1. Dr Saad Al-ShahraniChE 334: Separation Processes  Nonideal Liquid Solutions  If a molecule contains a hydrogen atom attached to a donor atom (O, N, F, and in certain cases C), the active hydrogen atom can form a bond with another molecule containing a donor atom.  Table 2.7 shows qualitative estimates of deviations from Raoult’s law for binary pairs when used in conjunction with Table 2.8.  Positive deviations correspond to values of  iL > 1. Nonideality results in a variety of variations of (  iL ) with composition, as shown in Figure 2.15 (Seader & Henely) for several binary systems, where the Roman numerals refer to classification groups in Tables 2.7 and 2.8. BINARY VAPOR-LIQUID EQUILIBRIUM two water molecules coming close together

2. Dr Saad Al-ShahraniChE 334: Separation Processes BINARY VAPOR-LIQUID EQUILIBRIUM

3. Dr Saad Al-ShahraniChE 334: Separation Processes BINARY VAPOR-LIQUID EQUILIBRIUM

4. Dr Saad Al-ShahraniChE 334: Separation Processes  Figure 2.15a: Normal heptane (V) breaks ethanol (II) hydrogen bonds, causing strong positive deviations. n-heptane(v)-Ethanol (II) system (Semi-log paper) Note: Ethanol molecules form H-bonds between each other and n-heptane breaks these bond causing strong (+) deviation. BINARY VAPOR-LIQUID EQUILIBRIUM

5. Dr Saad Al-ShahraniChE 334: Separation Processes  In Figure 2.15b, Similar Figure 2.15a but less positive deviations occur when acetone (III) is added to formamide (I). BINARY VAPOR-LIQUID EQUILIBRIUM  In Figure 2.15c, Hydrogen bonds are broken and formed with chloroform (IV) and methanol (II) resulting in an unusual positive deviation curve for chloroform that passes through a maximum.  iL >1

6. Dr Saad Al-ShahraniChE 334: Separation Processes BINARY VAPOR-LIQUID EQUILIBRIUM In Figure 2.15d, Chloroform (IV) provides active hydrogen atoms that can form hydrogen bonds with oxygen atoms of acetone (III), thus causing negative deviations  Non-ideal solution effects can be incorporate into K-value formation into different ways. 1. 2. Non-ideal liquid solution at near ambient pressure Non-ideal liquid solution at moderate pressure and T C.

7. Dr Saad Al-ShahraniChE 334: Separation Processes 1. Repulsion Molecules that are dissimilar enough from each other will exert repulsive forces BINARY VAPOR-LIQUID EQUILIBRIUM Component(1) x 1 Component(2) x 2 e. g: polar H 2 O molecules – organic hydrocarbon molecules.  i > 1 When dissimilar molecules are mixed together due to the repulsion effects, a greater partial pressure is exerted, resulting in positive deviation from ideality. + +  

8. Dr Saad Al-ShahraniChE 334: Separation Processes  Fore the last two figures, as the mole fraction x 1 increases its  1 →1, as its mole fraction x 1 decreases  1 increases till it reaches to  1  (activity coefficient at infinite dilution) BINARY VAPOR-LIQUID EQUILIBRIUM

9. Dr Saad Al-ShahraniChE 334: Separation Processes  Attraction When dissimilar molecules are mixed together, due to the attraction effects, a lower partial pressure is exerted, resulting in negative deviation from ideality. BINARY VAPOR-LIQUID EQUILIBRIUM  i < 1 are called negative deviation from ideality. Component(1) x 1 Component(2) x 2 - -

10. Dr Saad Al-ShahraniChE 334: Separation Processes  Example: calculate  ij of methanol – water system for the following data 760 mmHg Vapor phase y m = 0.665 y w = 0.33 BINARY VAPOR-LIQUID EQUILIBRIUM Liquid phase x m = 0.3 x w = 0.7 Vapor Pressure Data at 78 o C (172.1°F) Methanol: P m sat = 1.64 atm Water: P w sat = 0.43 atm Vapor phase y m = 0.665 y w = 0.33 Liquid phase x m = 0.3 x w = 0.7

11. Dr Saad Al-ShahraniChE 334: Separation Processes BINARY VAPOR-LIQUID EQUILIBRIUM solution For methanol For water

12. Dr Saad Al-ShahraniChE 334: Separation Processes BINARY VAPOR-LIQUID EQUILIBRIUM  How to calculate  iL of Binary Pairs Many empirical and semi-theoritical equations exists for estimating activity coefficients of binary mixtures containing polar and/ or non- polar species. These equations contain binary interaction parameters, which are back calculated from experimental data. Table (2.9) show the different equations used to calculate  iL.

13. Dr Saad Al-ShahraniChE 334: Separation Processes BINARY VAPOR-LIQUID EQUILIBRIUM

14. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS Table (2.10) shows the equations used to calculate excess volume, excess enthalpy and excess energy.

15. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS Example. (problem 2.23 ( Benzene can be used to break the ethanol/water azeotrope so as to produce nearly pure ethanol. The Wilson constants for the ethanol(1)/benzene(2) system at 45°C are A 12 = 0.124 and A 21 = 0.523. Use these constants with the Wilson equation to predict the liquid-phase activity coefficients for this system over the entire range of composition and compare them, in a plot like Figure 2.16, with the following experimental results [Austral. J. Chem., 7, 264 (1954)]:

16. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS Let: 1 = ethanol and 2 = benzene The Wilson constants are A 12 = 0.124 and A 21 = 0.523 From Eqs. (4), Table 2.9, Using a spreadsheet and noting that  = exp(ln  ), the following values are obtained,

17. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS

18. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS

19. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS  Activity coefficient at infinite dilution Modern experimental techniques are available for accurately and rapidly determining activity coefficient at infinite dilution (  iL  ) Appling equaion(3) in table (2.9) (van Laar (two-constant)) to conditions: X i = 0 and then x j = 0

20. Dr Saad Al-ShahraniChE 334: Separation Processes THERMODYNAMICS OF SEPARATION OPERATIONS Component(1) x 1 Component(2) x 2 + + Repulsive  > 1.0  