Thermodynamics of Solutions Why important? Why are liquid solutions nonideal?

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Trevor Townsend
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1 Thermodynamics of Solutions Why important? Why are liquid solutions nonideal? mixtures of different chemical components are everywhere : biochemical, geological, environmental and industrial systems chemically-reacting systems are mixtures of reactants and products solubilities and crystallization vapor pressures osmotic pressure multicomponent phase equilibria provides information about molecular interactions

2 Ideal Solutions equal interactions between the molecules in a mixture good approximation for molecules of similar size and polarity, such as benzene + toluene mix n moles of component and n moles of component, for an ideal solution: U mix H mix V mix G mix n RT ln x nrt ln x 0 S mix nr ln x nrln x 0

3 Ideal Solutions of Components and a good start! equal, and intermolecular interactions Raoult s law applies p x p * p x p * chemical potentials of the components are (pure) RT ln * x (pure ) RT ln * x components always mix to form ideal solutions

4 Real Solutions of Components and big problem!, and intermolecular interactions are never equal activity coefficient correction factors and needed to predict vapor pressures chemical potentials of nonideal solution components are p p x p x p x *(pure) RT ln( ) some components do not mix (e.g., oil and water) * * x *(pure ) RT ln( )

5 Regular Solutions of Components and useful for moderately nonideal solutions random molecular mixing assumed different ij molecular interaction energies gives a molecular interpretation of nonideal solution properties explains (at least qualitatively) why some liquids do not mix

6 Mix n and n moles of Components and - and - intermolecular interactions are broken new - intermolecular interactions are formed + if each molecule has Z nearest neighbors: initially (pure components): (n N A Z/) - interactions (n N A Z/) - interactions in the mixture: x (n +n )N A Z/ - interactions x (n +n )N A Z/ - interactions x x (n +n )N A Z/ - interactions Why? probability x x, x x, x x, x x

7 Mix n and n moles of Components and U mix = energy change = final minus initial molecular interaction energy NAZ [( n n )( x x x x ) ( n n )] NAZ [( n n )( x x x x ) (( n n )( x x )] NAZ ( n n ) x x ( ) U mix ( n n) xx w w = molecular interaction parameter w NAZ ( )

8 Regular Solutions different energy interactions,, between the molecules mix n moles of component and n moles of component, for a regular solution: U H G mix n n) mix n n) ( wxx ( wx x [ Why? (pv) 0 for liquids ] V mix 0 mix nrt ln x nrt ln x ( n n) wx x S mix n Rln x n Rln x (random mixing)

9 Regular Liquid Solutions If = = (identical interactions): w = 0 (ideal solution) U mix ( n n) wxx 0 NAZ ( If < + : w < 0 (e.g., chloroform + acetone) Molecules and associate more strongly than the pure liquids. Solution more stable than an ideal solution. U n n ) wx x 0 mix ( If > + : w > 0 (e.g., carbon disulfide + acetone) Molecules and associate less strongly than the pure liquids. Solution less stable than an ideal solution. U mix ( n n) wxx 0 solution less stable w )

10 Mix n moles of component and n moles of component, for a total of n + n = mole. For a regular solution: G mix nrt ln x nrt ln x ( n n) wx x 500 G mix / J w = 7000 J w = 3000 J w = For w = 7000 J, two minima (), indicating two liquid phases: components not completely miscible x

11 Chemical Potentials for Regular Solutions Mix n moles pure liquid and n moles pure liquid. Gibbs energy of the mixture: G = n * + n * + G mix = n + n For a regular solution: G n n * nrt ln x nrt ln x ( n n) * wx x n ( * RT ln x wx ) n( * RT ln x wx n ( ) n( ) Notice: RT ln * x wx RT ln * x wx )

12 Raoult s Law Activity Coefficients for Regular Solutions = * + RT ln( x ) = * + RT lnx + RT ln = * + RT lnx + w x (regular solution) RT ln = wx e wx / RT as x (x 0 ): as x 0 (x ): w/ e RT

13 Raoult s Law Activity Coefficients for Regular Solutions e wx / RT w Negative Deviations from Raoult s Law (w < 0, i ) (e.g., chloroform + acetone) - attraction stronger than - and - attractions. For example, N A =, N A = 9, N A = 0 kj mol. a molecular interpretation of activity coefficients Positive Deviations from Raoult s Law (w > 0, i ) (e.g., carbon disulfide + acetone) - attraction weaker than - and - attractions. For example, N A = 5, N A = 5, N A = kj mol.

