The heat of reaction at constant volume `(DeltaE)` and that at constant pressure `(DeltaH)` are related as-

Options

A. `DeltaE=DeltaH+DeltanRT`
B. `DeltaH=DeltaE-DeltanRT`
C. `DeltaH=DeltaE+DeltanRT`
D. `DeltaH=DeltaE+nRT`

Answer

To relate the heat of reaction at constant volume (ΔE) and at constant pressure (ΔH), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Definitions**:
- ΔE (Delta E) represents the change in internal energy of the system.
- ΔH (Delta H) represents the change in enthalpy of the system.

2. **Use the Relationship Between ΔH and ΔE**:
- The relationship between enthalpy (H) and internal energy (E) can be expressed as:
\[ \Delta H = \Delta E + P \Delta V \]
- Here, P is the pressure, and ΔV is the change in volume.

3. **Consider a Reaction Involving Gases**:
- For a reaction involving gases, we can express ΔV in terms of the change in the number of moles of gas (Δn):
\[ \Delta V = V_{\text{products}} - V_{\text{reactants}} = \frac{n_{\text{products}}RT}{P} - \frac{n_{\text{reactants}}RT}{P} \]
- This simplifies to:
\[ \Delta V = RT \Delta n / P \]
- Where Δn is the change in the number of moles of gas (Δn = n_products - n_reactants).

4. **Substituting ΔV into the ΔH Equation**:
- Substitute ΔV back into the equation for ΔH:
\[ \Delta H = \Delta E + P \left( \frac{RT \Delta n}{P} \right) \]
- This simplifies to:
\[ \Delta H = \Delta E + RT \Delta n \]

5. **Final Relationship**:
- Thus, the final relationship between ΔH and ΔE is:
\[ \Delta H = \Delta E + RT \Delta n \]

### Conclusion:
The heat of reaction at constant pressure (ΔH) is related to the heat of reaction at constant volume (ΔE) by the equation:
\[ \Delta H = \Delta E + RT \Delta n \]