If you can show me an example of one problem, I have no idea how to approach this.
Calculate where the number 40.67 came from.
Use the Clapeyron-Clausisus equation. Assuming that delta H vap does not change with temperature, this equation relates the change in vapor pressure and temperature to a substance's enthalpy of vaporization (R is the molar mass constant). Use this relationship and the fact that delta H vap of water at 25 degrees Celsius is 43.99 kJ/mol to calculate the vapor pressure of water at 5,25,50, and 95 degrees Celsius. Your results should be (in order and in Torr)
It's hard to explain a number that doesn't show up in the writing. But I think the 40.67 is the heat vaporization of water although the problem lists it as 43.99.
To calculate the vapor pressure of water at different temperatures using the Clapeyron-Clausius equation, you will need to follow these steps:
1. Gather the necessary information:
- The enthalpy of vaporization for water (∆Hvap) at a specific temperature (in this case, it's given as 43.99 kJ/mol at 25 degrees Celsius).
- The molar mass constant (R), which is 0.0821 L·atm/mol·K.
2. Use the Clapeyron-Clausius equation:
∆Hvap = -R * T * ln(P2/P1)
- ∆Hvap: Enthalpy of vaporization
- R: Molar mass constant
- T: Temperature (in Kelvin)
- P1: Vapor pressure at the first temperature
- P2: Vapor pressure at the second temperature
3. Convert the given temperature values from degrees Celsius to Kelvin:
- 5 degrees Celsius = 278 Kelvin
- 25 degrees Celsius = 298 Kelvin
- 50 degrees Celsius = 323 Kelvin
- 95 degrees Celsius = 368 Kelvin
4. Set up the equations for each temperature using the given enthalpy of vaporization and the Clapeyron-Clausius equation:
- For P2 at 5 degrees Celsius (278 Kelvin):
43.99 kJ/mol = -0.0821 L·atm/mol·K * 278 K * ln(P2/P1)
Solve for P2.
- For P2 at 25 degrees Celsius (298 Kelvin):
43.99 kJ/mol = -0.0821 L·atm/mol·K * 298 K * ln(P2/P1)
Solve for P2.
- For P2 at 50 degrees Celsius (323 Kelvin):
43.99 kJ/mol = -0.0821 L·atm/mol·K * 323 K * ln(P2/P1)
Solve for P2.
- For P2 at 95 degrees Celsius (368 Kelvin):
43.99 kJ/mol = -0.0821 L·atm/mol·K * 368 K * ln(P2/P1)
Solve for P2.
5. Solve each equation for P2 and convert the pressure values from atm to Torr:
The results you're looking for are the vapor pressures calculated using the Clapeyron-Clausius equation for each temperature mentioned (5, 25, 50, and 95 degrees Celsius).