Electrolyte Solutions Thermodynamics Crystallization-Books Pdf

Electrolyte Solutions Thermodynamics Crystallization
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Electrolyte Solutions,Thermodynamics Crystallization Separation. Kaj Thomsen Associate Professor,DTU Chemical Engineering. Technical University of Denmark,kth kt dtu dk,List of contents. 1 INTRODUCTION 5,2 CONCENTRATION UNITS 6,3 IDEAL SOLUTIONS 9. 3 1 DEFINITION 9,COLLIGATIVE PROPERTIES 13,4 CHEMICAL POTENTIAL AND ACTIVITY COEFFICIENTS 16.
4 1 CHEMICAL POTENTIAL 16, 4 2 EXCESS CHEMICAL POTENTIALS FOR REAL SOLUTIONS 16. 4 3 THE RATIONAL UNSYMMETRICAL ACTIVITY COEFFICIENT 17. 4 4 THE MOLALITY ACTIVITY COEFFICIENT 18,4 5 THE MOLARITY ACTIVITY COEFFICIENT 19. 4 6 THE ACTIVITY OF SPECIES 20,4 7 CHEMICAL POTENTIAL OF A SALT 20. 5 MEASUREMENT OF CHEMICAL POTENTIALS IN SALT SOLUTIONS 23. 5 1 MEASUREMENT OF THE CHEMICAL POTENTIALS OF IONS 23. 5 2 THE NERNST EQUATION 24,5 3 THE HARNED CELL 25,5 4 MEASUREMENT OF SOLVENT ACTIVITY 27. 5 4 1 FREEZING POINT DEPRESSION AND BOILING POINT ELEVATION MEASUREMENTS 27. 5 4 2 VAPOR PRESSURE METHODS 28,5 4 3 ISOPIESTIC MEASUREMENTS 29.
5 5 OSMOTIC COEFFICIENT 30, 5 5 1 THE VALUE OF THE OSMOTIC COEFFICIENT AT INFINITE DILUTION 31. 5 6 MEAN ACTIVITY COEFFICIENT FROM OSMOTIC COEFFICIENT 32. 5 7 OSMOTIC PRESSURE 33, 6 THERMODYNAMIC MODELS FOR ELECTROLYTE SOLUTIONS 35. 6 1 ELECTROSTATIC INTERACTIONS 35,6 1 1 DEBYE H CKEL THEORY 35. 6 1 2 DEBYE H CKEL EXTENDED LAW 37,6 1 3 DEBYE H CKEL LIMITING LAW 39. 6 1 4 THE H CKEL EQUATION 40,6 1 5 THE BORN EQUATION 42.
6 1 6 THE MEAN SPHERICAL APPROXIMATION 44, 6 2 EMPIRICAL MODELS FOR INTERMEDIATE SHORT RANGE INTERACTIONS 46. 6 2 1 THE MEISSNER CORRELATION 46,6 2 2 BROMLEY S METHOD 48. 6 2 3 THE PITZER METHOD 50, 6 3 INTERMEDIATE SHORT RANGE INTERACTIONS FROM LOCAL COMPOSITION MODELS 54. 6 3 1 THE EXTENDED UNIQUAC MODEL 54,6 3 2 THE ELECTROLYTE NRTL MODEL 57. 6 4 INTERMEDIATE SHORT RANGE INTERACTIONS FROM EQUATIONS OF STATE 58. 6 4 1 FUGACITY COEFFICIENTS AND ACTIVITY COEFFICIENTS 58. 6 4 2 THE F RST AND RENON EQUATION OF STATE 60,6 4 3 THE WU AND PRAUSNITZ EQUATION OF STATE 60.
6 4 4 THE MYERS SANDLER WOOD EQUATION OF STATE 61,6 4 5 COMPARATIVE STUDY OF EQUATIONS OF STATE 61. 7 EQUILIBRIUM CALCULATIONS 63,7 1 SPECIATION EQUILIBRIUM 63. 7 2 SOLID LIQUID EQUILIBRIUM 64,7 2 1 SATURATION INDEX 65. 7 3 VAPOR LIQUID EQUILIBRIUM 65,7 3 1 HENRY S CONSTANT 66. 7 4 LIQUID LIQUID EQUILIBRIUM 67, 7 5 COMPOSITION DEPENDENCE OF EQUILIBRIUM CONSTANTS 68.
7 6 TEMPERATURE DEPENDENCE OF EQUILIBRIUM CONSTANTS 71. 7 7 PRESSURE DEPENDENCE OF EQUILIBRIUM CONSTANTS 72. 7 7 1 THE PRESSURE DEPENDENCE OF ACTIVITY COEFFICIENTS 73. 8 THERMAL AND VOLUMETRIC PROPERTIES 75,8 1 PARTIAL AND APPARENT MOLAR PROPERTIES 75. 8 2 THERMAL PROPERTIES 75,8 2 1 HEAT OF DILUTION 78. 8 2 2 HEAT OF SOLUTION 78, 8 2 3 MEASUREMENT OF HEATS OF DILUTION AND SOLUTION 80. 8 2 4 MEASUREMENT OF HEAT CAPACITY 82,8 3 VOLUMETRIC PROPERTIES 84. 9 PHASE DIAGRAMS 90,9 1 PHASE RULE AND INVARIANT POINTS 90.
