Ch 11 Gases and Their Properties SCUBA diving Hot air balloons automobile air bags Only need 4 quantities to describe most gases Pressure P volume V temperature T and the amount of gas n moles R 0821 L atm mol K PV nRT Ideal gas law 1 11 1 Gas Pressure Pressure is the force exerted on an object divided by the area over which it is exerted Pressure is force per unit area lb in2 psi N m2 Atmospheric pressure is measured using a barometer Definitions of standard pressure KNOW 76 cm Hg 760 mm Hg 760 torr 1 atmosphere atm 101 3 kPa 1 01325 bar 14 69 psi 2 Hg density 13 6 g mL Fig 11 15 p 531 Conversions 4 11 2 Gas Laws The Experimental Basis Boyle s Law The Compressibility of Gases Boyle s Law The Volume Pressure Relationship At a given T the product of the pressure and volume of a definite mass of gas is constant PV k constant n T T always in Kelvin http www grc nasa gov WWW k 12 airplane aboyle html good example 5 At 25oC a sample of He has a volume of 4 00 x 102 mL under a pressure of 7 60 x 102 torr What volume would it occupy under a pressure of 2 00 atm at the same T Think what it should be first Known Values V1 400 mL P1 760 torr 1 atm P 2 atm V2 6 Boyle s Law The Volume Pressure Relationship Notice that in Boyle s law we can use any pressure or volume units as long as we consistently use the same units for both P1 and P2 or V1 and V2 Use your intuition to help you decide if the volume will go up or down as the pressure is changed and vice versa 7 What volume will 2 50 L of a gas occupy if the pressure is changed from 760 to 630 mm Hg 8 The Effect of Temperature on Gas Volume Charles s Law The Volume Temperature Relationship Charles s law states that the volume of a gas is directly proportional to the absolute temperature at constant pressure http www grc nasa gov WWW k 12 airplane aglussac html good one http group chem iastate edu Greenbowe sections projectfolder flashfiles gaslaw boyles law graph html cool one can change volume http www nclark net GasLaws good website with lots of examples Gas laws must use the Kelvin scale to be correct Relationship between Kelvin and centigrade o K C 273 9 Charles Law The Volume Temperature Relationship A sample of hydrogen H2 occupies 1 00 x 102 mL at 25 0oC and 1 00 atm What volume would it occupy at 50 0oC under the same pressure V1 100 mL T1 25C 298K P1 1 atm V2 T2 50C 323K P2 1 atm 10 3 00 l of hydrogen at 20 C is allowed to expand to 3 50 l What is the temperature in C P is constant 11 Standard Temperature and Pressure Standard temperature and pressure is given the symbol STP It is a reference point for some gas calculations Standard P 1 00000 atm or 101 3 kPa Standard T 273 15 K or 0 00oC 12 Combining Boyle s and Charles s Laws The General Gas Law Boyle s and Charles Laws combined into one statement is called the general or combined gas law equation Useful when the V T and P of a gas are changing http www mhhe com physsci chemistry essentialchemistry flash gases v6 swf awesome site for all gas laws Boyle s Law P1V1 P2 V2 Charles Law V1 V2 T1 T2 For a given sample of gas The combined gas law is PV P1 V1 P2 V2 k T T1 T2 13 Think about it P 1 atm T 280 K V 2 0 l if you cool the gas and let it expand what will be the P or 1 atm 14 A sample of nitrogen gas N2 occupies 7 50 x 102 mL at 75 00C under a pressure of 8 10 x 102 torr What volume would it occupy at STP Clicker Q ST In C SP In atm P1 810 torr V1 750 mL T1 75C 348K P2 1 atm 760 torr V2 T2 273K 15 Given 20 0 l of ammonia gas at 5 C and 730 torr calculate the volume at 50 C and 800 torr 16 Avogadro s Hypothesis Avogadro s Hypothesis states that at the same temperature and pressure equal volumes of two gases contain the same number of molecules or moles of gas If we set the temperature and pressure for any gas to be STP then one mole of that gas has a volume called the standard molar volume http www mhhe com physsci chemistry essentialchemistry flash gasesv6 swf awesome site for all gas laws 17 Avogadro s Hypothesis The standard molar volume is 22 4 L at STP This is another way to measure moles For gases the volume is proportional to the number of moles 11 2 L of a gas at STP 0 500 mole 44 8 L 18 One mole of a gas occupies 36 5 L and its density is 1 36 g L at a given temperature and pressure a What is its molar mass b What is its density at STP 19 2CO 2 NO 2CO2 N2 0 20 moles of CO and 0 20 moles of NO occupy 15 0 l what volume will products occupy 20 Summary of Gas Laws The Ideal Gas Law Boyle s Law V 1 P at constant T n Charles Law V T at constant P n Avogadro s Hypothesis V n at constant T P Combine these three laws into one statement V nT P Convert the proportionality into an equality V nRT P This provides the Ideal Gas Law PV nRT R is a proportionality constant called the universal gas constant 21 We must determine the value of R Recognize that for one mole of a gas at 1 00 atm and 273 K STP the volume is 22 4 L Use these values in the ideal gas law Derive the value of R Useful if you forget what R is 22 Summary of Gas Laws The Ideal Gas Law R has other values if the units are changed R 8 314 J mol K Use this value in thermodynamics R 8 314 kg m2 s2 K mol Use this later in this chapter for gas velocities R 8 314 dm3 kPa K mol This is R in all metric units R 1 987 cal K mol This the value of R in calories rather than J 23 11 3 The Ideal Gas Law PV nRT What volume would 50 0 g of ethane C2H6 occupy at 1 40 x 102 C under a pressure of 1 82 x 103 torr 24 Derive V from ideal gas law Avogadro s Law proof 25 Calculate the pressure exerted by 50 0 g of ethane C2H6 in a 25 0 L container at 25 0oC 26 Calculate …