Chapter 10 - Gases

Chemistry 100Gases and Gas Laws1The Definition of a GasGas - a substance that is characterised by widely separated molecules in rapid motion.Mixtures of gases are uniform. Gases will expand to fill containers.

2Examples of Gaseous SubstancesCommon gases O2 and N2, the major components of "air" Other gases F2, Cl2, H2 gaseous diatomic moleculesH2 and He are the lighter than air gasesN2O (laughing gas)

3Three States of Matter SolidsLiquidsGases4Gases (contd)Most molecular compounds are solids or liquids at room temperature, but they can be converted to a gas relatively easily Important exception ionic solids (e.g., NaCl) can't be easily coverted to gases

5Gases and VapoursWhat is the difference between a gas and a vapour? Gases normally in the gaseous state at 25C and 1 atm pressure A vapour is the gaseous form of any substance that is normally in the liquid or solid state at normal temperatures and pressures

6The Definition of PressureThe pressure of a gas is best defined as the forces exerted by gas on the walls of the containerDefine P = force/areaThe SI unit of pressure is the Pascal 1 Pa = N/m2 = (kg m/s2)/m2

7The Measurement of PressureHow do we measure gas pressure?Barometer - invented by Torricelli Gas pressure conversion factors1 atm = 760 mm Hg = 760 Torr1 atm = 101.325 kpa = 1.01325 bar

8The Barometer

9The Gas LawsFour variables were sufficient to fully describe the state of a gas Pressure (P)Volume (V) Temperature (T)The amount of the gas in moles (n)

10Boyle's Law The gas volume/pressure relationshipThe volume occupied by the gas is inversely proportional to the pressure V 1/PTemperature and the amount of the gas are fixed V = k1/ P or PV = k1 k1 is a proportionality constant

11Boyle's Law

12Charles and Gay-Lussac's LawDefines the gas volume/temperature relationshipV T (constant pressure and amount of gas)Note T represents the temperature on Lord Kelvin's temperature ScaleV = k2 T k2 proportionality constant13Charles and Gay-Lussac's Law

14An AsideThe Kelvin temperature scale - Lord Kelvin recognised the significance of the intercept in the volume/temperature relationshipAll temperature (C) vs. volume plots extrapolated to 0 volume at -273.15CKelvin - absolute 0 all thermal motion ceases15The Kelvin Temperature ScaleRelating Kelvin scale and the Celcius scaleT (K) = [ tc (C) + 273.15C] K/CFreezing point of water: tc = 0 C; T = 273.15 KBoiling point of water: tc = 100 C; T = 373.15 K Room temperature: tc = 25 C; T = 298 KNOTE tc = C; T (K) = K NO DEGREE SIGN16Amontons LawThe pressure/temperature relationshipFor a given quantity of gas at a fixed volume, P TP = k3 TP1 = k3T1P2 = k3T2 P1 / T1 = P2 / T2 Amonton's law17Amontons LawP / atmt / Ct = -273.15CV1V2V3V418Avogadros LawThe volume of a gas at constant T and P is directly proportional to the number of moles of gas V = k4 n => n = number of moles of gas19Avogadros Law

20The Ideal Gas Equation of StateWe have four relationshipsV 1/P; Boyles law V T; Charles and Gay-Lussac's law V n; Avogadros lawP T; Amontons law21Ideal Gas Equation of StateWe combine these relationships into a single fundamental equation of state the ideal gas equationPV = nRTR is the universal gas constant R = 0.082057 L atm / (K mol) = 8.314 J / (K mol)22The Definition of an Ideal GasAn ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T rangeIdeal gases - molecules have negligible intermolecular attractive forces Occupy a negligible volume compared to the container volume23Standard Temperature and PressureDefine:STP (Standard Temperature and Pressure)Temperature 0.00 C = 273.15 KPressure 1.000 atmThe volume occupied by 1.000 mole of an ideal gas at STP is 22.41 L!24Gas Density CalculationsA simple expression for calculating the molar mass of an unknown gas. Molar mass and gas densityM = (dRT) / Pd = the gas density 25Partial PressuresLet's consider two ideal gases (gas 1 and gas 2) in a container of volume V. 1222221111112226Dalton's Law of Partial PressureIn a gaseous mixture, each gas exerts the same pressure as if it was alone and occupied the same volume.the partial pressure of each gas, Pi, is related to the total pressure by Pi = Xi PT Xi is the mole fraction of gas i.27Partial Pressures (contd)The pressure exerted by the gases is the sum of the partial pressures of the individual gases Let P1 and P2 be the partial pressures of gas 1 and 2, respectively. PT = P1 + P2 = nT (RT/V),PT = n1 (RT/V) + n2 (RT / V)28The Mole FractionThe mole fraction is defined as follows For a two component mixturen1 = moles of substance 1n2 = moles of substance 2nT = n1 + n2X1 = n1 / nT; X2 = n2 / nT29Gas Collection Over Water