9 2 BINARY PHASE DIAGRAM 90,9 3 TERNARY PHASE DIAGRAM 92. 9 4 QUATERNARY SYSTEMS 94,10 CRYSTALLIZATION 98,10 1 SUPERSATURATION 98. 10 2 THE KELVIN EQUATION FOR NUCLEATION 99,10 3 ACTIVATION ENERGY FOR CRYSTAL FORMATION 101. 10 4 PRIMARY NUCLEATION RATE 101,11 FRACTIONAL CRYSTALLIZATION 102. 11 1 PRODUCTION OF KNO3 105, 11 2 OPTIMIZATION OF FRACTIONAL CRYSTALLIZATION PROCESSES 107.
11 3 SIMULATION OF K2SO4 PRODUCTION PROCESS 108,1 Introduction. Phase equilibria with systems containing electrolytes are of great importance A few. examples may illustrate this Production of fertilizers and salts is often performed by. precipitation of pure solids from multi component ionic solutions Scaling in heat exchangers. is caused by some salts for which the solubility decrease with increasing temperature Scaling. in oil production and in geothermal heat production is caused by some salts for which the. solubility decrease with decreasing pressure and decreasing temperature Solubility of gases. in electrolyte solutions is of importance in many pollution abatement processes The. influence of salts on the vapor pressure of aqueous solutions of organic material may be. important for the proper choice of a separation process Salts may even introduce a liquid. liquid phase splitting in aqueous solutions of organic substances. Electrolytes dissociate into ions when they are dissolved in polar solvents like water or. alcohols A strong electrolyte will dissociate completely while a weak electrolyte will only. dissociate partly The presence of the charged ions causes the electrolyte solution to deviate. much more from ideal solution behavior than a non electrolyte solution does This is the case. even at very low electrolyte concentrations The reason is that the ions interact with. electrostatic forces which are of much longer range than those involved in the interaction of. neutral molecules This effect is stronger the greater the charge on the ions. For a proper description of electrolyte solutions not only the short range energetic. interactions but also the long range electrostatic interactions have to be considered Another. basic difference between electrolyte and non electrolyte solutions is the constraint of electro. neutrality on electrolyte solutions Because of this constraint a system consisting of water. and two ions is a binary system The concentrations of the two ions cannot be chosen. independently so the system has two independent components. Consider salt S that dissociates into C cations C and A anions A with ionic charges ZC and. S C C Z C A AZ A 1 1,Table 1 1 Salt dissociation,S C ZC vC A ZA vA. NaCl Na 1 1 Cl 1 1,Na2SO4 Na 1 2 SO42 2 1,CaCl2 Ca2 2 1 Cl 1 2. The electro neutrality requirement gives for salt S. C ZC AZ A 0 1 2, In general the electro neutrality of a multi component solution containing ni moles of ion i. with the charge Zi relative to a hydrogen ion can be expressed as. Sodium chloride is often described as a 1 1 salt sodium sulfate as a 1 2 salt calcium chloride. as a 2 1 salt and calcium sulfate as a 2 2 salt based on the values of the ionic charges. 2 Concentration units, In the following it is assumed that the electrolytes are dissolved in water Water is.
considered to be the only solvent electrolytes and non electrolytes are considered to be. solutes In a solution containing water salts and methanol water is considered to be the. solvent The ions and methanol are considered to be solutes As it will be shown this. approach has significant advantages when performing solid liquid equilibrium calculations. and liquid liquid equilibrium calculations for solutions containing non electrolytes in. addition to electrolytes In another approach often seen in the literature mixtures of water and. certain non electrolytes such as organic solvents are considered to be separate species. mixed solvents or pseudo solvents while other non electrolytes and electrolytes are. considered to be solutes, For the description of electrolyte solutions the most common concentration unit is the. molality The molality unit is very often used in the presentation of experimental data while. the mole fraction unit most often is used in thermodynamic models for electrolytes The. molarity unit is also often used but is dependent on temperature and to a certain extent also. on pressure It is not a practical unit because the density needs to be known in order to. convert molarity units to molality units or mole fraction units. The molality mi of an ion i is the number of moles ni of the ion per kg water in the liquid. mi mol kg water 2 1, The amount of water in the solution is here calculated as the product of nw the number of. moles of water and Mw the molar mass of water in kg mol. The molarity ci of an ion i is the number of moles of the ion per liter solution. ci mol liter solution 2 2, The volume of the solution Vsolution is related to its mass and its density. nw M w ni M i,d solution ions, If the density of the solution dsolution is given in kg liter and the molar masses of water and. ions are given in kg mol the volume of the solution will be calculated in liter. From equation 2 1 it can be seen that the molality concentration unit is only dependent on. the amount of the relevant solute and the amount of solvent The mole fraction unit and the. molarity units on the other hand are also dependent on the amount of other solutes present In. addition the molarity unit is also dependent on temperature and pressure because the density. of the solution depends on temperature and pressure. Example 2 1 A solution containing 6 mol of sodium chloride and one kg of water is a 6. molal solution of sodium chloride The molality of the sodium ion in the solution is 6 The. molar mass of water is 18 02 gram mol and the number of mol water in one kg water can. therefore be calculated as 1000 18 02 The molality of the chloride ion in the solution is also. 6 The mole fraction of the sodium ion is,xNa 0 0889.
