*Physical Chemistry

*Key NotesIdeal Gases/Perfect GasesSummaryGases: a fluid which has no intrinsic shape, and which expands indefinitely to fill any container in which it is held.The ideal gas equations: the relations among the amount of gas substance, temperature, pressure and volume. PV = nRTPVm = RTVm: molar gas volume

*Key NotesIdeal Gases/Perfect GasesSummaryPhysical ChemistryDaltons law: the total pressure exerted by a mixture of ideal gases in a volume is equal to the arithmetric sum of the partial pressures.Ptotal = ntotalRT/VPartial pressure: the pressure exerted by each component in a gaseous mixture.Px = nxRT/VPi = xiPtotalnx: molexi: mole fraction

*Isothermal: A system which is held at constant temperatureAdiabatic: A system in which energy may be transferred as work, but not as heat.CHAPTER 2 The First Law of Thermodynamics Basic ConceptsDiathermic: A system which allows energy to escape as heat through its boundary if there is a difference in temperature between the system and its surroundings.Chapter 2

*Internal energy: Total amount of energy in a system. The sum total of all kinetic and potential energy within the system. Internal energy changes: The sign of UNegative values: a system loses energy to the surroundingsPositive values: a system gains energy from the surroundings Chapter 2Internal Energy

*Extensive property The value of the property changes according to the amount of material which is present (e.g., mass, volume, internal energy)Intensive propertyindependent of the amount of material which is present (e.g., temperature, density)Thermodynamic Properties of systemState functions: the value of a particular property for a system depends solely on the state of the system at time (e.g., pressure, volume, internal energy, entropy)Path functions: A property depends upon the path by which a system in one state is changed into another state (e.g., work, heat)Physical ChemistryChapter 2

*Work: the transfer of energy as orderly motiondue to energy being expanded against an opposing force (in mechanical terms)Chapter 2WorkReversible P-V Work

*Reversible P-V Work(a) Expansion (dV > 0)(b) Compression (dV < 0)Chapter 2

*exothermic: a process that releases energy as heat (all combustion reactions)endothermic: processes that adsorb energy as heat(the vaporization of water)Heat: the transfer of energy as disorderly motion as the result of a temperature difference between the system and its surroundings.Chapter 2an adiabatic system(a) an endothermic process(b) an exothermic process

*Heat: the transfer of energy as disorderly motion as the result of a temperature difference between the system and its surroundings.a diathermic container Chapter 2endothermic: energy enters as heat from the surroundings, the system remains at the same T (c)exothermic: energy leaves as heat from the system, the system remains at the same T (d)An isothermal process

*Two bodies at unequal temperatures are placed in contactm1, c1, T1m2, c2, T2 (T2>T1)TfHeatPhysical ChemistryChapter 2T1

*HeatChapter 2

*The total energy of an isolated thermodynamic system is constantthe conservation of energyThe First Law of Thermodynamics Energy cannot be created or destroyedClosed system at rest in the absence of external fieldsq is the heat supplied to the systemw is the work done on the systemU is the internal energy of the systemChapter 2

*Heat and WorkThe calorie defined by (2.44) is called thermodynamical calorie, calthBoth are measures of energy transfer, and both have the same units as energy.The unit of heat can be defined in terms of joule.Chapter 2

*EnthalpyLet qP be the heat adsorbed in a constant-pressure process in a closed system, from the first lawSince U, P, V are state functions, H is a state function.P1=P2=PChapter 2

*For any change of state, the enthalpy change HU and V are extensive, H is extensive.(2.47)The molar enthalpy of a pure substance EnthalpyChapter 2

*(closed syst., P-V work only, V const.)Let qV be the heat adsorbed in a constant-volume process in a closed system, if it can do only P-V work, thendw = - PdV = 0Since dV = 0Then dw = 0So w = 0From the first law(2.49)EnthalpyPhysical ChemistryChapter 2

*For a reaction involving a perfect gas(1 mole of gaseous CO2 is created)Exampleat 298 K EnthalpyChapter 2

*Exothermic and EndothermicThe sign of enthalpy change indicates the direction of heat flowChapter 2

Heat change in systemProcessValue of HHeat loss(heat lost to the surroundings)Heat gain(heat gained from the surroundings)Exothermic

EndothermicNegative (H < 0)

Positive(H > 0)

*Heat Capacitiesheat capacity at constant volume CV (isochoric heat capacity)heat capacity at constant pressure CP (isobaric heat capacity)Chapter 2

*Heat Capacities CP and CV give the rates of change of H and U with temperature T.(2.53)*Chapter 2

*Heat CapacitiesThe slope of the curve at any temperature constant volume heat capacity (isochoric heat capacity) CVChapter 2

*Heat CapacitiesThe slope of the H-T curve at any temperature constant pressure heat capacity (isobaric heat capacity) CpChapter 2

*The relation between CP and CVChapter 2

*At constant PSubstitution of (2.59) into (2.57)Chapter 2

*Why?(first law)Chapter 2

*(1) In a constant pressure process, part of the added heat goes into the work of expansion internal pressureintermolecular potential energyChapter 2

