GASES Gases differ sigificaly from solids ad liquids. A gas expads spoaeously o fill is coaier. Gases are highly compressible. Gases form homogeeous mixures wih each oher regardless of he ideiies or relaive proporios of he compoe gases. Subsaces ha are liquids or solids uder ordiary codiios ca usually also exis i he gaseous sae, where hey are ofe referred o as vapors. RESSURE I geeral erms, pressure coveys he idea of a force. ressure,, is he force, F ha acs o a give area, A: F A AMOSHERIC RESSURE he force exered by ay objec is he produc of is mass, m, imes is acceleraio (Fma. Earh s graviy exers a acceleraio of 9.8m/s. A colum of air m is cross secio exedig hrough he amosphere has a mass of roughly 0,000 kg. F (0,000 kg)(9.8 m/s ) x 0 5 kg-m/s he SI ui for forces is kg-m/s ad is called he ewo (N) he pressure exered by he colum is he force divided by is cross-secioal area, A: 5 F x0 N 5 5 x0 N/m x0 a x0 ka A m he SI ui of pressure is N/m. I is give he ame pascal (a) afer Blaise ascal (63-66), a Frech mahemaicia ad scieis: a N/m Joule m 3 a Amospheric pressure ca be measured by use of mercury baromeer. he mercury surface i he dish experieces he full force of Earh s amosphere. Because here is o air i he ube, he mercury is pushed up he ube uil he pressure due o he mass of he mercury colum balaces he amospheric pressure.
Sadard amospheric pressure, which correspods o he ypical pressure a sea level, is he pressure sufficie o suppor a colum of mercury 760 mm i heigh. I SI uis, his pressure equals.035 x 0 5 a. I is used o defie some o-si uis uis used o express gas pressures: he amosphere (am) ad he millimeer of mercury (mm Hg). he laer ui is also called he orr, afer he Ialia scieis Evagelisa orricelli. am 760 mm Hg 760 orr 0.35 ka Shows a closed-ube maomeer, used o measure pressures below amospheric pressure. (b) ad (c) use a ope-ube maomeer o measure gas pressures ha are ear amospheric pressure. BOYLE S LAW he volume of a fixed quaiy of gas maiaied a cosa emperaure is iversely proporioal o he he pressure. I mahemaical erms: cosa or cosa CHARLES S LAW he volume of a fixed amou of gas maiaied a cosa pressure is direcly proporioal o is absolue emperaure. cosa or cosa Avogadro s Law Gay-Lussac carried ou several experimes o he properies of gases. I 808 he discovered he law of combiig volumes: A a give pressure ad emperaure he volumes of gases ha reac wih oe aoher are i he raios of small whole umbers hree years laer Amdeo Avogadro ierpreed Gay-Lussac s observaio by proposig wha is ow kow as Avogadro s hypohesis: Equal volumes of gases a he same emperaure ad pressure coai equal umbers of molecules. Avogadro s law follows from Avogadro s hypohesis: he volume of a gas maiaied a cosa emperaure ad pressure is direcly proporioal o he umber of moles of he gas. cosa x
he Ideal-Gas Equaio We have examied hree hisorically impora gas laws. Each law was obaied by holdig wo variables cosa i order o see how he oher variables affec each oher. All hree ca be combied o make a more geeral gas law: a If we call he proporioaliy cosa R, we obai: R or May imes,, ad all chage for a fixed umber of moles of gas. R cosa If he iiial ad fial codiios of pressure, emperaure, ad volume by subscrips, ad, respecively, we ca wrie: he ideal-gas equaio ca be arraged o yield: Muliplyig boh sides of his equaio by molar mass (M) yields:? M hus, he desiy, d, of he gas is: d M Which ca be rearraged for empirically deermiig molar mass. d M GAS MIXURES AND AIAL RESSURES hus far we have cosidered oly he behavior of pure gases, hose ha cosis of oly oe subsace i he gaseous sae. Joh Dalo s law of parial pressure: he oal pressure of a mixure of gases equals he sum of he pressures ha each would exer if i were prese aloe. he pressure exered by a paricular compoe of a mixure of a mixure of gases is called he parial pressure of he gas 3
If we le equal he oal pressure, ad,, 3, ad so forh. Dalo s law ca be wrie as follows: + + 3 + his equaio implies ha each gas i he mixure behaves idepedely of he oher. Le,, 3, ad so forh, be he umber of moles of each of he gases i he mixure.,, 3 3, ad so forh. Because all he gases experiece he same emperaure ad volume, / ca be facored ou: ( + + 3 + Κ) AIAL RESSURES AND MOLE FRACIONS Because each gas i mixure behaves idepedely, oe ca easily relae he amou of a give gas i a mixure o is parial pressure. / / Here we see ha sum of he moles prese deermie he oal pressure. / / he raio / is called he mole fracio of gas, which we deoe X. he mole fracio, X, is a dimesioless umber ha expresses he raio of he umber of moles of oe compoe o he oal umber of moles i he mixure. hus, he parial pressure of a gas i a mixure is is mole fracio imes he oal pressure. he sum of he mole fracio of a mixure mus equal, i.e. Σ X i X KINEIC MOLECULAR HEORY. Gases cosis of large umbers of molecules ha are i coiuous radom moio (molecules, as used here, meas smalles paricles of ay gas).. he volume of all he molecules of he gas is egligible compared o he oal volume i which he gas is coaied. Aracive ad repulsive forces bewee gas molecules are egligible. Eergy ca be rasferred bewee molecules durig collisio, bu he average kieic eergy of he molecules does o chage wih ime, as log as he emperaure of he gas remais cosa (i.e. he collisios are perfecly elasic). he average kieic eergy of he molecules is proporioal o he absolue emperaure. A ay give emperaure he molecules of all gases have he same average kieic eergy. he kieic-molecular heory gives us a udersadig of boh pressure ad emperaure a a molecular level. he pressure of a gas is caused by collisios of he molecules wih he walls of he coaier. he magiude of he pressure is deermied by boh how ofe ad how hard he molecules srike he walls. 4
Alhough he molecules i a sample of gas have a average kieic eergy ad hece ad average speed, he idividual molecules move a varyig speeds. Disribuio of molecular speeds. Roo-measquare (rms) speed µ, of he molecules a each emperaure. he rms speed is impora because he average kieic eergy of he gas molecules,e, is relaed direcly o µ ½mµ MOLECULAR EFFUSION AND DIFFUSION For all gases a he same emperaure, he average kieic eergies are ideical. hus, a a fixed emperaure, he average speed of a ligh gas is greaer he ha of a heavier gas. A equaio ha expresses his fac quaiaively ca be derived from he heory: 3 µ Noice ha molar mass, M, appears i M he deomiaor. hus, he less massive he gas molecules, he higher he rms speed, µ. he depedece of molecular speeds o mass has several ieresig cosequeces. homas Graham discovered ha he effusio rae of a gas is iversely proporioal o he square of is molar mass. 5