GASES
Gases
The physical state of gases is defined byseveral physical properties
Volume
Temperature
Amount (commonly expressed as number ofmoles)
Pressure
p = f(T, V, n)
THE Perfect Gas
The perfect gas
A gas that obeys the perfect gas equation
The product of pressure and volume isproportional to the product of amount andtemperature
PV = nRT
For a fixed amount of gas(constant n) plot of theproperties of a gas gives asurface
Isobar - pressureconstant - line, V T
Isotherm -temperature constant,hyperbola, PV =constant
Isochore- volumeconstant - line P T
Kinetic Molecular Theory
Problems
•What is the pressure if 1 mole of N2 occupy 1L of volume at 1000 K?
•At standard temperature and pressure, howmany grams of CO2 is contained in a 3.0 Lcontainer?
•What is the density of acetone, C3H6O, vaporat 1.0 atm and 400 K?
Problems
•The density of dry air at 750 torr and 28°C is1.145 g/L. What is the composition of dry air,assuming that only nitrogen and oxygen arepresent?
•A 19.5 L flask at 15 °C contains a mixture ofthree gases: N2 (2.50 mol), He (0.38 mol), andNe (1.34 mol). Calculate the partial pressureof neon gas in the mixture.
Real Gases
Compressibility factor z
Compressibility factor z
z > 1
•Happens at high pressures
•Repulsive forces betweengas molecules are nowdominant
•As a result, the real gas hasa larger molar volume thanthe corresponding ideal gas
z < 1
•Happens at low pressures
•Attractive forces betweengas molecules are nowdominant
•As a result, the molarvolume of the real gas isnow smaller than that ofthe corresponding ideal gas
Selected equations of state
* Please take note that the equations here assume 1 mole ofthe substance, hence the use of Vm. For proper calculations, usethe standard and default equations.
Surface of possible states for anideal gas
Surface of possible states for agas obeying the Van der Waal’sequation
Virial equations and coefficients
•The virial equation shows that as pressuresapproach zero (p→0), it coincides with theideal gas law.
•At low pressures, usually the first term of thevirial equation is necessary. At higherpressures, the other terms become moresignificant.
Boyle Temperature
•The temperature wherein the properties of a realgas coincide with those of a perfect gas as p→0
•Can also be defined as the temperature where areal gas obeys the ideal gas law over anappreciable pressure range.
•Deviations of z from unity are positive when thegas is above the Boyle temperature
•Below the Boyle temperature, the value of zdecreases below unity before approaching itagain and increasing above 1.
Critical constants
•A gas can becondensed throughcompression when itsbelow the criticaltemperature.
•If not, it will just form asupercritical fluid.
•These are found at thecritical point of a gas:
–Critical temperature (TC)
–Critical pressure (PC)
–Critical volume (VC)
Principle of corresponding states
•We can use a certain property and set up arelative scale for the purpose of comparingthe properties of objects
•The critical constants are characteristicproperties of gases and we can use them toset up a scale.
•This leads to the reduced variables, which canbe found by dividing the actual variable withthe corresponding critical constant.
Principle of corresponding states
Principle of corresponding states
•The principle of corresponding states postulatesthat real gases at the same reduced volume andreduced temperature exert the same reducedpressure.
•It does not follow that this is true for allconditions as the principle is only anapproximation, but it does suggest that at theircorresponding states, frequently bettercorrelation of experimental data may beobtained.
