For a reaction `A rarr B, E_(a) = 10 kJ mol^(-1), DeltaH = 5 kJ mol^(-1)`. Thus, potential energy profile for this reaction is:

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Answer

To solve the problem regarding the potential energy profile for the reaction \( A \rightarrow B \) with given values of activation energy (\( E_a = 10 \, \text{kJ mol}^{-1} \)) and enthalpy change (\( \Delta H = 5 \, \text{kJ mol}^{-1} \)), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Activation Energy (\( E_a \))**: This is the minimum energy required for a reaction to occur. The given \( E_a = 10 \, \text{kJ mol}^{-1} \) is for the forward reaction.
- **Enthalpy Change (\( \Delta H \))**: This indicates whether a reaction is exothermic or endothermic. A positive \( \Delta H = 5 \, \text{kJ mol}^{-1} \) means the reaction is endothermic.

2. **Determine the Activation Energy for the Backward Reaction**:
- We can use the relationship:
\[ \Delta H = E_a^{\text{forward}} - E_a^{\text{backward}} \]
- Plugging in the values:
\[ 5 = 10 - E_a^{\text{backward}} \]
- Rearranging gives:
\[ E_a^{\text{backward}} = 10 - 5 = 5 \, \text{kJ mol}^{-1} \]

3. **Sketch the Potential Energy Profile**:
- On the y-axis, represent potential energy.
- Start with the potential energy of reactant \( A \) at a certain level.
- Draw a peak at the activation energy for the forward reaction, which is \( 10 \, \text{kJ mol}^{-1} \) above the energy level of \( A \).
- From the peak, drop down to the energy level of product \( B \). Since \( \Delta H = 5 \, \text{kJ mol}^{-1} \), the energy level of \( B \) will be \( 5 \, \text{kJ mol}^{-1} \) higher than that of \( A \).

4. **Label the Diagram**:
- Label the starting point as \( A \), the peak as the transition state, and the endpoint as \( B \).
- Indicate the activation energy for the forward reaction (\( E_a^{\text{forward}} = 10 \, \text{kJ mol}^{-1} \)) and the activation energy for the backward reaction (\( E_a^{\text{backward}} = 5 \, \text{kJ mol}^{-1} \)).

5. **Conclusion**:
- The potential energy profile illustrates that the reaction is endothermic, as the products are at a higher energy level compared to the reactants.