correct)**
- (iii) The heat of reaction is 6 kJ/mol. **(Correct)**
- The reaction is endothermic. **(Correct)**

### Final Conclusion
All statements are correct.

---