GASES

Gases  The physical state of gases is defined by several physical properties  Volume  Temperature  Amount (commonly expressed as number of moles)  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 is proportional to the product of amount and temperature PV = nRT

For a fixed amount of gas (constant n) plot of the properties of a gas gives a surface Isobar - pressure constant - line, V  T Isotherm - temperature constant, hyperbola, PV = constant Isochore- volume constant - line P  T

Kinetic Molecular Theory

Problems What is the pressure if 1 mole of N 2 occupy 1 L of volume at 1000 K? At standard temperature and pressure, how many grams of CO 2 is contained in a 3.0 L container? What is the density of acetone, C 3 H 6 O, vapor at 1.0 atm and 400 K?

Problems The density of dry air at 750 torr and 28°C is g/L. What is the composition of dry air, assuming that only nitrogen and oxygen are present? A 19.5 L flask at 15 °C contains a mixture of three gases: N 2 (2.50 mol), He (0.38 mol), and Ne (1.34 mol). Calculate the partial pressure of neon gas in the mixture.

Real Gases

Compressibility factor z

z > 1 Happens at high pressures Repulsive forces between gas molecules are now dominant As a result, the real gas has a larger molar volume than the corresponding ideal gas

z < 1 Happens at low pressures Attractive forces between gas molecules are now dominant As a result, the molar volume of the real gas is now smaller than that of the corresponding ideal gas

Selected equations of state * Please take note that the equations here assume 1 mole of the substance, hence the use of V m. For proper calculations, use the standard and default equations.

Surface of possible states for an ideal gas Surface of possible states for a gas obeying the Van der Waal’s equation

Virial equations and coefficients The virial equation shows that as pressures approach zero (p→0), it coincides with the ideal gas law. At low pressures, usually the first term of the virial equation is necessary. At higher pressures, the other terms become more significant.

Boyle Temperature The temperature wherein the properties of a real gas coincide with those of a perfect gas as p→0 Can also be defined as the temperature where a real gas obeys the ideal gas law over an appreciable pressure range. Deviations of z from unity are positive when the gas is above the Boyle temperature Below the Boyle temperature, the value of z decreases below unity before approaching it again and increasing above 1.

Critical constants A gas can be condensed through compression when its below the critical temperature. If not, it will just form a supercritical fluid. These are found at the critical point of a gas: – Critical temperature (T C ) – Critical pressure (P C ) – Critical volume (V C )

Principle of corresponding states We can use a certain property and set up a relative scale for the purpose of comparing the properties of objects The critical constants are characteristic properties of gases and we can use them to set up a scale. This leads to the reduced variables, which can be found by dividing the actual variable with the corresponding critical constant.

Principle of corresponding states

The principle of corresponding states postulates that real gases at the same reduced volume and reduced temperature exert the same reduced pressure. It does not follow that this is true for all conditions as the principle is only an approximation, but it does suggest that at their corresponding states, frequently better correlation of experimental data may be obtained.