CHM1045 Lecture 16 Outline of Last Lecture I Density Calculation II Molar Mass a Gaseous Substance III Gas Stoichiometry IV Dalton s Law of Partial Pressures V Mole fraction Xi Ni Nr VI Collecting a Gas over Water Outline of Current Lecture I Kinetic Molecular Theory of Gases II Kinetic theory of gases and III Gas diffusion IV Gas effusion V Deviations from Ideal Behavior Current Lecture Kinetic Molecular Theory of Gases 1 A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions The molecules can be considered to be points that is they possess mass but have negligible volume 2 Gas molecules are in constant motion in random directions and they frequently collide with one another Collisions among molecules are perfectly elastic 3 Gas molecules exert neither attractive nor repulsive forces on one another 4 The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins Any two gases at the same temperature will have the same average kinetic energy KE mu2 Kinetic theory of gases and Compressibility of Gases Boyle s Law P a collision rate with wall Collision rate a number density Number density a 1 V P a 1 V Gay Lussac s Law P a collision rate with wall Collision rate a average kinetic energy of gas molecules Average kinetic energy a T PaT Avogadro s Law P a collision rate with wall Collision rate a number density Number density a n Pan Dalton s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas Ptotal SPi The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature urms 3R M T Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties M2 r1 r2 Gas effusion is the process by which gas under pressure escapes from one compartment of a container to another by passing through a small opening r2 M1 r1 Example 1 A flammable gas made up only of carbon and hydrogen is found to effuse through a porous barrier in 1 50 min Under the same conditions of temperature and pressure it takes an equal volume of bromine vapor 4 73 min to effuse through the same barrier Calculate the molar mass of the unknown gas and suggest what this gas might be 1 50 min M 159 8 g mol 4 73 min M 1 50 min 2 159 8 g mol 4 73 min 16 1g mol Deviations from Ideal Behavior 1 mole of ideal gas PV nRT N PV 1 0 RT
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