General Chemistry CHEM 1310
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This 0 page Class Notes was uploaded by Tierra Ernser on Monday November 2, 2015. The Class Notes belongs to CHEM 1310 at Georgia Institute of Technology - Main Campus taught by Charles Sherrill in Fall. Since its upload, it has received 19 views. For similar materials see /class/234326/chem-1310-georgia-institute-of-technology-main-campus in Chemistry at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
CHAPTER 5 Gases Chemistry of Gases Pressure and Boyle s Law Temperature and Charles Law The Ideal Gas Law Chemical Calculations of Gases Mixtures of Gases Kinetic Theory of Gases Real Gases CHEM 1310 NB Fall 2006 Gases The states of matter Gas fluid occupies all available volume Liquid fluid fixed volume Solid fixed volume fixed shape Others Gases are the easiest to understand can model them more precisely than liquids or solids using simple equations CHEM 1310 NB Fall 2006 Ways to produce gases include Decomposition 2 H90 8 gt 2 H9 I 02 g CaCO3 s heat gt CaO s 002 g etc Acids reacting with carbonates or hydrogen carbonates to release 002 chapter 4 NaHCO3 s HCI aq gt NaCl aq H20 I 002 g Acids react with metal Zn 3 2 HCI aq gt ZnCl2 aq H2 g CHEM 1310 NB Fall 2006 Some properties of gases Pressure P how much force it exerts per unit area Temperature T how hot or cold kinetic energy of gas molecules Volume V space it takes up the whole volume of the container it s in CHEM 1310 NB Fall 2006 Pressure Often measured by a barometer The height of a column of mercury is related to the air pressure Standard atmospheric pressure gives a column of mercury 76 cm high How does this work I 76 cm i Mercury al 2003 ThnmsangtBrocksICoE CHEM 1310 NB Fall 2006 Pressure by barometer Atmosphere pushes down on mercury in beaker causes it ll 395 to rise in column Push of atmosphere exactly balanced by force due to weight of mercury Fma Mass of mercury is m d A h and ag so F ma dAhg P FA dgh bl CHEM 1310 NB Fall 2006 Units of pressure PFANm2kgms2m2 kg msz SI unit pascal Pa 105 Pa 1 bar Atmospheric pressure is 76 cm of Hg or 760 mm Hg Density is 13596 g cm1 at 00 C or 13596 x 104 kg m3 P gdh 980665 ms2 X13596 x 104 kgm3 x 07600 m 10133 x 105 kg msz 101325 x 105 Pa 1 atmosphere 1 atm CHEM 1310 NB Fall 2006 Connection between P amp V Boyle s Law Pressure and volume of a gas Pm 760 mm Hg pm 760 mm Hg are related Use a J tube to figure out Height mm 500 hOW 500 In a pressure of atm exactly 7400 4quot balances pressure of trapped M 300 gas Pgas Patm 200 In b pressure of gas is 20quot pressure balanced by Patm that due to extra mercury added gdh Pgas Patm gdh Gas is compressed takes less V and at higher pressure if more Hg is added 100 o 2003 ThomsonBYODKSICOIE CHEM 1310 NB Fall 2006 Boyle s Law Boyle did experiments to show that if the pressure doubled the gas took up 12 as much room etc Pressure and volume are inversely related P1 V1 P2 V2 for fixed T and amt of gas or more generally PV C constant at fixed T and amount of gas where C is independent of the particular gas chosen C 224 L atm at 0 C and 1 mol of gas 0 C 1atm are standard temperature and pressure STP At STP one mol of gas occupies 224L CHEM 1310 NB Fall 2006 Relationship between VampT Charles Law As T goes up at constant pressure Patm gas expands V V0 or V0 Tcel Tcel in Celcius All gases expand by the same relative amount when heated ie or is nearly the same for all gases Celcius temperature scale water freezes at 0 C water boils at 100 C by definition Easy On Celcius scale or 127315 C has a weird result when T27315 C Absolute zero Can t get below 273150C Absolute temperature scale T Kelvin 27315 Tcel Celcius CHEM 1310 NB Fall 2006 Relationship between V and T Thermometer P aim Glass tube Moveable mercury plug 0 C 20 C 100 C ice water mom Boiling m 2003 ThemsonErookslcule temperature water CHEM 1310 AB Fall 2006 Charles Law in Kelvin T scale If we substitute TGel T Kelvin 27315 we get V a T where a V0 27315 So now V1V2 T1T2 for a fixed pressure and amount of gas Lots of easy problems can be worked with this for example ifT in Kelvin is doubled what happens to V CHEM 1310 NB Fall 2006 Ideal Gas Law Combines Charles Law and Boyle s Law V or nT P Volume is proportional to amount of gas and temperature and inversely proportional to pressure Call the constant of proportionality R universal gas constant PV nRT R 0082058 L atm mol1 K1 83145 J mol1 K1 Can do lots of easy problems relating P V n T of a gas using this simple equation CHEM 1310 NB Fall 2006 Example problem A gas cylinder weighs 15 kg empty and 20 kg when filled with 002 gas If the cylinder has a volume of 10 L what s the pressure of the gas at 25 C CHEM 1310 NB Fall 2006 Ideal gas