Assumptions:
* Constant Pressure: We'll assume the vaporization occurs at constant atmospheric pressure.
* Ideal Gas Behavior: We'll assume the vapor behaves ideally.
Key Concepts:
* Work (w): In this case, the work done is due to expansion against the constant atmospheric pressure. For an ideal gas, the work is calculated as: `w = -P * delta V` where:
* `P` is the external pressure (atmospheric pressure).
* `delta V` is the change in volume during vaporization.
* Internal Energy (delta E): This represents the change in the total energy of the system. For a process at constant pressure, it can be related to enthalpy (delta H) by: `delta E = delta H - P * delta V`
* Enthalpy of Vaporization (delta Hvap): This is the amount of heat required to vaporize one mole of liquid at its boiling point.
Calculations:
1. Work (w):
* The change in volume (delta V) is the difference in volume between the vapor and the liquid. Since the liquid volume is negligible compared to the vapor volume, we can approximate `delta V` as the volume of one mole of the vapor.
* Using the ideal gas law (`PV = nRT`), we can calculate the volume of the vapor: `V = nRT/P`.
* Substituting into the work equation: `w = -P * (nRT/P) = -nRT`
* For one mole (n = 1): `w = -RT`.
2. Internal Energy (delta E):
* Using the relationship `delta E = delta H - P * delta V`, we can substitute:
* `delta E = delta Hvap - (-nRT)`
* For one mole: `delta E = delta Hvap + RT`
Key Points:
* Sign Conventions: Work done by the system (expansion) is negative.
* Enthalpy of Vaporization: The value of `delta Hvap` is a specific property of the substance and will need to be looked up.
* Temperature: The temperature 'T' must be in Kelvin.
Example:
Let's say the enthalpy of vaporization of water is 40.7 kJ/mol and its boiling point is 100°C (373 K). We can calculate:
* `w = -RT = -(8.314 J/mol*K) * (373 K) = -3100 J/mol`
* `delta E = delta Hvap + RT = (40.7 kJ/mol) + (8.314 J/mol*K) * (373 K) = 43.6 kJ/mol`
Conclusion:
When one mole of liquid is vaporized at its boiling point:
* The work done by the system (w) is negative, indicating expansion.
* The change in internal energy (delta E) is positive, indicating that the system has absorbed energy.
Let me know if you'd like to calculate these values for a specific substance!
