H = E + PV

Enthalpy Change in Isothermal Expansion of Ideal Gas

Given:
- Number of moles of gas = 2
- Initial volume = 1 L
- Final volume = 10 L
- Temperature = 300 K

Formula:
For an ideal gas, the enthalpy change during an isothermal process is given by the equation:
ΔH = 0

Explanation:

1. Ideal Gas Law:
The ideal gas law equation is given by:
PV = nRT

Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the ideal gas constant
- T is the temperature of the gas

2. Isothermal Process:
In an isothermal process, the temperature remains constant. Therefore, the equation can be simplified to:
PV = constant

3. Enthalpy Change:
The enthalpy change (ΔH) is given by the equation:
ΔH = q + w

Where:
- q is the heat transferred to or from the system
- w is the work done by or on the system

4. Isothermal Expansion:
During an isothermal expansion, the gas does work on the surroundings. This work is given by the equation:
w = -PΔV

Where:
- P is the pressure of the gas
- ΔV is the change in volume of the gas

5. Enthalpy Change in Isothermal Expansion:
Substituting the work equation into the enthalpy change equation, we get:
ΔH = q - PΔV

Since the process is isothermal, the temperature remains constant. Therefore, there is no change in internal energy (ΔU = 0). Hence, the heat transferred (q) is equal to the work done (w).

Therefore, ΔH = q - PΔV = w - PΔV = -PΔV - PΔV = -2PΔV

6. Calculation:
In this case, the initial volume (V1) is 1 L and the final volume (V2) is 10 L. Therefore, the change in volume (ΔV) is given by:
ΔV = V2 - V1 = 10 L - 1 L = 9 L

Substituting the values into the equation, we get:
ΔH = -2PΔV = -2 * nRT * ΔV / V = -2 * 2 * 8.314 J/mol·K * 300 K * 9 L / 1 L = -8980.272 J

Converting the value to kJ:
ΔH = -8.980272 kJ

Since the value is negative, it indicates that the system has lost energy to the surroundings. However, the question asks for the enthalpy change, not the energy change. In an isothermal process, the enthalpy change is zero, as there is no change in heat transfer. Therefore, the correct answer is 0 kJ.