Assuming that the vapor pressure is due entirely to hydrochloric acid,
(a) Show that the HCl component obeys Henry's law in this concentration range; calculate the Henry's law constant.
(b) Predict the vapor pressure of HCl above the solution if the concentration is 0.10 mole HCl / kg GeCl4.
8.3 A solution of 35 mole % aniline and 65 mole % hexane is cooled from a high temperature. Phase separation occurs at 56.5oC. Aniline and hexane obey regular solution theory.
(a) What is the interaction energy Q?
(b) What is the critical solution temperature?
(c) The vapor pressure of pure aniline and pure hexane at 70oC are 0.011 atm and 1.11 atm, respectively. What is the total pressure of a 50 mole % mixture at this temperature?
8.4 Derive the equation for the elevation of the normal boiling point of water in which a nonvolatile solute is present. Assume that Raoult's law applies to the water solvent.
(a) Method 1: Consider the partial pressure of water over the solution to be a function of temperature and mole fraction of the solute, or pw(T,x). Take the differential of pw and set it equal to zero (because the normal boiling point is defined as the condition that pw = 1 atm). Use Eq (5.13) for the vapor pressure of water and where needed, assume x << 1.
(b) Method 2: Use the condition of the equality of the chemical potentials of water in the vapor and in the solution. In evaluating the chemical potentials, the water pressure over the solution is 1 atm for all x. The temperature is T = To + AT, where To is the normal boiling point of pure water and AT is the boiling point elevation. Taylor series approximations may be used because AT/To << 1 and x << 1.
Hint: You will need to use the analog of Eq (3.27b) applied to vapor-liquid equilibrium.
(c) What is AT for a solute mole fraction of 0.04?
8.5 Pure solid A is in equilibrium with an ideal liquid A-B solution. The phase diagram for the system resembles the left hand portion of Fig. 8.11 with Au replaced by A.
(a) Starting from the criterion of chemical equilibrium (i.e. equality of chemical potentials of A), derive the relation for the solubility of A in liquid B (xAL) at a temperature T. The melting point of A is TMA and the enthalpy of fusion of pure A is AhMA.
(b) Alternatively, the equation developed in (a) can be viewed as giving the "melting point" of an solid A-B solution of specified mole fraction of A. By melting point is meant the temperature at which the last solid disappears on heating the alloy.
Pure silver (component A) melts at 962oC and has an enthalpy of fusion of 11.3 kJ/mole. What is the melting point of an alloy with a mole fraction of silver of 0.945, assuming it to be ideal?
(c)The observed melting point of the Ag-Pb solution in (b) is 930oC. Use this information to determine the activity coefficient of Ag in the liquid in which its mole fraction is .945.
(d) Sketch the Ag-rich portion of the phase Ag-Pb diagram and show the Ag-rich liquidus curves that correspond to the ideal solution assumption and to the nonideal case.
8.6 FeO and MnO form ideal liquid and solid solutions. The melting properties of the pure oxides are:
(a) At what temperature does an equimolar solid solution first melt? What is the composition of the first-formed liquid?
(b) At what temperature is melting complete?
8.7 In the phase diagram shown below, a congruently melting compound of A and B is formed at = 0.667.
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