Mixture of gases Mix 5 moles of CO2 2 moles of N2 1 mole of Cl2 What is P Mary J Bojan V 40L T 0 C Chem 110 1 Partial Pressure Partial pressure the pressure a gas would have if it was the only gas in the container Dalton s Law of Partial Pressures Total pressure is equal to the sum of partial pressures The fraction of the total pressure contributed by each gas is equal to its mole fraction I Mary J Bojan Chem 110 2 Sample Problem 3 0L of He at 5 0 atm and 25 C is combined with 4 5 L of Ne at 2 0 atm and 25 C at constant T into a 10L vessel What is the partial pressure of the He in the 10L vessel What is the total pressure in the 10L vessel Mary J Bojan Chem 110 3 Sample Problem What is the partial pressure of O2 in the vessel 1 2 3 4 5 75 6 torr 378 torr 680 torr 756 torr There is not enough data Mary J Bojan Chem 110 4 Composition of the atmosphere mole fraction xi moles of i total moles N2 and O2 represent 99 of atm Mary J Bojan Chem 110 5 Composition of the atmosphere For other components use parts per million ppm ppm xi 106 Eg Neon xNe 0 00001818 Ne concentration 18 18 ppm If you know the barometric pressure you can determine the partial pressure PBAR 0 987 atm PTOT PNe xNe PTOT 18 18 10 6 0 987 atm 17 94 10 6 atm Mary J Bojan Chem 110 6 Collecting Gas over water Example Pbar V T During a reaction N2 is collected over H2O 742 torr PTOT 55 7 ml 23 C How much N2 moles was collected Mary J Bojan Chem 110 7 Regions of Atmosphere Temperature Profile Thermosphere High energy radiation is absorbed Ions formed Mesosphere Density of gases is small Stratosphere Warming caused by ozone cycle Ultraviolet light absorbed Troposphere Life where we live weather planes What is temperature Mary J Bojan Chem 110 8 KINETIC MOLECULAR THEORY gives a view of gases on a molecular level 5 key postulates 1 Molecules move in straight lines their direction is random 2 Molecules are small The volume they occupy is small compared to the total V 3 Molecules do not attract or repel each other no intermolecular forces 4 Elastic collisions If 5 Mean kinetic energy T K Mary J Bojan Chem 110 9 T 1 2 mu2 average kinetic energy of molecule u root mean square speed of molecule m mass of molecule in kg When T increases less molecules move slowly more molecules move quickly average speed is greater Mary J Bojan Chem 110 10 Kinetic Molecular Theory provides explanations for why gases behave as they do Experimentally Observed Behavior P T n V fixed As T increase P increases WHY Mary J Bojan Chem 110 11 Why gases behave as they do Experimentally Observed Behavior V 1 P n T constant As V increase V P decreases WHY Mary J Bojan Chem 110 12 Kinetic Molecular Theory of Gases 3 2 RT Mu2 different gases at the same T have different average speeds On average lighter gases move faster heavier gases move slower Mary J Bojan Chem 110 13 What is the rms speed u of N2 at 20 C Mary J Bojan Chem 110 14 Motion of gases Effusion leakage of gas through a small opening Diffusion spread of gas through space Rate of effusion diffusion Usually we compare the rate of two gases Heavy molecules effuse diffuse more slowly than lighter molecules Graham s Law Mary J Bojan Chem 110 15 Motion of Gases An unknown gas effuses at a rate 1 49 times as fast as Cl2 What is the molecular weight of the gas Mary J Bojan Chem 110 16 Non Ideal Gas Behavior PV nRT for low P high T Real gases deviate from ideal behavior Reasons 1 Molecules have finite size 2 Molecules exert attractive forces In general As P increases non ideality increases As T decreases non ideality increases Mary J Bojan Chem 110 17 At high P Postulate 2 in KMT not true As P increases PV RT increases H2 V of container is not than V of gas use of ideal gas law leads to appearance of larger n Mary J Bojan Chem 110 18 At low T postulate 3 in KMT not true As P increases PV RT decreases CO2 attractive forces lead to the appearance of a smaller n molecules stick together Different gases behave differently Eg CO2 has stronger intermolecular forces than CH4 or N2 therefore it deviates more from ideality at low pressures Mary J Bojan Chem 110 19 Behavior at high T As T increase effect if intermolecular forces is not as pronounced One mole of the same gas at different temperatures Mary J Bojan Chem 110 20 Correcting the ideal gas law at intermediate pressures P is too small deviation is related to size of attractive interactions a frequency of collisions n 2 a V at high pressure V is too large actual V Vcont Vexcluded V nb b volume per mole of molecules P Mary J Bojan V nRT van der Waals Equation Chem 110 21
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