Property changes of mixing

All three quantities are for the same T, P, and physical state. Eq. (4-126) defines a partial molar property change of mixing, and Eq. (4-125) is the summability relation for these properties. Each of Eqs. (4-93) through (4-96) is an expression for an ideal solution property, and each may be combined with the defining equation for an excess property (Eq. [4-99]), yielding ... 

Property changes of mixing and excess properties find greatest application in the description of hqnid mixtures at low reduced tempera-... 

Whereas the fundamental residual property relation derives its usefulness from its direct relation to experimental PHT data and equations of state, the excess property formulation is useful because 1 E, HE, and y are all experimentally accessible. Activity coefficients are found from vapor—liquid equilibrium data, and T E and HE values come from mixing experiments. Property changes of mixing are defined by the equation,... 

Extensive properties of multicomponent phases (solutions) are related to the amount of material in the phase, but may not be just the sum of the properties of the constituent components. Probably the best known example of this difference is the observation that mixing 1.0 L of ethanol with 1.0 L of water at standard temperature and pressure (STP) produces 1.93 L of water-ethanol solution. We define the difference between an extensive property of the solution and the sum of the properties of its pure components as the property change of mixing for the solution ... 

In each of these equations there appears to the right of the equals sign a difference that is expressed in general as Af - XfM,. We call this quantity a property change of mixing and give it the symbol AM Thus by definition,... 

Upon mixing of pure components, the thermodynamic properties change as shown by A. In Eqs. (1.201)—(1.204), we have the property change of mixing... 

Molar or unit-mass value of any extensive property of pure species i Partial molar property of species i in solution Property change of mixing Standard property change of reaction j Mass... 

All three quantities are for the same T, F, and physical state. Eq. (4-126) defines a partial molar property change of mixing, and Eq. (4-125) is the summabihty relation for these properties. 

The first two tenns on the right side of each equation express a difference liaving the form, M — These quantities are property changes of mixing, symbol AM. By definition. 

Figure 12.13 illustrates the composition dependence of AG, AH, and T AS for six binary liquid systems at 323.15 K (50°C) and approximately atmosphericpressure. The related quantities G , H , and FS are shownfortlie same systemsinFig. 11.4. As witlitlie excess properties, property changes of mixing exliibit diverse beliavior, but again all systems liave certain common features ...

Figure 12.13 Property changes of mixing at 323.15 K (50°C) for six binary liquid systems (a) chloroform(1)/n-heptane(2) (b) acetone(1)/methanoi(2) (c) acetone(1)/chloroform(2) ( dj ethanol 1) -heptane(2) (e) ethanol(1)/chloroform(2) (f) ethanol(1)/water(2).

The relations between excess properties and property changes of mixing (Sec. 12.3) facilitate discnssionof the molecular phenomena which give rise to observed excess-property behavior. An essential coimectionis provided by Eq. (12.33), which asserts the identity of and AH. Tims we focus on the mixing process (and hence on for explainingthe behavior of. ... 

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