FME 522 – THERMODYNAMICS V
TUTORIAL 2 (Thermodynamics of state)
Clausius-Clapeyron Equation
1. Calculate ΔHvap for ethanol, given vapor pressure at 40oC = 150 torr. The normal boiling point for
ethanol is 78oC (39 kJ/mole)
2. Dry ice (solid CO2) has a vapor pressure of 1.00 atm at -72.25°C and 2.00 atm at -69.12°C. Calculate
the ΔH of sublimation for solid CO2. (75.5 kJ/mole)
3. The vapor pressure of diethyl ether is 100.0 torr at -11.5°C and 400.0 torr at 17.9°C. Calculate the
enthalpy of vaporization of diethyl ether. (29.9 kJ/mole)
4. The vapor pressure of liquid bromine (Br 2) at 9.30°C is 100.0 torr and enthalpy of vaporization is 30.91
kJ/mole. Calculate the normal boiling point of Br 2. (334K or 61°C)
5. Using the data from Q2, calculate the normal boiling point of diethyl ether. (307 K or 33.9°C)
6. The heat of vaporization of water is 44.01 kJ/mole and the normal boiling point is 100°C. Calculate the
atmospheric pressure in Denver where the boiling point of water is 97.10°C. (680 torr)
7. Using the data from Q2 & 4 calculate the pressure on top of Mt. Whitney (14,495 ft above sea level)
where the boiling point of diethyl ether is 22.00° C. (475 torr)
8. Calculate the melting point of ice under a pressure of 50 bar given that the melting point at 1 bar is 0°C.
Assume that the density of ice under these conditions is 0.92 g/mL and the density of liquid water is
1.00 g/mL. The molar enthalpy of fusion of water is 6.01 kJ/mol. (272.8 K or -0.35° C)
9. If it takes an increase of 1.334 megabars of pressure to change the melting point of a substance from
222°C to 122°C for a change in molar volume of –3.22 cm3/mol, what is the molar enthalpy of fusion
of the substance in J/mol? (2.127 × 106 J/mol. or 2127 kJ/mol.)
10. The vapor pressure of liquid benzene obeys the relation
𝑙𝑛 𝑃 = 29.411 −
11.
12.
13.
14.
5893.5
𝑇
,
where the pressure is in torr and temperature is in Kelvin. Calculate the molar enthalpy of vaporization
of benzene and the normal boiling point. (49 kJ/mol; 258.7 K or -14.45°C)
At what pressure does the boiling point of water become 300°C? If oceanic pressure increases by 1
atm for every 10 m, to what ocean depth does this pressure correspond? (142 atm, 1420 m)
The sublimation pressures of solid Cl2 are 352 Pa at –112°C and 35 Pa at –126.5°C. The vapor pressures
of liquid Cl2 are 1590 Pa at –100°C and 7830 Pa at –80°C. Calculate the molar enthalpies of
sublimation, vaporization, and fusion. (31.28 kJ/mol.; 22.16 kJ/mol; 9.12 kJ/mol)
Freon-12 (CF2Cl2) was commonly used in spray cans prior to the discovery that it was harmful to the
ozone layer. Its enthalpy of vaporization is 20.25 kJ/mol and its normal boiling point is –29.2°C.
Determine the vapor pressure of Freon-12 at 40°C. (9.08 atm.)
The vapour pressure of solid uranium hexafluoride, UF 6 follows the equation
5893.5
𝑇
Where the pressure is in Pa and temperature is in kelvin. The vapour pressure of liquid Uranium
hexafluoride follows the equation
3479.9
ln 𝑃 = 22.254 −
𝑇
𝑙𝑛 𝑃 = 29.411 −
Determine the temperature and pressure of the triple point (337.24K; 1.526×10 5 Pa)
15. The vapor pressure of liquid mercury is 0.133 bar at 260°C and 0.533 bar at 330°C. Assume that the
mercury vapor can be treated as an ideal gas and that the enthalpy of vaporization is independent of
temperature. Calculate the molar enthalpy and the molar Gibbs free energy of vaporization at 25°C.
(53.02 kJ/mol; 28.36 kJ/mol.)
Note:
The Clausius-Clapeyron equation can be expressed as follows for various co-existence lines:
a) Solid-liquid phase equilibrium:
𝑑𝑃
𝑑𝑇
=
∆𝐻𝑓𝑢𝑠,𝑚
𝑇𝑓𝑢𝑠 ∆𝑉𝑚
b) Liquid-vapour phase equilibrium:
ln 𝑃 = −
∆𝐻𝑣𝑎𝑝,𝑚
+𝐶
𝑅𝑇
c) Solid – vapour phase equilibrium:
ln 𝑃 = −
∆𝐻𝑠𝑢𝑏,𝑚
+𝐶
𝑅𝑇
Where temperature is in Kelvin, and Pressure can be in any units. m denotes molar, fus. denotes fusion, vap
denotes vaporization and sub denotes sublimation.