2 Overview Characteristics of Gas Pressure Gas Laws Ideal Gases Partial PressuresMole FractionsGas LawsBoyles LawCharles LawAvogadro’s LawGuy-Lussac’s LawIdeal Gas LawIdeal GasesReal GasesDensity of GasesVolumes of GasesStandard molar volumeGas stoichiometryEffusion/DiffusionGraham’s Law
3 Characteristics of Gases Expansion – gases expand to fill their containersCompression – gases can be compressedFluids – gas particles flow past each otherDensity – gases have low density1/1000 the density of the equivalent liquid or solidGases effuse and diffuse
4 Kinetic Molecular Theory Gases consist of large numbers of tiny particles that are far apart relative to their size.Collisions between gas particles and between particles and container walls are elastic.Elastic collision – collision in which there is no net loss of kinetic energyGas particles are in continuous, rapid, random motion. They therefore possess kinetic energy.There are no forces of attraction between gas particles.The temperature of a gas depends on the average kinetic energy of the particles of the gas.
5 Kinetic Energy of Gas Particles At the same conditions of temperature, all gases have the same average kinetic energym = massv = velocityAt the same temperature, small molecules move FASTER than large molecules
6 Speed of Molecules V = velocity of molecules M = molar mass R = gas constantT = temperature
7 PressureA force that acts on a given areaPressure =ForceArea
8 Measuring PressureThe first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th centuryCalled a barometerThe normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high
9 Units of Pressure 1 atmosphere (atm) 760 mm Hg (millimeters of mercury)760 torr1.013 barPa (pascals)101.3 kPa (kilopascals)14.7 psi (pounds per square inch)
11 STPStandard Temperature and Pressure (STP)1 atmosphere273 K
12 Dalton’s Law of Partial Pressures Partial pressure – pressure exerted by particular component in a mixture of gasesDalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the component gasesPt = P1 + P2 + P3+…
13 Mole Fraction P1 = Pt or P1 = X1Pt X1 = mole fraction of gas 1 Mole fraction – expresses the ratio of the number of moles of one component to the total number of moles in the mixtureP1 = Pt or P1 = X1PtX1 = mole fraction of gas 1Example: The mole fraction of N2 in air is 0.78 (78% of air is nitrogen). What is the partial pressure of nitrogen in mmHg?PN2 = (0.78)(760 mmHg) = 590 mmHg
14 Collecting Gas Over Water Gas collected by water displacement is always mixed with a small amount of water vaporMust account for the vapor pressure of the water moleculesPtotal = Pgas + PH2ONote: The vapor pressure of water varies with temperature
15 The Gas Laws Robert Boyle Amadeo Avogadro Joseph Louis Gay-Lussac Jacques Charles
16 Boyles LawPressure is inversely proportional to volume when temperature is held constant.
17 Temperature MUST be in KELVINS! Charles LawThe volume of a gas is directly proportional to temperature.(P = constant)Temperature MUST be in KELVINS!
18 Temperature MUST be in KELVINS! Gay-Lussac’s LawThe pressure and temperature of a gas aredirectly related, provided that the volumeremains constant.Temperature MUST be in KELVINS!
19 Combined Gas LawExpresses the relationship between pressure, volume and temperature of a fixed amount of gas
20 For example, doubling the moles will double the volume of a gas Avogadro’s LawFor a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).V = constant × nV = volume of the gasn = number of moles of gasFor example, doubling the moles will double the volume of a gas
21 Ideal GasesImaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory
22 Ideal Gas Law PV = nRT P = pressure V = volume n = moles R = ideal gas constantT = temperature (Kelvin)Numerical Value of RUnits0.0821(atm∙L)/(mol∙K)8.314J/(mol∙K)62.4(mmHg∙L)/(mol∙K)Note: 1 J = 1 Pa∙m3
23 Standard Volume STP of 1 mole of gas = 1 atm and 273K PV = nRT (1atm)(V) = (1mol)(.0821)(273)V = 22.4 LVolume of 1 mole of gas at STP = 22.4 liters
24 Real GasesReal Gas – does not behave completely according to the assumptions of the kinetic molecular theoryAt high pressure (smaller volume) and low temperature gases deviate from ideal behaviorParticles will be closer together so there is insufficient kinetic energy to overcome attractive forces
25 Real GasesThe Van der Waals Equation adjusts for non-ideal behavior of gases (p. 423 of book)corrected pressurecorrected volumePidealVideal
27 Density of Gases Combine density with the ideal gas law (V = p/RT) M = Molar MassP = PressureR = Gas ConstantT = Temperature in Kelvins
28 Gas Stoichiometry #1If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.3 H2(g) N2(g) NH3(g)3 moles H mole N moles NH33 liters H liter N liters NH3
29 Gas Stoichiometry #2 3 H2(g) + N2(g) 2NH3(g) How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?3 H2(g) + N2(g) 2NH3(g)12 L H22L NH3= L NH38.03L H2
30 Gas Stoichiometry #3How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?2 KClO3(s) 2 KCl(s) + 3 O2(g)50.0 g KClO31 mol KClO33 mol O222.4 L O2g KClO32 mol KClO31 mol O2= 13.7 L O2
31 Stoichiometry #4How many liters of oxygen gas, at 37.0C and atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?2 KClO3(s) 2 KCl(s) + 3 O2(g)50.0 g KClO31 mol KClO33 mol O20.612=mol O2g KClO32 mol KClO3= 16.7 L
32 DiffusionSpontaneous mixing of two substances caused by the random motion of particlesThe rate of diffusion is the rate of gas mixingThe rate of diffusion increases with temperatureSmall molecules diffuse faster than large molecules
33 EffusionProcess by which gas particles pass through a tiny opening
34 Graham’s Law of Effusion Rate of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.M1 = Molar Mass of gas 1M2 = Molar Mass of gas 2