*Joule experimentChamber A: filled with a gasChamber B: is evacuatedValve: is closedValve: is openedChamber A: releases a gasChamber B: filled with a gasAfter equilibrium is reachedThe temperature change in the system is measured by the thermometer. Chapter 2

*Joule experimentq = 0 (the system is surrounded by adiabatic walls)w = 0 (gas expansion into a vacuum)U = q + w = 0 + 0 = 0 (a constant-energy process)The experiment measures T with V at constant internal energy,Joule coefficientChapter 2

*Joule experimenttotal differential of z(x,y)When y is kept constanttotal differential of z(r,s,t)When x is kept constantChapter 2

*Joule experimentDivision by dzy givesWhen z stays constantFrom the definition of the partial derivativeChapter 2

*Joule experimentDivision by dyz givesUsing (1.32) with x and y interchanged and multiplied byChapter 2

*Joule experimentReplaced x, y, z with T, U, and V, givesWhen (1.32), (2.53) and (2.62) were usedChapter 2

*Joule-Thomson experimentP1P1, V1, T1Porous PlugP2(a)(b)(c)P1P2P2, V2, T2P1P1P2P2Adiabatic WallFig. 2.7 The Joule-Thomson experiment.P2 < P1BChapter 2

*The slow throttling of a gas through a rigid, porous plug. The system is enclosed in adiabatic walls. The left piston is held at a fixed pressure P1, the right piston is held at a fixed pressure P2 (

*The work done on the gas in throttling it through the plug w P1V1 P2 V2q 0 (adiabatic process)U2 - U1 q + w w P1V1 P2 V2 U2P2 V2U1P1V1 H2H1orH 0Joule-Thomson coefficientJoule-Thomson experimentChapter 2

*Calculate the work done when 50 g of iron reacts with hydrochloric acid in (a) a closed vessel of fixed volume (b) an open beaker at 25 oC.Example:In (a) the volume cannot change, so no work is doneIn (b) the gas gives back the atmosphere and thereforeThe amount of H2 producedChapter 2

*Calculate the work done when 50 g of iron reacts with hydrochloric acid in (a) a closed vessel of fixed volume (b) an open beaker at 25 oC.Example:The reaction is1 mole H2 is generated when 1 mole Fe is consumed Molar mass of FeThe system does 2.2 kJ of work driving back the atmosphereChapter 2

*Reversible isothermal process in a perfect gasReversible adiabatic process in a perfect gasA perfect gasChapter 2

*Reversible adiabatic process, CV is constantIf CV,m is constant (independent of T over a wide temperature range)A perfect gasChapter 2

*An alternative equation can be obtained by usingA perfect gasChapter 2

*A perfect gasHeat capacity ratioChapter 2

*Thermodynamic Processes Key NotesCyclic process: the systems final state is the same as the initial state.Chapter 2Reversible process: the system is always infinitesimally close to equilibrium, and an infinitesimal change in conditions can restore both system and surroundings to their initial state.Isothermal process: temperature is held constant throughout the process.Adiabatic process: dq=0 and q=0Isochoric (isobaric) process: volume (pressure) is held constant throughout the process.

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state: Reversible isothermal process in a perfect gas Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state: Reversible isothermal process in a perfect gas Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state: Reversible isothermal process in a perfect gasReversible adiabatic process in a perfect gas:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state: Reversible isothermal process in a perfect gasReversible adiabatic process in a perfect gas:Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P: Constant-pressure heating with no phase change: Constant-volume heating with no phase change:Perfect-gas change of state:Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state: Reversible isothermal process in a perfect gasReversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Calculation of First-Law QuantitiesChapter 2

*Reversible phase change at constant T and P:Constant-pressure heating with no phase change:Constant-volume heating with no phase change:Perfect-gas change of state: Reversible isothermal process in a perfect gasReversible adiabatic process in a perfect gas:Adiabatic expansion of a perfect gas into vacuum.Calculation of First-Law QuantitiesChapter 2

*Molecular interpretation of heat and workHeat is the transfer of energy that makes use of chaotic molecular motionWork is the transfer of energy that makes use of organized motion(thermal motion)Heat is identified as energy transfer making use of thermal motion in the surroundingsWork is identified as energy transfer making use of the organized motion of atoms in the surroundingsChapter 2

*WorkIn a uniform manner(b) HeatIn a chaotic mannerChapter 2Molecular interpretation of heat and work

*The molecular nature of internal energyThe internal energy is energy at the molecular level.gas: CO2A translationA rotationA vibrationFig. 2.14moves the same distance in the same directionthe atoms oscillate about their equilibrium positionsThe spatial orientation changes, but the distances remain fixedChapter 2

*The internal energyTransnational energy, UtrRotational energy, UrotVibrational energy, UvibElectronic energy, UelEnergy due to intermolecular forces, UintemolRest-mass energy of the electrons & nuclei, UrestChapter 2

*For a gas or liquid, the molar internal energyconstantconstantFor a perfect gas0constantNo chemical reactionsT is not extremely highChapter 2The internal energy