30Gas Collection Over WaterMany gas measurements are carried out over water. Water vapour is collected with the gas. PT = Pgas + PH2O31Kinetic Molecular Theory of GasesMacroscopic (i.e., large quantity) behaviour of gases.The kinetic molecular theory of gases attempts to explain the behaviour of gases on a molecular level.32Kinetic Theory of GasesGases consist of molecules widely separated in space. Volume of molecules is negligible compared to total gas volume.Gas molecules are in constant, rapid, straight-line motion. Collisions are elastic.Average kinetic energy (K.E.) of molecules depends on absolute temperature (T) only.Attractive forces between molecules are negligible.33Kinetic Theory of Gases

34Gas Laws Explanations Gas pressure results from collisions of gas molecules with the container walls. Pressure depends on the number of collisions per unit time how hard gas molecules strike the container wall! 35Avogadros LawLet's increase the amount of gas in the container (T, P constant)

More collisions of gas with container wall. V n at constant P, T.36Boyle's LawLet's decrease the volume of the container (constant n and T). More collisions of the gas molecules with the container wall and P increases. (V 1/P)37Charles and Gay-Lussacs LawLet container volume increase (P, n are held constant). Low Temp.High Temp.The molecules must move fasterT must increase.38Molecular SpeedsK.E. = 1/2 M U2 M = the molar mass of the gasU2 =the mean square speed of the gasThis speed is an average speed (some will always be fast, some slow). 39The Mean Square SpeedKinetic Molecular Theory of Gases allows us to relate macroscopic measurements to molecular quantities P, V are related to the molar mass and mean square seed, U2P V = 1/3 n M U2 = n R T40The Root Mean Square Speed1/3 MU2 = RTU2 = 3RT / M(U2)1/2 = urms = (3RT/M)1/2urms = the root mean square speed41The Root Mean Square Speed

42The Mean Free PathGas molecules encounter collisions with other gas molecules and with the walls of the containerDefine the mean free path as the average distance between successive molecular collisions43The Mean Free Path

44The Mean Free PathAs the pressure of the gas increases, the mean free path decreases, i.e., the higher the pressure, the greater the number of collisions encountered by a gas molecule.45Diffusion Diffusion - gradual mixing of gas molecules caused by kinetic properties.Graham's Law Under constant T, P, the diffusion rates for gaseous substances are inversely proportional to the square roots of their molar masses. 46Grahams Lawr1/r2 = (M2 / M1)1/2r1 and r2 are the diffusion rates of gases 1 and 2.M1 and M2 are the molar masses of gas 1 and gas 2, respectively. 47EffusionEffusion - the process by which a gas under pressure goes (escapes) from one compartment of a container to another by passing through a small opening.48Effusion

49The Effusion EquationGrahams Law - estimate the ratio of the effusion times for two different gases.t1/t2 = (M1 / M2)1/2t1 and t2 are the effusion times of gases 1 and 2.M1 and M2 are the molar masses of gas 1 and gas 2, respectively.50Deviations from Ideal Gas BehaviourThe ideal gas equation is not an adequate description of the P,V, and T behaviour of most real gases. Most real gases depart from ideal behaviour at deviation from low temperaturehigh pressure51Deviations from Ideal Gas Behaviour at Low Temperatures

52Deviations from Ideal Gas Behaviour at High Pressures

53Deviations from Ideal Behaviour Look at assumptions for ideal gasReal gas molecules do attract one another.(i.e., Pid = Pobs + constant). Real gas molecules do not occupy an infinitely small volume (they are not point masses). (Vid = Vobs - const.)54The Van der Waals Equation Vid = Vobs - nb where b is a constant for specific different gases. Pid = Pobs + a (n / V)2 where a is also different for different gases. Ideal gas Law Pid Vid = nRT

55The Van der Waal's Equation (contd)(Pobs + a (n / V)2) x (Vobs - nb) = nRTVan der Waalss equation of state for real gases. Two constants (a, b) that are experimentally determined for each separate gasTable 10.3 in text.56