In a hypothetical reaction `X to Y`, the activation energy for the forward and the backward reaction are 15 and `9" kJ mol"^(-1)` respectively. The potential energy of X is `10" kJ mol"^(-1)`. Then

Options

A. Threshold energy of the reaction is 25 kJ
B. The potential energy of Y is 16 kJ
C. Heat of reaction is 6 kJ
D. The reaction is endothermic.

Explanation

To solve the problem step by step, let's analyze the information given and derive the required values.

### Given Data:
1. Activation energy for the forward reaction (E_f) = 15 kJ/mol
2. Activation energy for the backward reaction (E_b) = 9 kJ/mol
3. Potential energy of X (P_x) = 10 kJ/mol

### Step 1: Calculate the Enthalpy Change (ΔH)
The enthalpy change (ΔH) for the reaction can be calculated using the formula:
\[ \Delta H = E_f - E_b \]
Substituting the values:
\[ \Delta H = 15 \, \text{kJ/mol} - 9 \, \text{kJ/mol} = 6 \, \text{kJ/mol} \]
This indicates that the reaction is endothermic since ΔH is positive.

### Step 2: Calculate the Threshold Energy (E_th)
The threshold energy (E_th) is the energy required to initiate the reaction, which can be calculated as:
\[ E_{th} = P_x + E_f \]
Substituting the values:
\[ E_{th} = 10 \, \text{kJ/mol} + 15 \, \text{kJ/mol} = 25 \, \text{kJ/mol} \]

### Step 3: Calculate the Potential Energy of Y (P_y)
To find the potential energy of Y (P_y), we can use the relationship:
\[ E_{th} = E_b + P_y \]
Rearranging gives:
\[ P_y = E_{th} - E_b \]
Substituting the values:
\[ P_y = 25 \, \text{kJ/mol} - 9 \, \text{kJ/mol} = 16 \, \text{kJ/mol} \]

### Summary of Results:
- Enthalpy change (ΔH) = 6 kJ/mol (endothermic reaction)
- Threshold energy (E_th) = 25 kJ/mol
- Potential energy of Y (P_y) = 16 kJ/mol

### Final Answer:
1. The reaction is endothermic with ΔH = 6 kJ/mol.
2. The threshold energy (E_th) = 25 kJ/mol.
3. The potential energy of Y (P_y) = 16 kJ/mol.