Chapter 10 What is pressure Gases Pressure and Boyle s Law Temperature and Charles Law Avogadro s Law Ideal gas equation of state PV nRT Density and Molecular Weight d PM RT or M dRT P Ideal Gas Law and Chemical Reactions Stoichiometry Partial Pressures Dalton s Law 1 PRESSURE Pressure force area F newtons A m2 SI Units 1N m2 1Pa Pascal Standard atmospheric pressure 1 atm 1 013x105 Pa 1 atm 760 torr mm Hg 1 atm 14 7 lb in2 real atmospheric pressure varies with altitude and weather What causes atmospheric pressure 2 Pressure at any altitude depends on weight of gas above it Pressure decreases exponentially with altitude What is pressure What is pressure Force on a surface exerted by colliding gas molecules More gas molecules faster gas molecules Higher pressure Altitude km 0 50 100 200 P atm 1 10 3 10 6 10 13 collision frequency sec 1 1010 107 103 1 4 Measuring Pressure Barometer to measure Patm Pressure balance Patm F A F A Patm F A gd h g x d Ah A where g gravitational constant d density of liquid Patm constant x h Patm height of liquid column measure P in terms of Hg column height 1 atm 760 torr 760 mmHg 5 Manometer Used to measure gas pressure P 0 6 What is the pressure in the flask Patm 742 torr Patm 756 torr 7 What is the pressure of the gas in the bulb 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Pgas Ph Pgas Patm Pgas Ph Patm Pgas Ph Patm Pgas Patm Ph Pgas Ph Pgas Patm Pgas Ph Patm Pgas Ph Patm Pgas Patm Ph Pgas Ph Pgas Patm Pgas Ph Patm Pgas Ph Patm Pgas Patm Ph PVT relationships State of gas described by n P V T n moles P pressure V volume T absolute temperature K add T absolute temperature K 273 to oC Avogadro s Law V of gas at constant T and P is proportional to the number of moles of gas V n P T fixed V n constant 22 4L 1 mol at STP STP 0 C 273K and 1 atm Standard Temperature and Pressure Think about collision of gas molecules inside a balloon higher n more gas molecules to collide on the balloon more inflation larger volume constant of proportionality is the same for ALL gases PVT relationships Boyles Law V of a fixed amount of gas at constant T is inversely proportional to P V 1 P n T fixed PV constant 10 PVT relationships Charle s Law V of fixed amount of gas at constant P is proportional to the absolute temperature V T n P fixed V T constant Think about collision of gas molecules inside a balloon higher temperature more frequent collision of molecules more inflation larger volume 11 PVT relationships So far V 1 P Boyle s law V T Charles s law V n Avogadro s law Think about collision of gas molecules inside a balloon Higher outer pressure to compact the balloon smaller volume Higher temperature faster moving gas molecules more frequent collisions more inflation larger volume More gas molecules more frequent collisions more inflation larger volume Combining these nT nT V const P P PV const R nT PV nRT 12 Sample problems What is the volume of a gas at 30oC if the gas has a volume of 2 0L at 50oC What is the pressure of a gas at 30oC if the gas has a pressure of 2 0atm at 50oC What is the pressure of a gas in a 2 0L flask if the gas has 1 0atm pressure in a 1 0L flask Ideal Gas Law PV nRT PV nT constant R T units K R gas constant Units of R are important J L atm R 8 314 R 0 08206 mol K mol K When we deal with ideal gas behavior PVT relationship identity of molecules does not matter Example V occupied by 1 00 What is the volume mole of gas at exactly 0 C and 1 atm V nRT P 1 00 mol x 0 08206 Latm molK x 273K 1atm 22 4 L Typically For pressure or volume use R in Latm molK For speed or energy use R in J molK STP Standard Temperature and Pressure 0 C 273K and 1 atm VSTP 22 4L mol Note STP for gases is not the same as standard state conditions used for H Density and Molecular Weight density mass volume mass nM From Ideal Gas Law g mass Units L volume n of moles M molecular weight n P V RT nM PM d V RT PM density d RT dRT Molecular weight M P 15 Density and Molecular Weight What is the density of CO2 at 2 50 atm and 30 0oC What is the molecular weight of a gas that has a density of 2 00 x 10 3 g mL at 1 50 atm and 20oC 16 Mixture of gases Mix 5 moles of CO2 2 moles of N2 1 mole of Cl2 What is the total P When we deal with ideal gas behavior Identity of molecules does not matter V 40L T 0 C PTOT RT nTOT V Or the total pressure can be calculated by summing up the partial pressures by individual components PTOT PCO 2 PN2 PCl 2 PTOT nCO 2 RT RT RT nN2 nCl 2 V V V Partial pressures 17 Partial Pressure Partial pressure the pressure a gas would have if it was the only gas in the container PTOT nCO 2 RT RT RT nN2 nCl 2 V V V 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 ni ntotal ni Pi ni Pi X i PTOT PTOT i nTOT PTOT n TOT For Example what is the mole fraction of CO2 in a 5L container if its partial pressure is 2 8atm and the total pressure is 4 5atm 18 Sample Problems 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 PV T constant nR What is the total pressure in the 10L vessel What is the partial pressure of O2 in the vessel PTOT 756 TORR T 300 0 C VTOT 5 00 L 1 2 3 4 5 GAS Ar N2 CO2 Ne O2 MOLE FRACTION 0 320 0 270 0 150 0 160 75 6 torr 378 torr 680 torr 756 torr There is not enough data 19 Collecting Gas over water Example During a reaction N2 is collected over H2O Pbar 742 torr PTOT V 55 7 ml T 23 C How much N2 moles was collected vapor pressure of water at 23oC 21 torr 20 More practice questions 21 Composition of the atmosphere mole fraction …