CHEM 1515 1st Edition Exam 3 Study Guide Lectures 12 19 Ch 10 3 10 7 5 7 8 1 8 4 Lecture 12 March 17 Ch 10 3 Ideal Gas Laws The Ideal Gas Equation pV nRT Boyle V is proportional to 1 p Charles V is proportional to T Avogadro V is proportional to n Combined V is proportional to nT p or V R nT Reshuffled p V n R T p How to find a value for the universal gas constant R Take 1 mole of any gas at STP p V 1 atm x 22 4 L R nT 1 mol x 273 15 K L atm Best value R 0 082058 mol K Watch the units Use liters for volume atm for pressure K for temperature Problem Air or nitrogen gas is added to tennis balls to improve their bounce A tennis ball that has a volume of 144 mL contains 0 33 g of nitrogen gas N2 What is the pressure inside the ball at 24oC V 0 144 L You must use liters in this equation n 4 622 mol T 297 K Must use Kelvin P R 0 082058 L atm mol K 0 144 L P 4 622 mol 0 082058 L atm mol K 297 K P 782 atm all units except the atm cancel To calculate densities of gases Use molar mass molar volume take one mole find its mass find its volume What is the density of methane gas CH4 MW 16 0 at STP oxygen gas O2 MW 32 0 at STP oxygen gas O2 MW 32 0 at 25oC and 0 850 atm Density of a gas usually given in g L very much smaller than d of a liquid directly proportional to its MW inversely proportional to absolute T Ch 10 4 Experimental Determination of Molecular Weights MW for gases and volatile liquids Molecular Weight MW and Molar Mass Mm same number but different units for water molecular weight MW 18 amu molar mass Mm 18 g mol For a substance that is a gas or that can be easily converted to a gas we can use the ideal gas law to find the number n of moles pV nRT Mm grams moles A 0 970 g sample of the vapor of a volatile liquid occupies 200 0 mL at 733 torr and 99oC What is its molar mass Reactions with Gaseous Reactants or Products We can use pV nRT to convert mol L L mol Air bags in automobiles are inflated using the rapid reaction of sodium azide NaN3 with iron III oxide which is initiated by a spark 6 NaN3 Fe2O3 3 Na2O 2 Fe 9 N2 How many moles and how many liters of N2 at STP are formed by the reaction of 130 g of NaN3 FW 65 0 Ch 10 5 In Gas Mixtures each gas exerts its own partial pressure Dalton s Law of Partial Pressures The sum of the partial pressures of the gases in a mixture is equal to the total pressure ptotal pA pB pC Individual partial pressures follow the ideal gas law For component A pA V nA R T Mole fraction X used to indicate composition of a mixture Mole fraction XA equals moles of component A over total number of moles For a gaseous mixture Mole fraction XA equals partial pressure of component A over total pressure nA pA XA So nA XA x ntotal ntotal p total and pA XA x ptotal A gaseous mixture consists of 3 mol N2 and 2 mol O2 What are the mole fractions XN2 and XO2 If ptotal 10 atm what are the partial pressures pN2 and pO2 Mole fractions Also do not have a unit add up to exactly 1 mol mole fraction x 100 An industrial gas contains H2 under a pressure of 0 45 atm CO 0 60 atm CO2 0 45 atm N2 3 00 atm What is the total pressure What are the mole fractions of the individual gases A 5 60 L vessel at 273 K contains 6 40 g O2 0 200 mol and 35 0 g N2 1 25 mol Calculate the partial pressure of O2 the partial pressure of N2 the total pressure the mole fraction X of O2 from partial pressures the mole fraction X of O2 from the number of moles Gases collected over water are saturated with water vapor The vapor pressure of water changes with temperature See table in text or Lab Manual 2 KClO3 s 2 KCl s 3 O2 g When a sample of potassium chlorate KClO3 was decomposed 0 250 L of O2 gas were collected over water at 26oC pH2O 25 2 torr and 765 torr total pressure 1 What is the partial pressure of O2 in the gas 2 How many moles of of O2 gas were collected 3 How many moles of KClO3 and how many grams of KClO3 FW 122 55 were decomposed Lecture 13 March 19 Ch 10 6 Kinetic molecular Theory of Gases 1 Gas molecules are in constant random motion They move in straight lines and in all directions Evidence a Brownian motion b Pressure caused by collisions of gas molecules with container walls is the same in all directions 2 The size of gas molecules is negligibly small compared to the distance between them Evidence Gases are highly compressible 3 Forces of attraction and repulsion between gas molecules are negligibly small Evidence Gases fill any available volume 4 Collisions between gas molecules are elastic No kinetic energy is lost Evidence A closed container insulated from heat exchanges does not show a steady drop in pressure 5 The average kinetic energy of a gas molecule 1 2 mu2 is directly proportional to the absolute temperature Evidence Brownian motion increases with temperature 6 At any given temperature molecules of all gases have the same average kinetic energy mA uA2 mB uB2 K M Theory explains why p is proportional to n Avogadro to 1 V Boyle to T Charles Gaseous Diffusion A gas spreads through another gas to occupy the space with uniform partial pressure Gaseous Effusion A gas flows through a small hole in a container Graham s Law of Effusion The rate of effusion of gas molecules from a particular hole is inversely proportional to the square root of the molecular weight of the gas at constant temperature and pressure rate A MWB Rate of effusion proportional to 1 MW 1 2 or rate B MW A Ex How many times faster than O2 MW 32 will H2 MW 2 effuse from a particular pinhole RateH2 RateO2 32 2 16 4 Thus H2 will effuse at a rate 4x faster than O2 Ex An unknown gas composed of diatomic molecules X2 effuses at a rate that is only 0 355 times that of O2 at the same temperature What is the molecular weight and what is the identity of the gas K M Theory says At any given temperature molecules of all gases have the same average kinetic energy mA uA2 mB uB2 From that we can derive Molecular speed proportional …