nNa nCl nH 2O 6 6 1000 18 02, The mole fraction of the chloride ion is also 0 0889 The mole fraction of water is. 1000 18 02,6 6 1000 18 02, Sometimes the composition of an electrolyte solution is given in terms of the amounts of. water and salts instead of water and ions If this approach is used the composition of the. same solution can be described by the mole fraction of sodium chloride. xNaCl 0 0975,nNaCl nH 2O 6 1000 18 02, The mole fraction of water is 1 0 0975 0 9025 when this approach is used. The density of this solution is 1 1942 kg liter at 25 C and 1 bar The volume of the solution. can be calculated from equation 2 3, nw M w nNa M Na nCl M Cl 1 000 6 0 0 02299 6 0 0 035453. Vsolution 1 1310 liter,1 1942 1 1942, The molarity of the sodium ion the chloride ion and of sodium chloride in the solution is.
cNa cCl cNaCl 5 305 mol liter, At 100 C and 1 bar the density of the same sodium chloride solution is 1 1490 kg liter The. volume of the solution is 1 1755 liter and the molarity of sodium chloride is 5 104 mol liter. For a salt S the molality is, If the salt dissociates into C cations and A anions the molality of the cation C is. mC C mS 2 5,The molality of the anion A is,mA AmS 2 6. The molality mS of the salt can therefore be expressed either in terms of the cation molality or. in terms of the anion molality,mS or mS 2 7, Most thermodynamic models use the traditional mole fraction scale. The summation in the denominator is over all solute and solvent species A relation between. the molality unit and the mole fraction unit can be derived as follows. ni n nw M w,xi i mi xw M w 2 9,n j n j nw M w,Mw is the molar mass of water given in kg mol.
The molarity unit is related to the mole fraction unit by. ni n Vsolution ciVsolution,n j n j Vsolution n j, A large number of different concentration units are used to present experimental data for. electrolytes These include,1 Mass percent,2 molality. 3 Mole fraction water ions and non electrolytes,4 Mole fraction water salts and non electrolytes. 5 Mass of salt per mass of H2O,6 Mass of salt per volume solution. 7 Mole salt per volume of solution,8 Mole salt per mass of solution.
9 J necke coordinates Charge fraction gram H2O per mole salts. 10 Mass percent solvent salt free molality of salt. 11 Mass percent solvent salt free mass of salt per mass of mixed solvent. 12 Mole percent solvent salt free molality salt, One reason why molality is a popular unit for salt solutions is that the concentrations in. molality units give practical numbers often between 0 and 20 for most salts while the. concentrations in mole fraction units are very small as indicated in figure 2 1 The figures. show the phase diagram of the ternary system NaCl KCl H2O using these two different. concentration units The lines in the phase diagrams mark concentrations saturated with either. NaCl or KCl At 25 C the solubility of NaCl is 6 15 mol kg water 0 0997 salt mole fraction. or 26 4 mass percent The corresponding numbers for KCl are 4 79 mol kg water 0 0795 salt. mole fraction or 20 7 mass percent,T 25 0 C T 25 0 C. KCl mole fraction,KCl molality,0 1 2 3 4 5 6 0 0 02 0 04 0 06 0 08 0 1. NaCl molality NaCl mole fraction, Figure 2 1 Phase diagram for the NaCl KCl H2O system using molality as concentration unit left and. salt mole fraction right The phase diagram consists of two curves On the curve a b solid potassium. chloride is in equilibrium with saturated solutions On b c solid sodium chloride is in equilibrium with. saturated solutions In the point b both solid salts are in equilibrium with a saturated solution. 3 Ideal solutions,3 1 Definition, An ideal solution can be defined as a solution in which the molar Gibbs energy of species i is.
calculated as,Giid Gi0 RT ln xi 3 1, R is the gas constant T is the absolute temperature in Kelvin and xi is the mole fraction of. component i Based on the definition of the ideal solution the properties of real solutions can. be calculated by the sum of two terms an ideal term and an excess term Equation 3 1. defines the ideal term of the Gibbs energy and is therefore given the superscript id Gi0 is the. molar standard state Gibbs energy and is a function of temperature and pressure. If there is only one component the mole fraction xi of component i is equal to one The term. RTlnxi then becomes zero and the Gibbs energy of i is equal. in electrolyte solutions is of importance in many pollution abatement processes The influence of salts on the vapor pressure of aqueous solutions of organic material may be important for the proper choice of a separation process Salts may even introduce a liquid liquid phase splitting in aqueous solutions of organic substances Electrolytes dissociate into ions when they are dissolved in

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