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`

Explanation

To find the relationship between the heat of reaction at constant volume (ΔE) and at constant pressure (ΔH), we start with the definitions of these two terms:

1. **Definitions**:
- ΔE (change in internal energy) is the heat of reaction at constant volume.
- ΔH (enthalpy change) is the heat of reaction at constant pressure.

2. **Basic Relationship**:
The relationship between ΔH and ΔE can be expressed as:
\[ \Delta H = \Delta E + P \Delta V \]
where P is the pressure and ΔV is the change in volume.

3. **Using Ideal Gas Law**:
For reactions involving gases, we can express the change in volume in terms of the change in the number of moles of gas (ΔN):
\[ \Delta V = \frac{\Delta NRT}{P} \]
where R is the gas constant and T is the temperature.

4. **Substituting ΔV**:
Substituting ΔV into the equation gives:
\[ \Delta H = \Delta E + P \left(\frac{\Delta NRT}{P}\right) \]
Simplifying this, we get:
\[ \Delta H = \Delta E + \Delta NRT \]

5. **Rearranging the Equation**:
To express ΔE in terms of ΔH, we rearrange the equation:
\[ \Delta E = \Delta H - \Delta NRT \]

6. **Final Relationship**:
Thus, the final relationship between ΔH and ΔE is:
\[ \Delta H = \Delta E + \Delta NRT \]

### Summary of the Relationship:
The heat of reaction at constant pressure (ΔH) is equal to the heat of reaction at constant volume (ΔE) plus the product of the change in the number of moles of gas (ΔN), the gas constant (R), and the temperature (T).