Prof Gilbert LECTURE 15 CHEM 1211 10 14 10 Announcements Reminders Mid Term Exam Average was 74 75 If you scored less than a 50 you should plan to see me in Chem Central today at noon or next Tuesday during my office hours Last time Chapter 5 Thermochemistry Calculating H0 rxn values from standard enthalpies of formation H0 f of the products and reactants Application of Hess s law to calculate H0 rxn values Fuel values and the impact of oxygenated additives in gasoline This time Chapter 6 Gases Barometric Pressure is the force F exerted by the weight of the atmosphere over the surface area A of the Earth That is P Pa F N A m2 Where Pa is pascals the SI unit of pressure and N is newtons the SI unit of force It s more common to use kPa kilopascals where an atmosphere of pressure atm 1 atm 101 325 kPa 1013 6 mbar 760 mmHg That 760 mm value is the height of the column of Hg d 13 595 g cm3 at 0 C in this Hg pool barometer For any other liquid the height of the column above the pool is inversely proportional to the density of the liquid Why Working barometers don t rely on liquid mercury A popular design for making a recording barometer or barograph is shown on the left Variations in barometric pressure 1 meteorological Here for example is a satellite view of Hurricane Katrina as it intensified to a Category 5 hurricane with maximum sustained winds of 175 mph 280 km h and a minimum central pressure of 902 mbar Generally the lower the central pressure of a hurricane the higher the wind speeds Why 2 Pressure decreases with increasing altitude Why The Gas Laws Based on personal experience you know that The pressure of a volume of gas is proportional to the amount of gas in the volume as in inflating a bicycle tire P n The pressure of a volume of gas increases with increasing temperature P T The volume of a quantity of gas is inversely proportional to the applied pressure V 1 P 1 2 3 Combining these observations we have or PV nT Turning this expression into an equation by installing a constant of proportionality R we have the ideal gas law PV nRT Keep in mind that this equation works only if temperature values are on an absolute temperature e g Kelvin scale Also the value of R called the gas constant depends on the units Most of the time we use 0 0821 L atm mol K Calculations Use PV nRT when 3 of the 4 variables are known and you seek the 4th Often the key variable is the number of moles n of a gas produced or consumed in a chemical reaction You may first need to convert a mass of gas into an equivalent number of moles by dividing by its molar mass Inquiry 1 The volume of helium in this balloon which was flown around the world by the late Steve Fossett in 2002 was about 1 56 107 liters at 20 C and 1 00 atm of pressure What mass of helium was needed to fill the balloon Inquiry 2 A weather balloon filled with 100 0 liters of He is launched from sea level T 20 C P 755 torr What is the volume of the balloon when it rises to an altitude of 10 km where T 252 C and P 195 torr Solution When n is a constant then PV T is a constant and the following general gas equation may be used 1 2 3 Determining molar mass M The number of moles n of a substance is equal to its mass m divided by its molar mass M Substituting this into fraction into the ideal gas law we have or M Inquiry 3 A balloon is inflated with 4 62 g of a gas to a volume of 2 46 L at 27 C and 1 05 atm What is the molar mass of the gas Gas density and molar mass A mole of any ideal gas occupies the same volume at a given temperature and pressure But the mass m of that volume and therefore the density of the gas is proportional to the molar mass M M or d M Inquiry 4 What is the density of propane C3H8 at STP Would propane leaking from a tank stored in the basement of a house tend to collect in the basement or rise into the floors above Inquiry 5 The tanks used in barbecue grills such as the one shown here contain about 20 pounds of propane If this much propane leaked out what volume would it occupy at 25 C and 1 00 atm Mixtures of gases Rule ideal gases behave independently in a mixture each contributing its own partial pressure so that the total pressure is the sum of the partial pressures Ptotal P1 P2 P3 This relationship is called Dalton s law of partial pressures One application collecting a gas by displacing a liquid with a significant vapor pressure e g water from a jar inverted in a pneumatic trough In this example PO2 Pbar PH2O where Pbar is barometric atmospheric pressure At 25 C PH2O 23 8 mm Note vapor pressure of a substance increases with increasing temperature Inquiry 6 Suppose you are setting up an O2 generator like the one on the right You add 5 00 g of KClO3 to the test tube If it all decomposed how big a bottle would you need to catch all the O2 at 25 C Partial pressure Px and the mole fraction Xx of gas x in a mixture Px Xx Ptotal Ex at 1 00 atm the values of PN2 and PO2 are 0 79 and 0 21 atm because the mole fractions XN2 and XO2 are 0 79 and 0 21 Inquiry 7 A high performance 100 stainless steel scuba tank weighs 7 4 pounds more when it is filled with air at 3500 psi than when it is empty and its internal pressure is only 1 00 atm or 14 7 psi If the temperature of the tank is 25 C what is its volume