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See Chap 7 for information on temperature-pressure phase relations, equation of state, gas mixture, and Gibb s phase rule Ideal Solutions The activity of each constituent of ideal liquid solutions is equal to its mole fraction under all conditions of temperature, pressure, and concentration The total volume of the solution exactly equals the sum of the volumes of its components The enthalpy when the components are mixed is zero The total vapor pressure is the sum of the contribution of the individual components following Raoult s law: the vapor pressure contribution of each individual component is the product of its mole fraction and the vapor pressure of the pure component This also applies to the vapor pressure of solutions containing nonvolatile components The freezing point of the solvent in ideal solutions occurs at the temperature where the vapor pressure of the solution equals the vapor pressure of the solid solvent Real Solutions Actual liquid solutions are seldom ideal, often showing deviations from the conditions of ideality described above Most signi cant are positive or negative deviations in the direct summation of vapor pressure component contributions; these affect distillation behavior in the separation of components Deviations from ideality increase with solute concentration; ie, dilute solutions behave reasonably ideally Henry s Law At a constant temperature, the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid Raoult s Law This states that pa where pa xa Pa xaPa (421)

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ApplicationException Array Console GC Math Object OperatingSystem String SystemException UInt32 Table D-1

partial pressure of component A in vapor mole fraction of A in liquid solution vapor pressure of pure liquid A

A parent class for non-terminating program errors Methods for creating, searching, and sorting arrays Standard input, output, and error streams These are used for console applications A class for controlling the system garbage collector Methods for common mathematical functions See the The Math Class section that follows for more details The parent class of every class A class that provides information about the operating system version and the like An immutable set of characters The base class for predefined exceptions A structure that represents 32-bit unsigned integers

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* Parts of this section are based on material taken from Technicka hemnija (Chemistry for Engineers 1984 by the author Parts are also taken from Elementary Lecture Notes); by E N Ganic Copyright 1978 Used by Principles of Chemical Processes, by R M Felder and R W Rousseau Copyright permission of Wiley All rights reserved

Figure D-5

Binary Solution Vapor-Liquid Equilibria In the vapor phase: Ptotal ntotal yi yi yi pi ni pi Ptotal 1 pj nj (422)

where pi is the partial pressure, yi is the mole fraction, and ni is the number of moles of i In the liquid phase: xi xi xj ntotal ni ntotal 1 ni nj (423)

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This summary page also shows you how safe the code is to use in multithreaded operations Notice, as well, that the platforms are listed on this page, along with the assembly in which the class is found (in this case Mscorlibdll) If you are interested in checking out the properties and methods that are available for use in this class, click the Math Members link You will see a screen that looks like the one in Figure D-6 There are two fields, E and PI, that are listed, along with their purpose As you can see from the list, there are many public methods in the Math class We will select one, the Round() method, in order to dig deeper into this documentation The Round() method is used to return the integer nearest to the number given, following the rules of rounding For example, the following code segment returns 12

where xi is the mole fraction of i Ideal Solutions Each component of an ideal solution obeys Raoult s law [Eq (421)] relating concentrations in vapor and liquid phases Real Solutions Numerical distillation calculations often use a vapor-liquid equilibrium ratio k for each component: ki yi xi of pure i at its vapor pressure at T of the system of pure i at T, P of the system (424)

using System; class Rounding { public static void Main() { ConsoleWriteLine (MathRound(1242)); } }

The volatility ratio between components of binary solutions is: ki kj yi xj xi yi (425)

Figure D-6

where is the volatility ratio For ideal binary solutions, where is constant, manipulation of Eqs (424) and (425) relates mole fraction in the vapor phase yi to volatility ratio and mole fraction in the liquid phase xi: yi 1 xi xi( 1) (426)

Binary Solution Vapor Pressure Composition Diagrams Ideal Solutions These follow Raoult s law [Eq (421)] As shown in Fig 45a, the vapor pressure of each component is linear and proportional to the mole fraction, and the vapor pressure of the mixture is the simple sum of the component vapor pressures The diagrams shown represent one xed temperature

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