Solutions Contributions by: John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO 80309-0424 Supported by the National Science Foundation

Phase a and b each contain component A Phase a and b each contain component A. The two phases are not in equilibrium. The direction of mass transport of component A is ________. from a to b from b to a Cannot tell from this information. No mass transfer occurs. CA=0.001 CA=0.020 a b ANSWER: C. Cannot tell from this information. No info is given on which phase has the higher fugacity of A.

Phase a and b each contain component A Phase a and b each contain component A. The two phases are not in equilibrium. What is the direction of mass transport of component A? From a to b From b to a Cannot tell from this information No mass transfer occurs CA=0.005 mol/L CA=0.100 mol/L a b ANSWER: C. Cannot tell from this information. . No info is given on which phase has the higher fugacity of A.

Consider two immiscible mixtures Consider two immiscible mixtures. The concentration of A is much greater in the bottom solution. The direction of mass transfer of component A is _________. CA=0.001 CA=0.200 Mixture 1 into mixture 1 into mixture 2 Could be in either direction. No mass transfer occurs. Mixture 2 ANSWER: C. Could be in either direction. Cannot tell direction without fugacity data.

The concentration of A is different in two liquids that do not mix The concentration of A is different in two liquids that do not mix. What determines the direction of mass transfer of component A? A in B A in C Concentration Pressure Solubility Energy Other ANSWER: E. Other. Fugacity determines mass transfer

Phases a and b are comprised of component A Phases a and b are comprised of component A. The two phases are not in equilibrium. If the system is at constant temperature, which phase has the higher fugacity? CA=0.01 mol/L CA=0.50 mol/L a Phase a Phase b Both phases have same fugacity Not enough information b ANSWER: D. Not enough info.

Two liquid phases are in equilibrium at 2 bar Two liquid phases are in equilibrium at 2 bar. The bottom liquid is pure A; the top liquid is a mixture of A and B with xA = 0.05. If PAsat = 0.5 bar, PBsat = 0.8 bar, the fugacity of liquid A in the mixture is _____ bar. Mixture of A & B xA=0.05 Liquid A 1.0 0.8 0.5 0.1 0.05 ANSWER: C. 0.5 bar. Fugacity of liquid A is close to its vapor pressure and fugacity of A is the same in both phases when at equilibrium.

Compounds A and B do not mix, and compound B is more dense Compounds A and B do not mix, and compound B is more dense. This figure shows the situation immediately after the 3 mol% C in A was added on top of the 4 mol% C in B solution. Over time, compound C will _________. 3 mol% C in A gC = 2 4 mol% C in B gC = 1.1 move from liquid A to liquid B move from liquid B to liquid A remains as they are since A & B are immiscible ANSWER: A. move from liquid A to liquid B. Fugacity of C is initially higher in solution A.

This system is not in equilibrium. Which happens to reach equilibrium? Liquid evaporates Vapor condenses Cannot predict without more information Vapor C1= 0.25 kg/m3 75°C ANSWER: C. Cannot predict without more information. Fugacity, not concentration, is the driving force. Need more info such as the vapor pressure. Water C1= 975 kg/m3

For the system below, which only contains component A, what will happen next? Liquid fALiq = 0.6 bar Vapor fAGas = 0.4 bar Some vapor will condense All the liquid will vaporize All the vapor will condense Some liquid will vaporize ANSWER: D. Some liquid will vaporize. Mass transfer takes place from high to low fugacity.

These tubes, with an aqueous BSA* solution on the left and pure water on the right are at equilibrium. When you add salt to the pure water on the right, __________________. the water level on the right increases the BSA solution level on the left increases no change in the levels occur Aqueous BSA Pure water ANSWER: A. the water level on the right increases. Adding salt to the pure water decreases its fugacity, so water moves across the membrane from the BSA (high fugacity) to the water and salt (low fugacity). H2O permeable membrane *BSA= bovine serum albumin protein

An aqueous BSA* solution on the left left and pure water on the right are at equilibrium. When you add more BSA to the solution on the left, ___________________. the water level on the right increases the BSA solution level on the left increases no change in levels occur Aqueous BSA Pure water ANSWER: B. the BSA solution level on the left increases. There is no change in fugacity of the water in the BSA solution by adding more of the same solution so only the level of the BSA solution increases. H2O permeable membrane *BSA= bovine serum albumin protein

