Page 258 - Physical Chemistry

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PROBLEMS

Section 7.1 7.8 (a) For pure liquid water, calculate c ind and f if we con-

7.1 True or false? (a) Since the three possible phases are sider that the chemical species present are H O, H , OH , and
2
solid, liquid, and gas, the maximum possible value of the num- hydrogen-bonded dimers (H O) formed by the association re-
2
2
ber of phases p in the phase rule is 3. (b) The number of degrees action 2H O ∆ (H O) . (b) What happens to c ind and f if we
2
2
2
of freedom f is the number of variables needed to specify the add hydrogen-bonded trimers (H O) to the list of species?
3
2
thermodynamic state of a system.
7.9 Find the relation between f, c , and p if (a) rigid, perme-
ind
7.2 For each of the following equilibrium systems, find the able, thermally conducting walls separate all the phases of a
number of degrees of freedom f and give a reasonable choice of system; (b) movable, impermeable, thermally conducting walls
the independent intensive variables. (Omit consideration of separate all the phases of a system.
water ionization.) (a) An aqueous solution of sucrose. (b) An
aqueous solution of sucrose and ribose. (c) Solid sucrose and an Section 7.2
aqueous solution of sucrose and ribose. (d) Solid sucrose, solid 7.10 True or false? (a) The normal boiling point is the tem-
ribose, and an aqueous solution of sucrose and ribose. (e) Liq- perature at which the vapor pressure of a liquid equals 1 atm.
uid water and water vapor. ( f ) An aqueous sucrose solution (b) At the critical point of a pure substance, the densities of the
and water vapor. (g) Solid sucrose, an aqueous sucrose solution, liquid and the vapor are equal. (c) The minimum possible value
and water vapor. (h) Liquid water, liquid benzene (these two of f in the phase rule is 1. (d) The normal boiling point of pure
liquids are essentially immiscible), and a mixture of the vapors water is precisely 100°C. (e) The enthalpy of vaporization of a
of these two liquids. liquid becomes zero at the critical point. (f) Along a line in
a one-component phase diagram, f 1. (g) At the solid–
7.3 (a)Ifa system has c independent components, what is
ind liquid–gas triple point of a one-component system, f 0. (h) CO
the maximum number of phases that can exist in equilibrium? 2
has no normal boiling point. (i) Ice melts above 0.00°C if the
(b)In the book Regular Solutions by J. H. Hildebrand and
pressure is 100 torr.
R. L. Scott (Prentice-Hall, 1962), there is a photograph of a sys-
tem with 10 liquid phases in equilibrium. What must be true 7.11 For each of the following conditions, state which phase
about the number of independent components in this system? (solid, liquid, or gas) of H O has the lowest chemical potential.
2
(a) 25°C and 1 atm; (b) 25°C and 0.1 torr; (c) 0°C and 500 atm;
7.4 (a) For an aqueous solution of H PO , write down the
3 4 (d) 100°C and 10 atm; (e) 100°C and 0.1 atm.
reaction-equilibrium conditions and the electroneutrality condi-
tion. What is f? Give a reasonable choice for the independent 7.12 For the H O phase diagram of Fig. 7.1a, state the num-
2
intensive variables. (b) For an aqueous solution of KBr and ber of degrees of freedom (a) along the line AC; (b) in the liq-
NaCl, write down the stoichiometric relations between ion uid area; (c) at the triple point A.
mole fractions. Does the electroneutrality condition give an
7.13 The vapor pressure of water at 25°C is 23.76 torr. (a) If
independent relation? What is f?
0.360 g of H O is placed in an empty rigid container at 25°C
2
7.5 Find f for the following systems and give a reasonable with V 10.0 L, state what phase(s) are present at equilibrium
choice for the independent intensive variables: (a) a gaseous and the mass of H O in each phase. (b) The same as (a), except
2
mixture of N , H , and NH with no catalyst present (so that the that V 20.0 L. State any approximations you make.
2
3
2
rate of reaction is zero); (b) a gaseous mixture of N , H , and
2
2
NH with a catalyst present to establish reaction equilibrium; 7.14 Ar has normal melting and boiling points of 83.8 and
3
(c) the system of (b) with the added condition that all the N and 87.3 K; its triple point is at 83.8 K and 0.7 atm, and its critical
2
H must come from the dissociation of the NH ; (d) A gas- temperature and pressure are 151 K and 48 atm. State whether
2
3
phase mixture of N and N in reaction equilibrium with the con- Ar is a solid, liquid, or gas under each of the following condi-
2
dition that all the N comes from the dissociation of N ; (e) a tions: (a) 0.9 atm and 90 K; (b) 0.7 atm and 80 K; (c) 0.8 atm
2
system formed by heating pure CaCO (s) to partially decom- and 88 K; (d) 0.8 atm and 84 K; (e) 1.2 atm and 83.5 K; (f) 1.2 atm
3
pose it into CaO(s) and CO (g), where, in addition, some of and 86 K; (g) 0.5 atm and 84 K.
2
each of the solids CaCO and CaO has sublimed to vapor. (No 7.15 Figure 3.7 shows a reversible isobaric path from liquid
3
CaO or CO is added from the outside.) water at 10°C and 1 atm to ice at 10°C and 1 atm. Use
2
7.6 In the HCN(aq) example in Sec. 7.1, the relation n H Fig. 7.1 to help devise a reversible isothermal path between
n OH n CN was considered to be an electroneutrality relation. these two states.
Show that this equation can be considered to be a stoichiome- 7.16 For each pair, state which substance has the greater
try relation. H at its normal boiling point: (a) Ne or Ar; (b) H O or
vap m 2
H S; (c) C H or C H .
7.7 For a system of NaCl(s) and NaCl(aq) in equilibrium, find 2 2 6 3 8
f if the solid is considered to consist of the single species NaCl 7.17 The normal boiling point of CS is 319.4 K. Estimate
2
and the solute species present in solution (a) is considered to be H and S of CS at the normal boiling point using
vap
2
vap m
m

NaCl(aq); (b) are taken to be Na (aq) and Cl (aq). (a)Trouton’s rule; (b) the Trouton–Hildebrand–Everett rule.