6 solution


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T. Y. Tan 1 6. BINARY SOLUTIONS OF CONDENSED MATTER A solution is a single-phase material containing more than one component, which may be a gas, a liquid, or a solid. Gases are in general miscible in all proportions so that practically all gases, at equilibrium, are solutions. Liquids can often dissolve a wide variety of gases, solids, or other liquids. The composition of these liquid solutions can be varied over a wide or narrow range, depending on the solubility relationships in the particular system. Solid solutions are formed when a gas, a liquid, or another solid dissolves in a solid. They are often characterized by having a limited concentration range, although pairs of solids, e.g., Cu/Ni and Si/Ge, are known to be mutually soluble in all proportions. The behavior of gaseous solutions are approximated well by that of ideal gases, for which a sufficiently accurate description is given by Dalton's law of partial pressures: in the same volume V, for n i moles of each gas with partial pressure P i , P i V = n i RT , the total pressure of the solution or gas mixture is P = P i i . The behavior of condensed matter solutions is considerably more complicated than that of ideal gases. In this chapter the behavior, models, and Gibbs free energy curves of binary con- densed matter solutions are discussed. 6.1 Raoult's Law and the Ideal Solution Model From experimental point of view, a condensed matter solution is ideal if its external vapor pressure of each component is proportional to the concentration of that component in the solu- tion, since then the solution behavior is a direct analogy to that of a mixture of ideal gases. It will be discussed in the next chapter that, in thermal equilibrium, a condensed matter cannot exist alone but can only co-exist with vapor phases of its constituent components. The equilibrium va- por pressures of the components of a solution of condensed matter are important measures of the state of affairs in the solution. From studies of the properties of these vapor phases we can obtain a description of the properties of the solution.
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T. Y. Tan 2 The law of behavior of an ideal solution was first described, based on experimental vapor pressure data, by Francois Marie Raoult in 1886. It is expressed as P i = x i P i o . (6.1) Here P i is the partial vapor pressure of component i whose fractional concentration in the solu- tion is x i , and P i o is P i when x i =1 holds. Equation (6.1) is known as the Raoult's law. All solutions containing different isotopes of the same atomic species follow Raoult's law perfectly. However, when containing components differing chemically, there are very few solutions follows Raoult's law even just closely. An example of such a rare case, the solution composed of ethylene- bromide (C 2 H 4 Br 2 ) and propylene-bromide (C 3 H 6 Br 3 ), is shown in Fig. 8.1.
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This note was uploaded on 07/13/2011 for the course ME 218 taught by Professor Dr.tan during the Fall '11 term at Duke.

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