law w molar mass Could have done the last problem more directly by recasting the ideal gas law N m mass M molar mass PV mM RT Also since density dmV d PMRT Can predict density from P T M Can determine M and notjust empirical formula from d P T CHEM 1310 NB Fall 2006 Gases in chemical reactions Can use ideal gas law to do stoichiometry problems now using P T V instead ofjust masses Example We want to make 150 kg of the rocket fuel hydrazine using the reaction 2 NH3 g NaOCl aq gt N2H4 aq NaCI aq H20 I If our ammonia is at 10 C and 363 atm how much of it in L do we need CHEM 1310 NB Fall 2006 Mixtures of gases Suppose 3 containers of equal volume V each of which contained 1 mol of gas at 1 atm of pressure H2 02 N2 V T 1atm 1mo V T 1atm 1mo V T 1atm 1mo What happens if we take the O2 and N2 from the 2nd and 3tOI containers and put them in the W container at constant T and of course constant V What s the total pressure CHEM 1310 NB Fall 2006 Mixtures of gases cont d V T H2 02 1 mol H2 N2 1 mol 02 1 mol N2 Partial pressure pressure exerted by each gas in a gas mixture Total pressure sum of partial pressures Each gas obeys ideal gas law separately for the number of moles of that gas and the partial pressure Ideal gas law also holds for Ptot ntot PH2 nH2 R T V etc Ptot ntot R TV Therefore PH2 Pt nHZ nt t 13 for this example This is also called e mole raction XH2 PH2 Ptot x XH2 13 Ptot for this example CHEM 1310 NB Fall 2006 Kinetic Theory of Gases Tries to explain gas behavior using basic physics Molecules of a gas fly around in random directions with a distribution of speeds The molecules are pictured as hard objects undergoing elastic collisions with each other and the walls of the container Pressure results from the many collisions of the gas molecules with the walls of the container P FA P on impulse per collision x rate of collisions with walls CHEM 1310 NB Fall 2006 Origin of pressure P FA P 0L impulse per collision x rate of collisions with walls P 0L m x u x NV x u Nmu2 V where u speed of molecules m mass of molecules NV number of molecules per unit volume more molecules more collisions note faster molecules u more collisions CHEM 1310 NB Fall 2006 Origin of pressure cont d So far we have PV or Nmu2 Problem notjust one speed u lots of them Solution ok to use an average over u2 the mean square speed ltu2gt Proportionality constant works out to be 13 so PV 13 Nmltu2gt But we also know PV nRT so nRT 13 Nmltu2gt or RT 13 N0 mltu2gt because N is just n times No Avogadro s number CHEM 1310 NB Fall 2006 Origin of pressure cont d So we see that RT 13 N0 mltu2gt Temperature is therefore due to the kinetic energy of the gas molecules KE 12 m u2 Average KE per mol is 12 Nom ltu2gt 32 RT or ltu2gt 3RT M since molar mass M Nom So molecules move faster at higher T and slower if they are more massive CHEM 1310 NB Fall 2006 MaxwellBoltzmann distribution of molecular speeds in N2 at 3 temps 0 C l E a i E a E g D i 3 1000 C E 1 Z 2000 C 139 500 1000 1500 2000 2500 3000 3500 ump9 Speed u m squot Iv gt Jame Note urms ump uav 2003 TthSunBmokslcole CHEM 1310 AB Fall 2006 Measurement of speed distributions 39 gt i A r g i 2 2 2003 ThemsenBrockleulE CHEM 1310 NB Fall 2006 Root mean square RMS speed UrmS sqrtltu2gt sqrt3RTM Example He at 298K has what RMS speed CHEM 1310 NB Fall 2006 Diffusion Result of previous example seems to large eg odors don t seem to travel this fast Reason direction of molecule keeps changing due to collisions with other gas molecules Diffusion random motion ofa molecule due to collisions with other molecules Typically about 1010 collisions per second Typically goes about 10397 m between collisions mean free path 2003 ThumsamBroaksCole CHEM 1310 AB Fall 2006 Rates of effusion and gaseous diffusion Effusion molecules escape through a very small hole Into vacuum a Gaseous diffusion molecules pass through a 3 39 large porous barrier into 0 a 3 039 another container o r The rates of both of both 1 processes are Inversey proportional to the molar 9 9 mass of the gas 0 0 Gaseous diffusion used to separate 235U from 238U 39 02 He in World War II CHEM 1310 NB Fall 2006 Real gases PVnRT is the ideal gas law Gases are not ideal Implicitly assumes Gas molecules are ideal point particles with no size No attraction between molecules In reality gas molecules do take up some volume and there IS some attraction between gas molecules which can cause clustering First effect reduces volume available to gas and second reduces pressure exerted by gas Van der Waals equation of state P a n2N2 V nb nRT IS more accuate ab depend on gas are tabulated n2N2 IS of pairs per volume and nb IS excluded volume CHEM 1310 NB Fall 2006
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