14 Molecular Interpretation of Raoult s-law Activity Coefficients 3.5 e wx / A RT N Z exp RT x activity coefficient w = 3000 J ( > ) w = 0 (ideal) w = 3000 J ( < ) x

15 Part.

16 Osmotic Pressure for dilute solutions of water () + solute () (x << ): RT V ln x RT ln( x l * V l * l * RT RT n RT n x V * n l V l * n n V l * solution volume V = n V m + n V m n V l * ) RT V x Raoult s law for water: p = x p * water activity: a = x = p /p * RT n RTc V c is the solute concentration in units of moles per unit volume (analogous to the ideal gas law)

17 Osmotic Pressure Example Estimate the osmotic pressure of a 0.5 M aqueous NaCl solution (the approximate composition of saline solution) at 5 o C. Careful! Each mole of dissolved NaCl produces two moles of dissolved solute ions (Na + and Cl ). The solute concentration for calculating osmotic pressure is therefore c = 0.30 M (not 0.5 M) RT n V ( bar L K mol ) (98.5 K) 0.30 mol L = 7.44 bar

18 Osmotic Pressure Applications molecular weight determinations measure molecular dissociation (e.g. HA = H + + A - ) use water activity measurements (a = p /p *) to calculate activities of electrolytes and other non-volatile solutes by integrating the Gibbs-Duhem equation 0 = n d + n NaCl d NaCl 0 = 55.5dlna + m NaCl dlna NaCl

19 Biomedical Applications? Osmotic Pressure Every day, millions of water activity measurements are made in hospitals (human and veterinary) and biomedical labs.. Physiological importance of water activity p /p *?. How can p /p * be measured rapidly and accurately?

20 . Why is water activity p /p * clinically important? Examples Consider how water activity is affected by: dehydration kidney failure congestive heart failure electrolyte imbalance drought or salt-stress for food crops

21 . How can water activity be measured rapidly and accurately? Physical chemists developed vapor pressure osmometers. Measure water activities (and activities for other solvents): in minutes for small solution samples (< 0. ml) using inexpensive and reliable equipment

22 Example Chilled-Mirror Vapor Pressure Osmometer A glass mirror on a thermoelectric plate is cooled at a rate of a few degrees/min. At the dew point of a solution, condensation of water vapor fogs the mirror, reducing the intensity of a beam of reflected light.

23 Example Chilled-Mirror Vapor Pressure Osmometer mirror cooling for pure water reflected light intensity I dew point temperature T* for pure water mirror temperature T

24 Example Chilled-Mirror Vapor Pressure Osmometer mirror cooling for a solution reflected light intensity I dew point temperature T of a solution mirror temperature T

25 Example Chilled-Mirror Vapor Pressure Osmometer water activity a W in solutions is measured reflected light intensity I T T* dissolved solute lowers the water vapor pressure from p W (T*) to p W (T) a W = p W (T)/p W (T*) mirror temperature T

26 Example Chilled-Mirror Vapor Pressure Osmometer water activity a W calculations (Clausius-Clapeyron equation): *) ( ) ( W W W T p T p a * exp vap,m o T T R H vap,m o *) ( * T T T R H for small T = T* T values K 6.79 * T T for T* = 98.5 K (5 o C)

Chilled-Wire Vapor Pressure Osmometer A thermocouple junction between two different metals is cooled at a steady rate by applying an electric current

27 Chilled-Wire Vapor Pressure Osmometer A thermocouple junction between two different metals is cooled at a steady rate by applying an electric current (thermo-electric effect). At the dew point, water condensation heats the thermocouple, halting the temperature drop. Vapro Model 5600 Vapor Pressure Osmometer

Outline of the Course

Outline of the Course 1) Review and Definitions 2) Molecules and their Energies 3) 1 st Law of Thermodynamics Conservation of Energy. 4) 2 nd Law of Thermodynamics Ever-Increasing Entropy. 5) Gibbs Free