The Boiling Point of Water at High Altitude The relationship between the equilibrium vapor pressure of a liquid or solid and temperature is given by the Clausius-Clapeyron equation. In this assignment you will measure the vapor pressure of water at a given temperature and use this data and the Clausius-Clapeyron equation to calculate the boiling point of water on the top of Mt. Denali in Alaska. Assignment The balloon is filled with 0.40 moles of water vapor at a pressure of 1500 Torr and a temperature of 400 K. Click the down arrows in the Live Data Temperature control area until the temperature stops decreasing. This temperature represents the equilibrium temperature where water as a gas exists in equilibrium with water as a liquid. The pressure at this temperature is the vapor pressure. Record the vapor pressure (in Torr) and the temperature (in K) below ππππ π π’ππ = 1500 π‘πππ ππππππππ‘π’ππ = 393.38 πΎ The Clausius-Clapeyron equation may be written in several forms. For this assignment, the most useful form can be written as βπ»π£ππ 1 π2 1 ππ ( ) = − ( − ) π1 π π2 π1 If P1 and T1 are the experimental vapor pressure and temperature that you measured and the pressure at the top of Mt. Denali, P2, is 340 Torr, the boiling point of water, T2, at the top of the mountain can be calculated by solving the Clausius-Clapeyron equation for T2. The value of R is 8.314 J·K-1·mol-1 and ΔHvap for water is 40.67 kJ/mol Calculate the boiling point of water at the top of Mt. Denali. βπ»π£ππ 1 π2 1 ππ ( ) = − ( − ) π1 π π2 π1 π πππππππππ πππ’ππ‘πππ π‘π ππππ π2 π‘βπ π π’πππππ‘ − π π2 1 1 ππ ( ) = ( − ) βπ»π£ππ π1 π2 π1 [− π π2 1 1 ππ ( )] + = βπ»π£ππ π1 π1 π2 πβπππππππ 1 π π2 1 = [− ππ ( )] + π2 βπ»π£ππ π1 π1 π1 = 1500 ππππ, π2 = 340 ππππ, π1 = 393.38 πΎ πππ π2 =? π = 8.314 π½ β πΎ −1 β πππ −1 βπ»π£ππ = 40.67πΎπ½/πππ = 40.67 × 103 π½ β πππ −1 1 8.314 π½ β πΎ −1 β πππ −1 340 ππππ 1 = [− × ππ ( )] + 3 −1 π2 40.67 × 10 π½ β πππ 1500 ππππ 393.38 πΎ 1 1 = [3.034 × 10−4 ]πΎ −1 + π2 393.38 πΎ 1 = (2.8455 × 10−3 )πΎ −1 π2 π2 = 1 (2.8455 × 10−3 )πΎ −1 π2 = 351.4 πΎ Therefore, the boiling point of water on top of Mt. Denali = 351.4 K
