Deviations from Ideal Behavior 1 mole of ideal gas PV = nRT n = PV RT = Repulsive Forces Attractive Forces

Maxwell distribution : In 1859, James Clerk Maxwell (1831 – 1879) worked out a formula for the most probable distribution of speeds in a gas. Molecules in a gas sample move at a variety of speeds. Speed of each molecule constantly changing due to countless collisions(about 1 billion per second for each molecule). At low temperature most molecules move close to the average speed, at higher temperature there is greater distribution of speeds.

Maxwell distribution of speeds : Just for your knowledge do not memorize

Boltzman Distribution. The behaviour of the gas molecules under the action of gravity. (Harcourt school Publishers)

The Kinetic Theory The ideal gas law is an empirical law gives a macroscopic explanation of gas behavior. Kinetic Theory starts with a set of assumptions about the microscopic behavior of matter at the atomic level. Supposes that the constituent particles (atoms) of the gas obey the laws of classical physics. Accounts for the random behavior of the particles with statistics, thereby establishing a new branch of physics - statistical mechanics. Predicts experimental phenomena that haven't been observed. (Maxwell-Boltzmann Speed Distribution)

An ideal gas molecule in a cube of sides L. J. B. Callis,Washington University

Calculating force exerted on a container by Collision of a single particle J. B. Callis,Washington University

Calculation of the Pressure in Terms of Microscopic Properties of the Gas Particles J. B. Callis,Washington University

Kinetic Theory Relates the Kinetic Energy of the Particles to Temperature J. B. Callis,Washington University

Mean Square Speed and Temperature By use of the facts that (a) PV and nRT have units of energy, and (b) the square of the component of velocity of a gas particle striking the wall is on average one third of the mean square speed, the following expression may be derived: where R is the gas constant (8.31 J/mol K), T is the temperature in kelvin, M is the molar mass expressed in kg/mol (to make the speed come out in units of m/s). J. B. Callis,Washington University

Relationship of kinetic energy of one gas particle to temperature: Conclusion: Temperature is a measure of the molecular motion. At the same temperature, all gases have the same average kinetic energy.

Gas diffusion and effusion Graham’s law governs effusion and diffusion of gas molecules. Graham’s law governs effusion and diffusion of gas molecules. KE=1/2 mv 2 Thomas Graham, Professor in Glasgow and London. Rate of effusion is inversely proportional to its molar mass.

Diffusion Diffusion is movement of one gas through another by thermal random motion. Diffusion is a very slow process in air because the mean free path is very short (for N 2 at STP it is 6.6x10 -8 m). Given the nitrogen molecule’s high velocity, the collision frequency is very high also (7.7x10 9 collisions/s). Effusion is the process whereby a gas escapes from its container through a tiny hole into an evacuated space. According to the kinetic theory a lighter gas effuses faster because the most probable speed of its molecules is higher. J. B. Callis,Washington University

GAS DIFFUSION AND EFFUSION diffusion is the gradual mixing of molecules of different gases.diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container.effusion is the movement of molecules through a small hole into an empty container.

The Process of Effusion J. B. Callis,Washington University

The inverse relation between diffusion rate and molar mass. NH 3 (g) + HCl(g) NH 4 Cl(s) Due to it’s light mass, ammonia travels 1.46 times as fast as hydrogen chloride J. B. Callis,Washington University

Relative Diffusion Rates of NH 3 and HCl J. B. Callis,Washington University

GAS DIFFUSION AND EFFUSION Molecules effuse thru holes in a rubber balloon, at a rate (= moles/time) that is proportional to T inversely proportional to M.inversely proportional to M.Question If you have 2 ballons flled with He & O 2 Which will effuse more? If you have 2 ballons flled with He & O 2 Left overnight at same T, Which will effuse more? He effuses more rapidly than O 2 at same T. He O2O2O2O2

Examples

Calculating Molecular Speeds : Question : Calculate the average speed of O 2 in air at 20 o C km/h! (1.6km=1mile). Question : What is the r.m.s. speed of SO2 atoms at 25°C? u rms = ms-1

Calculation of Molecular Speeds and Kinetic Energies, T = 300 K

Problem 15-1: Calculate the Kinetic Energy of (a) a Hydrogen Molecule traveling at 1.57 x 10 3 m/sec, at 300 K. Mass = KE =

Problem 15-1 Kinetic Energies for (b) CH 4 and (c) CO 2 at 200 K (b) For Methane, CH 4, u = 5.57 x 10 2 m/s KE = (c) For Carbon Dioxide, CO 2, u = 3.37 x 10 2 m/s KE =

Note At a given temperature, all gases have the same molecular kinetic energy distributions, and the same average molecular kinetic energy.

NH 3 (g) + HCl(g) = NH 4 Cl(s) HCl = g/mol NH 3 = g/mol Problem Relative Diffusion Rate of NH 3 compared to HCl: Rate NH3 =