Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

PROBLEMS 412

Problems

An underlined problem number or problem-part letter indicates that the numerical answer appears

in AppendixI.

12.1 Consider the heterogeneous equilibrium CaCO 3 .s/ ï CaO.s/CCO 2 .g/. Table12.3lists
pressures measured over a range of temperatures for this system.

Table 12.3 Pressure of an equilibrium system

containing CaCO 3 (s), CaO(s), and CO 2 (g)a

t=C p=Torr t=C p=Torr

842:3 343:0 904:3 879:0

852:9 398:6 906:5 875:0

854:5 404:1 937:0 1350

868:9 510:9 937:0 1340

aRef. [ 153 ].

(a)What is the approximate relation betweenpandK?

(b)Plot these data in the form lnKversus1=T, or fit lnKto a linear function of1=T. Then,

evaluate the temperature at which the partial pressure of the CO 2 is 1 bar, and the standard

molar reaction enthalpy at this temperature.

12.2 For a homogeneous reaction in which the reactants and products are solutes in a solution,
write a rigorous relation between the standard molar reaction enthalpy and the temperature
dependence of the thermodynamic equilibrium constant, with solute standard states based on
concentration.

12.3 Derive an expression for the standard molar reaction entropy of a reaction that can be used to
calculate its value from the thermodynamic equilibrium constant and its temperature derivative.
Assume that no solute standard states are based on concentration.

Table 12.4 Properties of H 2 O at 1 bar

M tf tb ÅfusH ÅvapH

18:0153g mol^1 0:00C 99:61C 6:010kJ mol^1 40:668kJ mol^1

12.4 Use the data in Table12.4to evaluate the molal freezing-point depression constant and the
molal boiling-point elevation constant for H 2 O at a pressure of 1 bar.

12.5 An aqueous solution of the protein bovine serum albumin, containing2:00 10 ^2 g of protein
per cubic centimeter, has an osmotic pressure of8:1 10 ^3 bar at 0 C. Estimate the molar
mass of this protein.

12.6 Figure12.8on page 393 shows a curve fitted to experimental points for the aqueous solubility
ofn-butylbenzene. The curve has the equation lnxBDa.t=Cb/^2 Cc, where the constants
have the valuesaD3:34 10 ^4 ,bD12:13, andcD 13:25. Assume that the saturated
solution behaves as an ideal-dilute solution, use a solute standard state based on mole frac-
tion, and calculateÅsol,BHandÅsol,BSat5:00C,12:13C (the temperature of minimum
solubility), and25:00C.