Solution of Thermodynamics: Theory and applications Chemical Engineering Thermodynamics Chapter 9 Solution of Thermodynamics: Theory and applications

Chapter Outline 9.1 Fundamental Property Relation 9.2 The Chemical Potential and Phase Equilibria 9.3 Partial Properties of Solution 9.4 Ideal Gas Mixture 9.5 Fugacity and Fugacity Coefficient: Pure Species and Species in Mixture/Solution 9.6 Fugacity Coefficient of Gas Mixture from the Virial Equation of State 9.7 Ideal Solution and Excess Properties 9.8 Liquid Phase Properties from VLE data 9.9 Property Changes of Mixing 9.10 Heat Effects of Mixing Process

Multi-component gases and liquids commonly undergoes composition changes by separation and mixing processes. This chapter gives the thermodynamics applications of both gas mixtures and liquid solutions.

9.1 Fundamental Property Relation The definition of the chemical potential of species i in the mixture of any closed system: the Gibbs energy which is the function of temperature, pressure and number of moles of the chemical species present.

9.2 The Chemical Potential and Phase Equilibria For a closed system consists of 2 phase in equilibrium, the mass transfer between phases may occur. At the same P and T, the chemical potential of each species of multiple phases in equilibrium is the same for all species.

9.3 Partial Properties in Solution Pure-species properties, In a mixture solution: A solution properties, The partial properties base on components in a solution, Partial molar property of species i in solution:

In a solution of liquids, its properties: For a binary solution, its properties: Similarly, for separate x1 and x2; (See Example 11.3)

9.4 Ideal Gas Mixture In an ideal gas mixture, partial molar properties of a species (except volume) is equal to its molar properties of the species as a pure ideal gas when the temperature is the mixture temperature and the pressure equal to its partial pressure in the mixture.

Partial pressure of a species i in ideal-gas mixture: Hence, for enthalpy; For entropy; integration constant For Gibbs energy;

9.5 Fugacity and Fugacity Coefficient: Pure Species and Species in Gas Mixture or Solution of Liquids For pure species in ideal-gas state; For pure species in real-gas state;

where is called fugacity coefficient of pure species.

For species i in a mixture of real gases or in a solution of liquids, in equilibrium; The fugacity of each species is the same in all phases. For vapor-liquid equilibrium,

For species in gas mixture or solution of liquids, Fugacity coefficient of species i in gas mixture; Fugacity coefficient of species i in solution; For species i in ideal-gas mixture,

9.6 Fugacity Coefficient for Gas Mixture from the Virial Equation of State i, j, k are run over all species in gas mixture.

(Examples 11.7, 11.8 & 11.9)

9.7 Ideal Solution and Excess Properties is defined as the difference between the actual value of solution and value from ideal solution;

9.8 Liquid Phase Properties from VLE data In a vapor which a gas mixture and a liquid solution coexist in vapor/liquid equilibrium, For species i in vapor mixture, Similar for species i in solution,

In vapor-liquid equilibrium, vapor is assumed ideal gas, hence, Thus, fugacity of species i (in both the liquid and vapor phases) is equal to the partial pressure of species i in the vapor phase.

In an ideal solution, By introducing an activity coefficient;

9.9 Property Changes of Mixing This is a mixing process for a binary system. The 2 pure species both at T and P initially separated by a partition, and then allow to mix.

As mixing occurs, expansion accompanied by movement of piston so that P is constant. Heat is added or removed to maintain the constant T. When mixing is completed, the volume changed as measured by piston displacement.

Property changes of mixing is given by; Thus, the volume change of mixing, and the enthalpy change of mixing are found from the measured quantities and . Association with , is called the heat effect of mixing per mole of solution.

For volume in binary system; For enthalpy in binary system;

9.10 Heat Effects of Mixing Heat of mixing per mole of solution; Solving for binary systems; This equation provides the calculation of the enthalpies of binary mixture for pure species 1 and 2.

Heat of mixing are similar in many respect to heat of reaction. When a mixture is formed, energy change occurs because interaction between the force fields of the molecules. However, the heat of mixing are generally much smaller than heats of reaction.

Heats of Solution When solids or gases are dissolved in liquids, the heat effect is called the heat of solution. This heat of solution is based on the dissolution of 1 mol of solute. If species 1 is the solute, x1 is the moles of solute per mole of solution. Since, is the heat effect of mixing per mole of solution, is the heat effect of mixing per mole of solute.

Mixing processes are presented by physical- change equations, same like chemical-reaction equations. When 1 mol of LiCl(s) is mixed with 12 mol of H2O, the process; LiCl(12H2O) means a solution of 1 mol of LiCl dissolved in 12 mol of H2O, giving heat effect of the process at 25°C and 1 bar;

(Try Example 12.4, 12.5, 12.6, 12.7, 12.9)