A B C D These tubes each have an aqueous BSA* solution on the left and pure water on the right. A membrane that is only permeable to water separates the two sides. Which one is at equilibrium? A B C D ANSWER: B. The water must have the same fugacity on both sides. H2O + BSA H2O + BSA H2O + BSA H2O + BSA H2O H2O H2O H2O *BSA= bovine serum albumin protein

Which component (A or B) has the higher molecule weight Which component (A or B) has the higher molecule weight? Neither A nor B dissociates. A B They are the same Need more information H2O + 10 g A H2O + 10 g B H2O H2O ANSWER: B. There are fewer moles for 10 g of B because the osmotic pressure is lower. H2O permeable membrane H2O permeable membrane

Which component (A or B) has the higher molecule weight Which component (A or B) has the higher molecule weight? Neither A nor B dissociates. A B They are the same Need more information H2O + 10g A H2O + 20g B H2O H2O ANSWER: B. B, It takes twice as many grams of B to have the same osmotic pressure so its moleuclar weight is greater. H2O permeable membrane H2O permeable membrane

A container with water and NaCl is boiling at 105°C on a stove A container with water and NaCl is boiling at 105°C on a stove. The amount of NaCl in the water is half of the maximum amount of salt that can dissolve. Which is the correct plot of the chemical potential of the liquid water versus time as the water boils away to 10% of its initial volume. μ(l) Time A Time B Time C Time D ANSWER: C. The chemical potential of the water will decrease as its mole fraction decreases, then will remain constant as solution becomes saturated with salt. None of the above.

Liquids A and B are immiscible Liquids A and B are immiscible. When each liquid is present, it exerts its own vapor pressure. A vapor contains a mixture of A and B at low pressure. The pressure is increased at constant temperature. At 4 bar, liquid A appears; At 6 bar, liquid B appears. Which is the correct plot of the partial pressures of A and B vs. total pressure? 2 4 6 8 Pi (bar) Pressure (bar) A 2 4 6 8 Pressure (bar) B 2 4 6 8 Pressure (bar) C ANSWER: A.

Components A and B are immiscible Components A and B are immiscible. When each liquid is present, it exerts its own vapor pressure. A vapor contains 5 mol A and 5 mol B at low pressure. The pressure is increased at constant temperature. At 4 bar, liquid A appears; At 6 bar, liquid B appears. Which is the correct plot of the partial pressures of A and B vs. total pressure? 2 4 6 8 Pi (bar) Pressure (bar) A 2 4 6 8 Pressure (bar) B 2 4 6 8 Pressure (bar) C ANSWER: A.

When component A is mixed with component B, the activity coefficient of component A is greater than one for all mixtures. When component A is mixed with component C, the activity coefficient of component A is less than one for all mixtures. Which plot is closest for the fugacity of A vs. the mole fraction of A for A-B mixtures (red) and for A-C mixtures (blue)? A B C D ANSWER: B. fA (bar) mole fraction xA mole fraction xA mole fraction xA mole fraction xA

When component A is mixed with component B, the activity coefficient of component A is greater than one for all mixtures. When component A is mixed with component C, the activity coefficient of component A is less than one for all mixtures. Which plot is closest for the fugacity of A vs. the mole fraction of A for A-B mixtures (red) and for A-C mixtures (blue)? A B C D ANSWER: B. fA (bar) mole fraction xA mole fraction xA mole fraction xA mole fraction xA

Which species has the higher fugacity in the liquid? A liquid containing 60 mol% salt and 40 mol% water is in equilibrium with water vapor at 0.5 atm. Which species has the higher fugacity in the liquid? Salt Water Their fugacities are equal Need more information ANSWER: B. Water. The fugacity of the water in its liquid state is equal to fugacity of water in its vapor state.

Sugar was dissolved in hot tea until it was saturated Sugar was dissolved in hot tea until it was saturated. When the tea was cooled, the solution was supersaturated with sugar and not at equilibrium. The chemical potential of the sugar in the solution is _____________ solid sugar at the same temperature . higher than lower than the same as Insufficient information. ANSWER: A. higher than. The chemical potential is higher because the driving force is for sugar to come out of solution and precipitate as a solid.

