If for a particular reaction, the difference in the heat evolved when the reaction is carried out at constant pressure and that at constant volume at `27^(@)C` is nearly `5 kJ mol^(-1)` , then the difference in the number of moles of gaseous eactants and products is

Answer

To solve the problem, we need to determine the difference in the number of moles of gaseous reactants and products (Δn_g) based on the difference in heat evolved at constant pressure and constant volume.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The difference in heat evolved at constant pressure (ΔH) and constant volume (ΔU) is given by the equation:
\[ \Delta H - \Delta U = \Delta n_g \cdot R \cdot T \]
where:
- ΔH = heat at constant pressure
- ΔU = heat at constant volume
- Δn_g = difference in the number of moles of gaseous reactants and products
- R = universal gas constant (8.314 J/(mol·K))
- T = temperature in Kelvin

2. **Given Data**:
We know that:
\[ \Delta H - \Delta U = 5 \text{ kJ/mol} = 5000 \text{ J/mol} \]
The temperature is given as 27°C, which we need to convert to Kelvin:
\[ T = 27 + 273 = 300 \text{ K} \]

3. **Substituting Values into the Equation**:
Now we can substitute the values into the equation:
\[ 5000 \text{ J/mol} = \Delta n_g \cdot 8.314 \text{ J/(mol·K)} \cdot 300 \text{ K} \]

4. **Calculating Δn_g**:
Rearranging the equation to solve for Δn_g:
\[ \Delta n_g = \frac{5000 \text{ J/mol}}{8.314 \text{ J/(mol·K)} \cdot 300 \text{ K}} \]
\[ \Delta n_g = \frac{5000}{2494.2} \approx 2.01 \]

5. **Final Result**:
Since Δn_g represents the difference in the number of moles of gaseous reactants and products, we can round this to:
\[ \Delta n_g \approx 2 \]

Thus, the difference in the number of moles of gaseous reactants and products is approximately **2**.