If the activation energy of both the forward and the backward reactions are equal, then change in internal energy is

Options

A. zero
B. `+Ve`
C. `-Ve`
D. cannot be predicted

Answer

To solve the problem, we need to analyze the relationship between activation energy, enthalpy change, and internal energy change in a chemical reaction. Here’s a step-by-step breakdown:

### Step 1: Understand Activation Energy
Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. In this case, we have two activation energies: one for the forward reaction (Ea forward) and one for the backward reaction (Ea backward).

### Step 2: Given Condition
The problem states that the activation energies for both the forward and backward reactions are equal:
\[ E_a \text{ (forward)} = E_a \text{ (backward)} \]

### Step 3: Energy Profile Diagram
To visualize this, we can draw an energy profile diagram. The x-axis represents the progress of the reaction, while the y-axis represents energy.
- The reactants start at a certain energy level.
- The products will also end at the same energy level since the activation energies are equal.

### Step 4: Change in Enthalpy (ΔH)
The change in enthalpy (ΔH) for a reaction is calculated as:
\[ \Delta H = E_a \text{ (forward)} - E_a \text{ (backward)} \]

Since both activation energies are equal, we can substitute:
\[ \Delta H = E_a - E_a = 0 \]

### Step 5: Change in Internal Energy (ΔE)
The change in internal energy (ΔE) is related to the change in enthalpy (ΔH) by the equation:
\[ \Delta E = \Delta H + P\Delta V \]
In this case, we are not considering any volume change (assuming constant pressure and volume), so:
\[ \Delta E = \Delta H \]
Since we found that ΔH = 0, it follows that:
\[ \Delta E = 0 \]

### Conclusion
Therefore, if the activation energy of both the forward and backward reactions are equal, the change in internal energy (ΔE) is:
\[ \Delta E = 0 \]

### Final Answer
The change in internal energy is **0**.

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