- How to identify a gas-liquid or a gas-solid system.
- The very important direct relationship between vapour pressure and temperature.
- Four interrelationships of pressure and pressure components that apply to systems with just one condensible species.
- Raoults Law:
- using it for a system with one or more condensable species
- and its relation to Daultons Law.

Explanation: Q: What is a gas-liquid system: A: As a general rule, any liquid that doesn't entirely fill a container involves a gas-liquid system in that container. When you take your glass of lemonade and smell it, you are smelling the vapour of the lemonade (the liquid). (Under some conditions, though, a liquid can have a negligible vapour above it. For instance, water under the right conditions, can have completely dry air above it.) It is also true that the pressure exerted by a liquid to the air applies to solids too. That is, just above a solid, there is an equilibrium between the solid and its vapor. Now that we understand that liquids and solids have (just above their surface) molecules in the gas phase due to their presence, we are ready for a relationship that tells us the pressure of this vapor. Before we lay out the rules, though. Two asides: 1) vapour (the European spelling) and vapor have both been used in this page (for fun?). 2) Perhaps, for a condensible gas phase species, it shouldn't be referring to as a gas, but rather as a vapor, thus we are talking about |

Explanation: It turns out that vapour pressure is a direct function of temperature. That is, if given a vapour pressure for a substance, you can get temperature without any other info, and vise versa! You can do this in a variety of ways in this course. We'll find that the following tables and graphs offer the relationships we need to move between vapour pressures and temperatures: The Cox Chart (Section 6.2)The Water Vapour Pressure Table (Appendix B4)The Antoine's Equation (appendix B4)Note: There are 2 major challenges to being able to use these interrelationships effectively: Recognition: In a mass balance problem, if you're given temperature, know that you can get the vapor pressure of the gas in a gas-liquid system (which will lead to other properties, eg. see the section on Raoult's Law). Tables/Graphs: Learn to use all the tables and graphs, and the advantages of each. For example, Appendix B4 means having to use Antoine's Equation which means an algebra exercise. For more information on Antoine's equation,
A propane tank is at a temperature of 100 degrees Fahrenheit. Determine its vapour pressure in lb-force/in.
Liquid water is heated from 10 degrees Celcius to 50 degrees Celcius. Find the vapour pressure of the water at 10, 20, 30, 40, and 50 degrees Celcius in mmHg. |

Explanation: How do I recognize if a gas-liquid system has only a single condensible species? The direct answer to this question is to compare the boiling points. Any boiling points that are far below the temperatures involved imply that those species are considered uncondesible. A cup of water: the gas above the water is composed of water and air (nitrogen and oxygen). Thus there are three gases present above the cup of water (water, nitrogen, and oxygen). However, only the water will condense upon a cooling from 70°C to 50°C (bp's: H A mixture of an alcohol (say, ethanol) and water: the gas above the liquid is composed of H |

So you now know how to identify if a gas-liquid system has a single condesible species. But, what are the interrelationships that will help us? There are four saturation formulas that apply to gas-liquid systems that have only a single condensible species, and they are listed here:
p is the Vapor Pressure of component i _{i}^{*}MW is the molecular weight of component i_{i}MW is the molecular weight of total gas mixture
_{dry}Special notation and terminology for air-water systemsThere is special notation and terminology that we use for air-water systems since they are so common. However, the term saturation in each of these equations is designated for any generic gas-vapor system: when the gas is air and the vapor is water vapor, then the word saturation is replaced with humidity for air-water systems.
A gas consists of 10% styrene and 90% air in a tank at 100 degrees Celcius and 1000 mmHg. Calculate the relative saturation, molal saturation, and percentage saturation.
Water enters a boiler at 80 degrees Celcius under atmospheric pressure. If its relative humidity is 60%, what is the vapor pressure, partial pressure, and mole fraction of water in the air. |

Explanation: Raoult's Law relates a component's partial pressure, vapor pressure, and mole fraction in the liquid phase in order to find the mole fraction in the gas phase. However, if we know any three of the variables, we can solve for the fourth one! We use this relationship for nearly pure liquids, that is, where x _{A} = x_{A} * p_{A}^{*}If we recall Dalton's law of partial pressures for a gas (p _{A} = x_{A} * p_{A}^{*} = y_{A} * PIf we have a completely pure liquid, x _{A} = p_{A}^{*} = y_{A} * PThis refers to a vapor that is saturated. This means the vapor pressure corresponds to the temperature of the dew point of the gas (the temperature at which the vapor begins to condense into a liquid state). For dilute components (x _{A} = x_{A} * H_{A} = y_{A} * PThese interrelations relate the fraction of a component in a liquid-phawse versus the fraction of a component in the gas phase. A reaction energy balance problem that I did for chapter 8 involved a balance on a condenser that required the implementation of these concepts. I challenge you to solve it!
An equimolar liquid mixture of benzene (B) and toluene (T) is in equilibrium with its vapor at 30.0 degrees Celcius. What is the system pressure and the composition of the vapor?
A gas stream containing 40.0 mole % hydrogen, 35.0% carbon monoxide, 20.0 % carbon dioxide, and 5.0% methane is cooled from 1000 degrees Celcius to 10 degrees Celcius at a constant absolute pressure of 35.0 atm. Gas enters the cooler at 120 m |

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