A liquid mixture that is 25% A and 75% B is in equilibrium with an ideal gas at 1 bar that is 60% A and 40% B. The chemical potential of component A is ___________ component B in the liquid phase. greater than less than the same as ANSWER: A. greater than component B in the liquid phase. The partial pressure in the gas phase is equal to the fugacity for an ideal gas, and the fugacity of the gas is the same as the fugacity of the liquid.

If you add salt to water, what happens to the fugacity of the water? It increases It decreases It remains the same ANSWER: B. It decreases. Fugacity decreases as mole fraction decreases

When 10 mL of liquid water and 10 mL of liquid ethanol are mixed, the resulting solution has a volume of about 19 mL. Heat is also released during the mixing process. Which of the following statements is true? Water and ethanol form an ideal solution Water and ethanol are immiscible (i.e. separate into two layers) Water and ethanol repel each other in liquid mixtures Water and ethanol experience attractive interactions ANSWER: D. Water and ethanol experience attractive interactions. Smaller volume of mixture than the sum of the individual components because of the attractive interactions.

Water and ethanol form an azeotrope at approximately 90% ethanol Water and ethanol form an azeotrope at approximately 90% ethanol. From a 50/50 mixture of water-ethanol, which is currently below its bubble T, your aim is to produce a phase containing 95% ethanol. What can you do? Heat up the mixture to the bubble T Heat up the mixture to the dew T Heat up the mixture to a very high T (above the dew T) None of the above ANSWER: D. None of the above.

Mixing two liquid compounds results in a decrease in the total Gibbs free energy of the system. Which of the following MUST be true? The solution is not ideal The two components attract each other The enthalpy of mixing is negative None of the above ANSWER: D. None of the above. Gibbs free energy decreases when a mixture forms.

For a 50/50 binary mixture, the activity coefficients in a modified Raoult’s law model of each component will be closest to ____________. one as the solution is more ideal one if the two components attract each other strongly zero if the components repel each other ANSWER: A. one as the solution is more ideal.

Consider a 95/5 mixture of the acetone(1) ‐ acetic acid(2) system Consider a 95/5 mixture of the acetone(1) ‐ acetic acid(2) system. Which component will have an activity coefficient closer to 1? Acetone Acetic acid Both should be close to 1. ANSWER: A. Acetone. As x approaches 1, approach Raoult's Law behavior.

Which of the following statements is true? For an ideal solution, __________. ΔHmix = 0 but HE > 0 ΔGmix = 0 but GE > 0 ΔSmix > 0 but SE = 0 ΔGmix < 0 but GE = 0 Answers C and D ANSWER: E Answers C and D.

When 1 mol ethylamine and 1 mol acetylacetone are mixed adiabatically, starting at 15°C, the mixture would be __________ 15oC. The excess enthalpy plot is shown in the figure. 0.25 0.5 0.75 0.10 0.15 0.30 0.00 1 HE x1 0.20 0.05 greater than less than equal to Depends on SE ANSWER: B. less than 15oC. If mixed isothermal, the product (the mixture) has more enthalpy than the starting materials. Since this is done adiabatically, must cool down the mixture to get the energy for mixing. That is, this same as an endothermic reaction, where products have more energy than reactants.

Activity coefficients Which curve is for component 1 of a binary mixture? 0.25 0.5 0.75 1.8 2.6 1.0 1 Activity coefficients x1 2.2 1.4 B A ANSWER: B. B. The pure component activity coefficient must approach one as its mole fraction goes to one. A B A or B

Which is the correct plot of Helmholtz free energy vs Which is the correct plot of Helmholtz free energy vs. the mole fraction for a binary, ideal liquid solution at constant temperature? yi A yi A yi A A B C ANSWER: C. Helmholtz free energy (A)= U –TS. yi A yi A D E

As the mole fraction of a species in an ideal solution approaches one, its partial molar Gibbs free energy ____________. increases decreases remains the same depends on the mole fraction ANSWER: A. increases. Entropy change is minimized.

As the mole fraction of a species in an ideal solution approaches one, its partial molar entropy _______. increases decreases remains the same ANSWER: B. decreases. Partial molar entropy approaches minimum at pure component (no mixing).

Which statement is most likely correct if molecule 1 is represented by blue and molecule by red? a22 = a11 a21 > a12 a12 > a22 & a12 > a11 a12 < (a11a22)½ a12 = a11a22 ANSWER: D. a12 < (a11a22)½