Ideal Gas LawCombining RelationshipsCounting AtomsMass IndependentIdeal Gas Law IBoltzmann’s ConstantThe MoleIdeal Gas Law IIMole SizeIdeal Gas LawIdeal Gas LawCombining RelationshipsCombining RelationshipsScience often relies on a controlled experiment.Science often relies on a controlled experiment.•Hold all variables fixed except oneHold all variables fixed except one•Measure change in another propertyMeasure change in another propertyGas laws were each made with all but two properties Gas laws were each made with all but two properties constant.constant.Combine those three laws into a single relationship.Combine those three laws into a single relationship.TPV Counting AtomsCounting AtomsAdding atoms increases the Adding atoms increases the volume of a gas.volume of a gas.Twice the air in a balloon Twice the air in a balloon doubles the volumedoubles the volume•Constant pressure and Constant pressure and temperaturetemperatureTry a relationship:Try a relationship:+=mTPV Mass IndependentMass IndependentDensity is mass divided by volume.Density is mass divided by volume.•Mass in an equation can be converted to densityMass in an equation can be converted to density•PVPV==amTamT becomes becomes PP = = aaTT• Experimentally Experimentally aa would vary for each type of gas would vary for each type of gasConstant is the same if the number of molecules Constant is the same if the number of molecules NN is is counted instead of the mass counted instead of the mass mm..Ideal Gas Law IIdeal Gas Law IThe equation of state links The equation of state links pressure, volume, pressure, volume, temperature, and amount of temperature, and amount of gas.gas.This is an ideal gas law, This is an ideal gas law, since real gases may vary since real gases may vary slightly.slightly.NkTPV ),,(),,(),,(),,(TVPNNVPTNTPVNTVPBoltzmann’s ConstantBoltzmann’s ConstantThe constant The constant kk applies to all gases. applies to all gases.It’s called Boltzmann’s constant.It’s called Boltzmann’s constant.•kk = 1.38 x 10 = 1.38 x 10-23-23 J/K J/K•Dimension links temperature and energy Dimension links temperature and energyThe MoleThe MoleBoltzmann’s constant has a very small value.Boltzmann’s constant has a very small value.•There are a vast number of atoms in a macroscopic systemThere are a vast number of atoms in a macroscopic system•Define a fundamental unit to count large numbersDefine a fundamental unit to count large numbersThe mole (mol) is a unit of amount.The mole (mol) is a unit of amount.•Number of carbon-12 atoms in 12.00 gNumber of carbon-12 atoms in 12.00 g•Amount of molecules equal to Avogadro’s numberAmount of molecules equal to Avogadro’s number•NNAA = 6.022 x 1023 = 6.022 x 1023Ideal Gas Law IIIdeal Gas Law IIThe amount of gas can be The amount of gas can be measured in moles.measured in moles.•nn = = NN / / NNAAR is the universal gas R is the universal gas constantconstant•R = NR = NAA k k•RR = 8.314 J / mol-K = 8.314 J / mol-KnRTPV ),,(),,(),,(),,(TVPnnVPTnTPVnTVPMole SizeMole SizeStandard temperature and Standard temperature and pressure (STP) is 0 pressure (STP) is 0 C and 1 C and 1 atm = 1.013 x 10atm = 1.013 x 1055 Pa. Pa.What is volume of one mole?What is volume of one mole?Convert temperature to K.Convert temperature to K.TT = 0 + 273.15 = 273.15 K = 0 + 273.15 = 273.15 KUse the molar form of the Use the molar form of the ideal gas law.ideal gas law.VV = = nRTnRT//PPSubstitute values:Substitute values:VV = (1.000 mol)(8.314 J/mol-K) = (1.000 mol)(8.314 J/mol-K)(273.15 K) / (1.013 x 10(273.15 K) / (1.013 x 1055 Pa) Pa)VV = 2.242 x 10 = 2.242 x 10-2-2 m m33 = 22.42 L = 22.42
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