1. Express (∂S/∂V)T = (∂p/∂T)V in terms of &alpha and kT.
2. The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression ΔG/J = -73.1 + 42.8 (T/K). Calculate the value of ΔS for the process.
3. Estimate the change in the Gibbs energy of 1.0 L of benzene when the pressure acting on it increased from 1.0 atm to 100 atm.
4. At 373 K, the second virial coefficient B of xenon is -81.7 cm3 mol -1. Calculate the value of B′ and hence estimate the fugacity coefficient φ of xenon at 50 atm and 373 K.
5. Calculate the change in the molar Gibbs energy of hydrogen gas when its pressure is increased isothermally from 1.0 atm to 100.0 atm at 298 K.
6. Write G as an exact differential. Derive an expression for dG from the fundamental equation. Equating the two expressions, derive formulae for (∂G/∂p)T and (∂G/∂T)p. From these formulae and the definition of the exact differential, derive a Maxwell relation.
7. Write the expression for the equilibrium constant of the reaction H2 + Br2 → 2 HBr in terms of fugacities.
8. The vapour pressure of dichloromethane at 24.1 oC is 400 Torr and its enthalphy of vaporization is 28.7 kJ mol -1. Estimate the temperature at which its vapour pressure is 500 Torr.
9. The vapour pressure of benzene between 10 oC and 30 oC was found to fit the expression log(p/Torr) = 7.960 - 1780/(T/K). Calculate (a) the enthalpy of vaporization and (b) the normal boiling point of benzene.
10. In August in Los Angeles, CA, the incident sunlight at ground level has a power density of 1.2 kW m -2 at noon. A swimming pool of area 50 m 2 is directly exposed to the sun. What is the maximum rate of loss of water assuming all radiation is absorbed?
11. Write the thermodynamic condition for equilibrium between two solid phases, α and β.
12. Draw a pT phase diagram for CO2, carefully labelling the region between 1 and 5.11 atm.
13. The contact angle for water on clean glass is close to zero. Calculate the surface tension of water at 30 oC given that at that temperature the water climbs to a height of 9.11 cm in a clean glass capillary tube of internal diameter 0.320 mm. The density of water at 30 oC is 0.9956 g cm -3.
14. The partial molar volumes of acetone and chloroform in a mixture in which the mole fraction of CHCl3 is 0.4693 are 74.166 cm3mol -1 and 80.235 cm3mol -1, respectively. What is the volume of a solution of mass 1.000 kg?
15. Draw a graph showing a pictorial way of representing the Gibbs energy of a perfect gas as an integral.
16. Derive the Gibbs-Helmoltz equation.
17. Define the chemical potential.
18. Show how the effect of pressure on the melting point depends on the slope of the solid-liquid equilibrium line in the phases diagram.
19. Draw graphs of the chemical potential vs. temperature at (a) a first-order, and (b) second-order, phase transition.
20. What is a super fluid?
© 2003 by Lawrence T. Sein. All rights reserved.
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