Page 312 - Physical Chemistry

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9.67 Show that well below the critical point, the vapor pres- Henry’s law, or neither: (a) x 0.5, x 0.5; (b) x
CCl 4 CH 3 OH CCl 4
sure P of pure liquid i is given by P P°exp( G°/RT), 0.99, x CH 3 OH 0.01; (c) x CCl 4 0.01, x CH 3 OH 0.99; (d) x CCl 4
i
vap
i
where P° 1 bar and G° is the standard Gibbs energy of 0.4, x SiCl 4 0.6.
vap
vaporization. State any approximations made.
9.70 True or false? (a) mix G at constant T and P must be nega-
9.68 State whether each of the following equations applies tive. (b) mix S at constant T and P must be positive. (c) Inter-
to no solutions, to all solutions, to ideal solutions only, to ide- molecular interactions are negligible in an ideal solution.
ally dilute solutions only, or to both ideal and ideally dilute (d) Solute–solute interactions are negligible in an ideally dilute
solutions. (a) G n m ; (b) m m* RT ln x for all com- solution. (e) The standard state of the solute in an ideally
i i i i i i
ponents; (c) m m° RT ln x for all components; (d) V dilute solution is the state of infinite dilution at the T and P of
i i i
; (e) V n V* ; (f ) P x P* for all components; the solution. ( f) When 30.0 mL of a 15.0 weight percent
l
i
i n V i i i m,i i i i
(g) ¢ H 0; (h) ¢ G 0. HCl(aq) solution is added to 50.0 mL of a 15.0 weight percent
mix mix
HCl(aq) solution at constant T and P, the final volume must be
9.69 For each component of each of the following liquid solu-
tions, state whether it will approximately obey Raoult’s law, 80.0 mL.
REVIEW PROBLEMS
R9.1 For a P-versus-T phase diagram of a pure substance R9.7 For each component of each of the following solutions,
how many degrees of freedom are there (a) at the solid– state whether it will approximately obey Raoult’s law, Henry’s
liquid–vapor triple point? (b) along the solid–vapor equilibrium law, or neither. (a) 0.30 mol of CH CH OH plus 0.70 mol
2
3
line? (c) in the liquid region? of H O. (b) 2.50 mol of CH COCH plus 0.01 mol of H O.
2
3
2
3
(c) 0.30 mol of C H CH CH plus 0.85 mol of C H CH .
R9.2 For a gas obeying the truncated virial equation of state 6 5 2 3 6 5 3

V m RT>P B1T2, find the expression for G m for an R9.8 (a) Prove that G i H i TS i . (b) Prove that

isothermal change of pressure from P to P . V i .
1
2
R9.3 The vapor pressure of liquid methane is 0.57 bar at 10m i >0P2 T,n j
for methane in R9.9 Use the equation in Prob. R9.8b to derive the expression
105.0 K and is 0.74 bar at 108.0 K. Find vap H m
this temperature range. Find the normal boiling point of for V i of a component of an ideal gas mixture.
methane. State all approximations made.
R9.10 For each of the following systems, find the number of
R9.4 True or false? (a) In an ideal solution, there are no in- degrees of freedom and give a reasonable choice for the inde-
termolecular interactions. (b) mix G (at constant T and P) must pendent intensive variables. (a) A liquid solution of benzene
be negative when a solution is formed from two pure liquids. and hexane in equilibrium with its vapor. (b) An equilibrium
(c) mix S (at constant T and P) must be negative when a solu- mixture of N (g), H (g), and NH (g) where all the N (g) and
2 2 3 2
tion is formed from two pure liquids. (d ) At pressures below H (g) comes from the dissociation of NH (g). (c) An aqueous
2 3
the pressure of the solid–liquid–vapor triple-point pressure of a solution of the weak acid HF.
pure substance, a stable liquid cannot exist. (e) The solid–vapor
equilibrium line on the P-versus-T phase diagram of a pure sub- R9.11 The change of air pressure with altitude is given by the
2
stance starts at the origin (P 0, T 0). (e) If liquids B and C approximate equation (14.71), where g 9.81 m/s , P
0
form an ideal solution and if P* P* at temperature T, then 760 torr, and M 29 g/mol. A mountain climber finds that the
B
C
the vapor in equilibrium with a liquid solution of B and C at T temperature of boiling water is 90.0°C. What is the altitude of
must have the same composition as the liquid solution. the climber? Use data from Prob. 2.49.
R9.5 (a) State the molecular definition of an ideal solution. R9.12 The volumes of solutions at 25°C and 1 bar that con-
(b) State the thermodynamic definition of an ideal solution. tain 1000 g of A and n moles of B are given by V a
B
2
(c) State the molecular definition of an ideally dilute solution. bn cn B en B 3 , where a, b, c, and e are constants. Find
B
(d) State the thermodynamic definition of an ideally dilute expressions for V B and V A for solutions of B and A at 25°C
solution. and 1 bar.
l
R9.6 An ideal solution of liquids B and F with x B 0.400 at R9.13 Find the pressure at which the melting point of ice is
25°C has a vapor pressure of 139 torr and a vapor composition 0.80°C. Use data from Prob. 2.49. State all approximations
v
of x B 0.650. Find the vapor pressures of pure B and of pure made.
F at 25°C.