Ideal solutions properties

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 ... 

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... 

Liquid solutions are most readily dealt with by excess properties, which are defined for extensive properties and in this case for the Gibbs free energy by the difference between the real solution property G and the ideal solution property G. Eq. (7) is the excess Gibbs free energy. 

Using expressions from 5.1.2 for Lewis-Randall ideal-solution properties and those from 4.1.4 for ideal-gas mixtures, (5.3.1) can be written as... 

In route IB, also shown in Figure 6.1, the required experimental data include mixture volumes, enthalpies, and some amoxmt of phase-equilibrium data. From those data, values for excess properties are extracted and fit to a model for g. However, before excess properties can be found, we must define the ideal solution that is, we must choose the standard state for each component. With the excess-property model plus values for ideal-solution properties, we can then compute property differences for the substance of interest. 

For ideal solutions (xab = 0), AT = (kTllAh ")XA, and the boiling point elevation, like the vapor pressure depression, depends linearly on the concentration of the nonvolatile solute A. Then the increase in the boiling temperature depends on a product of only two terms (1) the solute concentration Xa, and (2) quantities that depend only on the pure state of B, its enthalpy of vaporization and boiling temperature. Because ideal solution properties depend only on the concentration, and not on the chemical character, of the solute, the colligative laws are the analogs of the ideal gas law for dilute solultions. 

The aetivity eoeffieient was introdueed by G. N. Lewis [ 1—4] a eentury ago. As de-seribed by Lewis, the aetivity eoeffieient evolves as a rather eonvenient method for reeoneiling thermodynamie properties of ideal solutions (whieh ean usually be eal-eulated) with those of real solutions (whieh are in most eases inealeulable). Thus, the aetivity eoeffieient provides the bridge by whieh real solution properties ean be expressed in terms of ideal solution properties. Unfortunately, this is often a bridge to nowhere due to the diffieulty of ealeulating the aetivity eoeffieient. 

Derivation of a partial molar Helmholtz free energy equation for an ideal solution will provide a tool by which ideal and real solution behavior can be differentiated. Specifically, we will make use of the fact that the partial molar enthalpy of a real solution will depend on the type and eoncentration of solutes in a solution while for an ideal solution, the partial molar enthalpy for a solute is independent of the solution composition [18]. As a brief proof of this ideal solution property, consider the defining Eq. (12) for the chemical potential of a solute, Y y, in an ideal solution ... 

From earlier discussions, it was found that this free energy difference represents a difference in screened and unscreened partial molar Helmholtz free energies. Thus, the activity coefficient can be seen to result from the partial molar free energy, which is due to the screening of the counter ion atmosphere surrounding each ion in any real solution. This definition is consistent with the view that the activity coefficient predicts electrostatic screening in real solutions or the difference between real and ideal solution properties. 

Excess Function = Real solution property (7, P, x) -Ideal solution property (T, P, x)... 

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