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Fugacities of Mixtures: Example Problems

Try to solve these problems before watching the solutions in the screencasts.

Example Problem 1

Use a Peng-Robinson EOS spreadsheet to calculate fugacities and fugacity coefficients for a three-component system, given pressure, temperature, and mole fractions in the phase. The spreadsheet can be downloaded from https://www.chethermo.net/software.

Example Problem 2

A) A binary liquid mixture (70 mol% A, 30 mol% B) is in the equilibrium with a vapor that has the partial pressures: PA = 0.2 bar   PB = 0.8 bar
Which component has the higher fugacity in the liquid phase?
B) Enough NaCl is added to liquid water so that salt crystals are present on the bottom of the container at 25°C. Does water or salt have the higher fugacity?
C) Compare pure water at 75°C with two concentrations in different phases: 0.014 mol/L and 54 mol/L? Which has the higher fugacity?

Try to explain why the statements below are true.

• When a can of soda is opened, the sound is due to escaping gas because the fugacity of CO2 in the soda can is higher than the fugacity of CO2 in the atmosphere.
• When oil and vinegar are mixed by shaking them in a container and then the contents allowed to reach equilibrium, two phases form. The fugacity of water in the bottom phase (which is almost all water) is the same as the fugacity of water in the top phase (which is almost all oil), even though the concentration of water in the bottom phase is orders of magnitude higher than the concentration of water in the top phase.
• When sufficient sugar is poured into a glass of iced tea so that sugar is seen at the bottom of the glass, the fugacity of the sugar at the bottom of the glass is equal to the fugacity of sugar in the iced tea.
• Supercritical CO2 is used to extract caffeine from coffee beans because the fugacity of caffeine in coffee beans is higher than the fugacity of caffeine in the supercritical CO2.
• Tea is make by extracting tannins, theobromine, and caffeine from tea leaves into water; the fugacity of these components are higher in tea leaves than in water. Boiling water is used to increase the rate of extraction.
• If a 50/50 ethanol/water liquid mixture is heated, ethanol evaporates faster than water because ethanol has a higher fugacity than water in the mixture.
If a mixture of sugar dissolved in water is heated, the water evaporates so that eventually only solid sugar remains because water has a higher fugacity in the mixture than sugar.
• Fresh water can be obtained from salt water by using a membrane only permeable to water and pressurizing the salt water to high enough pressure that the fugacity of water in the salt water is higher than the fugacity of pure water. This is the basis for large-scale desalination plants.
• A carrot placed in salt water will shrink as water leaves the carrot and goes into the salt water because the water has a higher fugacity in the carrot than in the salt water.
• A gas mask can be used to filter out some contaminates in air by adsorbing them on the surface of a high surface material in the gas mask filter. The contaminates adsorb on the filter surface because the fugacity of the contaminate is higher in air than on the filter surface.
• Adding salt to ice water at 0°C causes the ice to melt because the salt lowered the concentration of water in the liquid phase and thus lowered its fugacity below the fugacity of water in the ice.