Page 114 - Modern physical chemistry

104 Entropy and the Second Law

5.16 How do symmetry considerations let us relate the number of microstates in a macrostate
(a) to the statistical weight of the macrostate and (b) to the entropy?
5.17 What is the third law of thermodynamics?
5.18 Define and interpret the Helmholtz free energy.
5.19 Define and interpret the Gibbs free energy.
5.20 Describe how the key thermodynamic properties of a closed uniform system are related.
5.21 Define the chemical potential of a constituent whose mass can vary independently in a homo-
geneous uniform region.
5.22 How do E, H, A, and G vary in an open uniform system?
5.23 Explain why the chemical potential is given by the partial molar Gibbs energy.
5.24 What does a concentration gradient cause?
5.25 How is the corresponding diffusion coefficient defined? What is Fick's law?
5.26 Describe the thermodynamic force that causes diffusion.
5.27 How is the chemical potential related to the activity of a constituent?
5.28 Construct the Einstein-Stokes expression for the diffusion coefficient.
5.29 Why do we generally have AS total ?: O?
5.30 Under what circumstances is (a) M ?: 0, (b) tlG?: O?
5.31 What is the fourth law of thermodynamics?

Problems
5.1 Calculate the entropy change of 1.000 g helium when it is heated from 25° to 125° (a) at con-
stant volume, (b) at constant pressure.
5.2 If 1.000 mol helium is compressed reversibly and adiabatically from 22.4 I at 0° C to 2.24 1,
what is AS?
5.3 Calculate the entropy change when 10.00 g potassium is fused at its melting point, 336.35
K, where its heat of fusion is 2343 J mol-i.
5.4 At their melting points, the entropy of fusion of chlorine is 37.20 J Ki mo}"i , that of iodine
40.12 J K! mo}"! . Estimate the entropy of fusion and then the heat of fusion of bromine at
its melting point 265.9 K
5.5 A resistor is kept at 30° C by a stream of cooling water while 10,000 J of work is dissipated
in it. ( a) What is the change in entropy of the resistor? (b) What is the change in entropy of
the water if it leaves the resistor at 25° C?
5.6 One kilogram water at 0° C contacts a large heat reservoir at 100° C and the water warms
up to 100° C. Consider the specific heat of the water to be 1.000 and calculate the entropy
change ( a) of the water, (b) of the heat reservoir, and (c) of both.
5.7 Calculate the entropy of mixing 0.200 mol oxygen with 0.800 mol nitrogen at 25° C.
5.8 One mole benzene is vaporized at so. 1 ° C and 1.000 atm, its boiling point, where the heat
of vaporization is 393.7 J g-! Calculate (a) AS, (b) tlG, and (c) M.
5.9 Calculate Wrev for the electrolysis of 1.000 mol HP at 1.00 atm and 25° C, assuming that tlG
for the decomposition of H 20 is 237.14 kJ mo}"!.
5.10 Assuming that the liquid is incompressible, calculate tlG when the pressure on 1.000 mol
H20 is increased from 1.00 atm to 20.0 atm at 25° C.
5.11 Calculate tlG when the pressure on 10.0 mol ideal gas is reduced from 10.0 atm to 1.00 atm
at 25° C.
5.12 Show that
( aA) _ p(av)
ap -- aPT·
T
5.13 Show that
[ aH) =T[as) + v.
aPT
aPT

5.14 How much would the pressure on 1.000 mol argon initially at 0° C and 1.000 atm have to be
raised to keep the entropy constant when the temperature was raised to 150° C?