What is Physical Chemistry. Physical Chemistry for Chemical Engineers CHEM251. Basic Characteristics of a Gas

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7/6/0 hysical Chemistry for Chemical Egieers CHEM5 What is hysical Chemistry hysical Chemistry is the study of the uderlyig physical priciples that gover the properties ad behaviour of chemical

1 7/6/0 hysical Chemistry for Chemical Egieers CHEM5 What is hysical Chemistry hysical Chemistry is the study of the uderlyig physical priciples that gover the properties ad behaviour of chemical systems * LECURER: Dr. atrick Ndugu *Ref: hysical Chemistry 4 th Editio: Ira N. Levie Basic Characteristics of a Gas Why look at a gas? What is a gas? Expads Uiformly Ca be Compressed Low Desity Simplest Form of Matter Ideal (erfect) Gas Cotiuous Radom Motio No Iteractio betwee idividual uits (Move i Straight Lies) Speed Icreases with emperature Elemetal uits well separated & Occupy egligible Volume Collisios Do t exchage eergy (Elastic)

Gas Behaviour...Cot Charles Law circa 787 (Gay-Lussac circa 80): V k,...@ costat moles & ress k,...@ costat moles & Vol Need to Kow Somethig About emperature! What is emperature?

2 7/6/0 Empirical Observatios o Gas Behaviour Boyle s Law (66 ish): V k,...@ costat moles & emp ressure Defied: Force / Uit Area Molecules keep hittig the cotaier ~ Force/ more frequet the hits, the greater the force, thus the greater the pressure Empirical Observatios o Gas Behaviour...Cot Charles Law circa 787 (Gay-Lussac circa 80): V k,...@ costat moles & ress k,...@ costat moles & Vol Need to Kow Somethig About emperature! What is emperature?! A roperty that idicates the directio of flow of eergy Your Cold had o a hot cup of Mocha ava, i.e. he hot cup is at a higher temperature tha your cold had... A State Fuctio Does t matter what happeed before Oly depeds o the preset state More Stuff o emperature! ZEROH LAW: If A is i thermal eq m with B, ad B is i thermal eq m with C, the C is also i thermal eq m with A It s why old mercury thermometers work! hermal equilibrium: Whe two objects are i cotact through a diathermic boudary (a boudary that allows a free pass passage of heat) ad there is o chage i state

3 7/6/0 he Came... Avogadro's riciple (8): Equal volumes of differet gases at the same temp & press have equal umber of molecules V k,...@ costat ress & emp Molar Volume S ( bar, 0 C,.44L) SA ( bar, 98.5 K dm3 mol) Recall a mole is defied Amout of elemetary uits as there are atoms i exactly g of carbo x 0 3 roperties of Ideal Gases All three give you the ideal gas law V R R he Gas Costat K - mol - & Combied Gas Equatio V V R R V V Mixtures of Gases Dalto s Law: he ressure Exerted by a mixture of gases is the sum of the pressures that each oe would exert if it occupied the cotaier aloe A + B + c + D +... Gas Mixtures Fractio of each gas is give by the mole fractio (χ) χ A + + B C +... For each gas, he partial pressure of gas R V χ 3

4 7/6/0 Real Gases Deviate from a ideal gas at high pressures, ad low temperature Molecular Iteractios are Very high pressures, ad/or Low emperatures: Repulsive Forces ~ importat whe avg separatio of molecules is small (collisios) i.e. High pressures Attractive forces ~ Log rage iteractios that domiate whe molecules are close but ot touchig Low & large V ~ real gas behaves ideally Compressio Factor Z For a perfect gas Z V Z R For real gases, deviatio of Z values from, is a measure of departure from ideal behaviour Z < ; attractive forces domiate, & gas exerts a lower press tha a ideal gas Z > ; repulsive forces domiate, & gas has a larger volume tha ideal gas m Virial Coefficiets Correctio factors that accout for deviatios from ideal behaviour For a ideal gas Z For a real gas the deviatio with icrease i pressure is ~ liear: Better fit of the data is foud with more terms ' Z + B ' ' ' Z + B + C + D 3... Virial Equatio of State Recall Z: V Z R m V m + ' ' ' 3 B + C + D... R ' ' ' 3 V m R ( + B + C + D... ) B & C are the d & 3 rd Virial coefficiets ad are temperature depedat Boyle emperature: which a real gas behaves like a ideal gas as goes to 0 4

5 7/6/0 va der Waals Equatio Simpler to use Costat a takes ito accout the attractive forces betwee molecules Costat b accouts for the volume occupied by the molecules Eq is derived whe substitutig R () a V b R a () V b m V m V V m V Selected roblems from the ext....5 (b) What pressure differece must be geerated across the legth of a 5 cm vertical drikig straw i order to drik a water-like liquid of desity.0 g cm -3?.6 (b) A maometer cosists of a U shaped tube cotaiig a liquid. Oe side is coected to a apparatus ad the other is ope to atmosphere. he pressure iside the apparatus is determied from the differece i heights of the liquid. Suppose the exteral pressure is 760 orr, ad the ope side is 0.0 cm higher tha the side coected to the apparatus. What is the pressure i the apparatus? (he desity of Hg is 3.55 g cm -3 ).7 (b) he followig data have bee obtaied for oxyge gas at 73.5 K. Calculate the best value of the gas costat R from them ad the best value of the molar mass of O. p/atm Vm/(dm 3 mol - ) ρ/(g dm -3 ) Selected roblems From the ext....0 (b) A gas mixture cosists of 30 mg of methae, 75 mg o argo, ad 5 mg of eo. he partial pressure of eo at 300 K is 8.87 ka. Calculate (a) the volume ad (b) the total pressure of the mixture.. (b) A certai sample of a gas has a volume of 0.00 dm3 at 0 C ad.000 atm. A pot of the experimetal data of its volume agaist the Celsius temperature, q, at costat p, gives a straight lie slope dm 3 ( C) -. From these data aloe (without makig use of the perfect gas law), determie the absolute zero of temperature i degrees Celsius. Selected roblems From the ext....3 (b) Calculate the pressure exerted by.0 mol of H S behavig as (a) a perfect gas, (b) a va derwaals gas whe it is cofied uder the followig coditios: (i) at 73.5 K i.44 dm 3, (ii) at 000 K i 00 cm 3. he va der Waals parameters for H S: a atm dm 6 mol - b 4.34 x0- dm 3 mol -.5 (b) A gas at 350 k ad atm has a molar volume percet larger tha that calculated from the perfect gas law. Calculate (a) the compressio factor uder these coditios ad (b) the molar volume of the gas. Which are domiatig i the sample, the attractive or the repulsive forces? 5

7/6/0 Food for thought... Whe aircrafts go faster tha the speed of soud, or approach such high speeds, some iterestig thigs make for some very excitig photography.

6 7/6/0 Food for thought... Whe aircrafts go faster tha the speed of soud, or approach such high speeds, some iterestig thigs make for some very excitig photography. A good example is the water vapour plume i the adjoiig picture. Usig what you kow about the ideal gas law, formulate a plausible explaatio for the sudde appearace of the water vapour plume. 6

Chapter 5 Gases A Summary

Chapter 5 Gases A Summary 5. ressure A. roperties of gases. Gases uiformly fill ay cotaier. Gases are easily compressed 3. Gases mix completely with ay other gas 4. Gases exert pressure o their surroudigs