Kinetic Molecular Theory and Gases KMT operates under 5 assumptions: Gas particles are in constant, random, straight line motion. Particles are separated by great distances. Collisions are rapid and elastic. No force between particles. Total energy remains constant. Natural laws are explained by theories. Gas law led to development of kinetic-molecular theory of gases in the mid-nineteenth century. KMT Video Average kinetic energy is directly proportional to temperature!! As temp goes up, so does kinetic energy

Kinetic-Molecular Theory A gas consists of very small particles, each of which has a mass. A gas spreads out and takes on the volume of its container. The volume of the gas particles is assumed to be zero because it is negligible compared with the total volume of the gas. Gas particles are in constant, rapid, random motion. They move in straight lines, until they bump into something. Temperature is a measurement of the average kinetic energy (speed) of the particles (Video) Pressure is a measurement of the number and force of the collisions of the particles with the walls of the container Gas particles do not lose energy like most other things in our world. When gases hit something they never slow down and stop.

Kinetic-Molecular Theory cont. The collisions of gas particles with each other and with the container are totally elastic. Gas particles exert no force on one another because their attractions are so weak they are assumed to be zero.

Gas Properties Relating to the Kinetic-Molecular Theory Diffusion Migration of molecules that results in a homogenous mixture. Effusion Escape of gas molecules through a tiny hole.

Graham’s Law Molecules effuse through holes in a rubber balloon and deflate This occurs at a rate equal to moles/time: proportional to Temperature inversely proportional to molar mass. Therefore, He gas effuses more rapidly than O2 at the same T. He Graham’s Law Animation Graham’s Law Demo

Graham’s Law Rate of effusion “Proportional to” Rate of effusion ְ This also applies to diffusion, as heavier particles diffuse more slowly Grahams explanation

Graham’s Law Example: Ammonia gas has a molar mass of 17.0 g/mol; hydrogen chloride gas has a molar mass of 36.5 g/mol. What is the ratio of their diffusion rates?

Graham’s Law Example: What does this mean? Ammonia will diffuse 1.47 times faster than HCl because the gas particles have a smaller mass

Graham’s Law Example on your own: Carbon Monoxide gas is less massive than Carbon Dioxide gas. How much faster will CO diffuse compared to CO2?

Dalton’s Law of Partial Pressures

Units of Pressure Unit Compared with 1 atm Compared with 1 kPa kilopascal (kPa) 1.00atm = 101.3 kPa Millimeters of mercury (mmHg) 1 atm = 760. mm Hg 1 kPa = 7.501 mm Hg torr 1 atm = 760. torr* 1 kPa = 7.501 torr Pound per square inch (psi) 1 atm = 14.7 psi 1 kPa = 0.145 psi Atmosphere (atm) 1 kPa = 0.009869 atm *1atm, 760 mm Hg and 760 torr are defined units, they DO NOT determine how many sig figs a problem should have when used as equalities.

Ptotal = P1 + P2 + … + Pn Dalton’s Law: the total pressure exerted by a mixture of gases is the sum of all the partial pressures Ptotal = P1 + P2 + … + Pn

Partial Pressures ? kPa 200 kPa 500 kPa 400 kPa 1100 kPa + = Dalton’s law of partial pressures states that the sum of the partial pressures of gases sum to the total pressure of the gases when combined. The ideal gas law assumes that all gases behave identically and that their behavior is independent of attractive and repulsive forces. If the volume and temperature are held constant, the ideal gas equation can be arranged to show that the pressure of a sample of gas is directly proportional to the number of moles of gas present: P = n(RT/V) = n(constant) Nothing in the equation depends on the nature of the gas, only on the quantity. The total pressure exerted by a mixture of gases at a given temperature and volume is the sum of the pressures exerted by each of the gases alone. If the volume, temperature, and number of moles of each gas in a mixture is known, then the pressure exerted by each gas individually, which is its partial pressure, can be calculated. Partial pressure is the pressure the gas would exert if it were the only one present (at the same temperature and volume). The total pressure exerted by a mixture of gases is the sum of the partial pressures of component gases. This law is known as Dalton’s law of partial pressures and can be written mathematically as Pt = P1 + P2 + P3 - - - + Pi where Pt is the total pressure and the other terms are the partial pressures of the individual gases. For a mixture of two ideal gases, A and B, the expression for the total pressure can be written as Pt = PA + PB = nA(RT/V) + nB(RT/V) = (nA + nB) (RT/V). • More generally, for a mixture of i components, the total pressure is given by Pt = (n1 + n2 + n3 + - - - +ni) (RT/V). • The above equation makes it clear that, at constant temperature and volume, the pressure exerted by a gas depends on only the total number of moles of gas present, whether the gas is a single chemical species or a mixture of gaseous species.

Dalton’s Law of Partial Pressures & Air Pressure 8 mm Hg P Ar 590 mm Hg P N2 P Total P O2 P N2 P CO2 P Ar = + + + 149 mm Hg P O2 149 590 3 8 mm Hg P Total = + + + 3 mm Hg P CO2 PTotal = 750 mm Hg EARTH

Dalton’s Law of Partial Pressures & Air Pressure 8 mm Hg P Ar 590 mm Hg P N2 P Total P O2 P N2 P CO2 P Ar = + + + 149 mm Hg P O2 149 590 3 8 mm Hg P Total = + + + 3 mm Hg P CO2 PTotal = 750 mm Hg EARTH

Examples A mixture of oxygen, carbon dioxide and nitrogen (this mix is known as “air”) has a total pressure of 0.97 atm. What is the partial pressure of O2 if the partial pressure of N2 is 0.12 atm and CO2 is 0.70 atm?