Understanding the Concepts
* Vaporization: This is the process of a liquid changing into a gas.
* Work Done: In thermodynamics, work done by a system is the energy transferred by the system due to a change in volume. For an ideal gas, this is calculated as:
* W = -PΔV (where P is pressure and ΔV is the change in volume)
* Ideal Gas Law: PV = nRT (where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is temperature)
Calculations
1. Determine the Initial Volume:
* Since water is a liquid, we can ignore its initial volume.
2. Determine the Final Volume (Volume of Water Vapor):
* Use the ideal gas law to find the volume of 1 mole of water vapor at 273 K and 1 atm pressure.
* V = (nRT)/P = (1 mol * 0.0821 L·atm/mol·K * 273 K) / 1 atm ≈ 22.4 L
3. Calculate the Change in Volume:
* ΔV = Final Volume - Initial Volume ≈ 22.4 L - 0 L = 22.4 L
4. Calculate Work Done:
* W = -PΔV = -(1 atm) * (22.4 L) ≈ -22.4 L·atm
Conversion to Joules
* 1 L·atm = 101.325 J
* Therefore, W ≈ -22.4 L·atm * 101.325 J/L·atm ≈ -2270 J
Important Note: This calculation assumes the vaporization process occurs at constant pressure (isobaric).
Conclusion
The work done when 1 mole of water vaporizes against atmospheric pressure at 273 K is approximately -2270 J. The negative sign indicates that work is done *by* the system (the water vapor) on the surroundings (the atmosphere).
