Physical Chemistry

Physical Chemistry Physical Chemistry Cheng Xuan February 2004, Spring Semester

Physical Chemistry Physical Chemistry Website http://210.34.14.15/teach/wsjx.htm Under “网上教学/物理化学/双语教学” ftp://student@210.34.14.15 Password: class2003 Password: class2003 You can read or download the files

Physical Chemistry Summary Ideal Gases/Perfect Gases Key Notes Gases: 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 = nRT PVm = RT Vm: molar gas volume

Physical Chemistry Summary Ideal Gases/Perfect Gases Key Notes Partial pressure: the pressure exerted by each component in a gaseous mixture. Px = nxRT/V nx: mole Pi = xiPtotal xi: mole fraction Dalton’s 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/V

Physical Chemistry Chapter 2 CHAPTER 2 The First Law of Thermodynamics Basic Concepts Isothermal: A system which is held at constant temperature Adiabatic:A system in which energy may be transferred as work, but not as heat. Diathermic: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.

Physical Chemistry Chapter 2 Internal Energy 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 U Negative values: a system loses energy to the surroundings Positive values: a system gains energy from the surroundings

Physical Chemistry Chapter 2 • Thermodynamic Properties of system • Extensive property： The value of the property changes according to the amount of material which is present (e.g., mass, volume, internal energy) • Intensive property：independent of the amount of material which is present (e.g., temperature, density) State 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)

dw  Fx dx (2.10)* dwrev= -PdV (2.30)* closed system, reversible process (2.31) closed system, reversible process Physical Chemistry Chapter 2 Work Work:the transfer of energy as orderly motion due to energy being expanded against an opposing force (in mechanical terms) Reversible P-V Work

dx dx V V Fx=F=PA Fx=F=PA Piston moving Piston moving Physical Chemistry Chapter 2 Reversible P-V Work (a) Expansion (dV > 0) (b) Compression (dV < 0)

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

Heat Heat (c) (d) Physical Chemistry Chapter 2 Heat:the transfer of energy as disorderly motion as the result of a temperature difference between the system and its surroundings. endothermic: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) a diathermic container An isothermal process

(2.34) Specific heat capacity Physical Chemistry Chapter 2 Heat Two bodies at unequal temperatures are placed in contact m2, c2, T2 (T2>T1) m1, c1, T1 Tf T1<Tf<T2

(2.34) (2.35) closed syst., P const. (2.36) (2.37) (2.38) Physical Chemistry Chapter 2 Heat

U = q + w (2.41)* Physical Chemistry Chapter 2 The First Law of Thermodynamics The total energy of an isolated thermodynamic system is constant the conservation of energy Energy cannot be created or destroyed Closed system at rest in the absence of external fields q is the heat supplied to the system w is the work done on the system Uis the internal energy of the system

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

(2.45)* at cons P,closed syst. P-V work only (2.46) Physical Chemistry Chapter 2 Enthalpy Since U, P, V are state functions, H is a state function. Let qPbe the heat adsorbed in a constant-pressure process in a closed system, from the first law P1=P2=P

(2.45)* at constant P (2.48) Physical Chemistry Chapter 2 Enthalpy For any change of state, the enthalpy change H (2.47) U and V are extensive, H is extensive. The molar enthalpy of a pure substance

Physical Chemistry Chapter 2 Enthalpy Let qVbe the heat adsorbed in a constant-volume process in a closed system, if it can do only P-V work, then dw = - PdV = 0 SincedV = 0 Thendw = 0 So w = 0 From the first law (closed syst., P-V work only, V const.) (2.49)

at constant P (2.48) Physical Chemistry Chapter 2 Enthalpy For a reaction involving a perfect gas Example (1 mole of gaseous CO2 is created) at 298 K

Physical Chemistry Chapter 2 Exothermic and Endothermic The sign of enthalpy change indicates the direction of heat flow

(2.50)* (2.52)* (2.51)* Physical Chemistry Chapter 2 Heat Capacities heat capacity at constant pressure CP (isobaric heat capacity) heat capacity at constant volume CV (isochoric heat capacity)

(2.50)* (2.52)* (2.51)* Physical Chemistry Chapter 2 Heat Capacities (2.53)* CPand CVgive the rates of change of H and U with temperature T.

B U A T (2.49) Physical Chemistry Chapter 2 Heat Capacities The slope of the curve at any temperature constant volume heat capacity (isochoric heat capacity) CV

B H A T (2.46) Physical Chemistry Chapter 2 Heat Capacities The slope of the H-T curve at any temperature constant pressure heat capacity (isobaric heat capacity) Cp

(2.57) Physical Chemistry Chapter 2 The relation between CP and CV

(2.57) (2.58) (2.59) (2.60) Physical Chemistry Chapter 2 At constant P Substitution of (2.59) into (2.57)

(2.60) (2.61) Physical Chemistry Chapter 2 Why? (first law)

(2) (2.60) (2.61) Physical Chemistry Chapter 2 (1) In a constant pressure process, part of the added heat goes into the work of expansion intermolecular potential energy internal pressure

Physical Chemistry Chapter 2 Homework (2.1-2.6) 2.6 2.12 2.26 2.29 Due next Monday before the class

thermometer Adiabatic wall valve A B Fig. 2.6 Physical Chemistry Chapter 2 Joule experiment Chamber A: filled with a gas Chamber B: is evacuated Valve: is closed Valve: is opened Chamber A: releases a gas Chamber B: filled with a gas After equilibrium is reached The temperature change in the system is measured by the thermometer.

thermometer Adiabatic wall valve A B Fig. 2.6 (2.62) Physical Chemistry Chapter 2 Joule experiment q = 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 Twith Vat constant internal energy, Joule coefficient

(1.30)* (2.62) (1.31) Physical Chemistry Chapter 2 Joule experiment total differential of z(x,y) total differential of z(r,s,t) When y is kept constant When x is kept constant

(1.32)* (1.30)* (2.62) (1.33) Physical Chemistry Chapter 2 Joule experiment Division by dzy gives From the definition of the partial derivative When z stays constant

(1.34)* (2.62) Physical Chemistry Chapter 2 Joule experiment Division by dyz gives Using (1.32) with x and y interchanged and multiplied by

(2.63) (2.62) Physical Chemistry Chapter 2 Joule experiment Replaced x, y, z with T, U, and V, gives When (1.32), (2.53) and (2.62) were used

Physical Chemistry Chapter 2 Joule-Thomson experiment Adiabatic Wall Porous Plug B P1 P2 P1 P2 P1, V1, T1 P1 P2 (b) (a) P1 P2 P2, V2, T2 P2 < P1 (c) Fig. 2.7 The Joule-Thomson experiment.

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 (<P1). Chapter 2 The partition B is porous but not greatly so. This allows the gas to be slowly forced from one chamber to the other. Because the throttling process is slow, pressure equilibrium is maintained in each chamber. Essentially all the pressure drop from P1 to P2 occurs in the porous plug. B P1 P2 P1 P2 P1, V1, T1 P1 P2 (b) (a) P1 P2 P2, V2, T2 (c) P2 < P1 Physical Chemistry

(2.64)* Physical Chemistry Chapter 2 Joule-Thomson experiment The work done on the gas in throttling it through the plug w ＝ P1V1 － P2V2 q ＝ 0 (adiabatic process) U2 - U1 ＝q + w ＝w ＝P1V1－ P2V2 U2＋P2V2＝U1＋P1V1 H2＝H1 or H＝0 Joule-Thomson coefficient

Physical Chemistry Chapter 2 Example: • 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. • In (a) the volume cannot change, so no work is done • In (b) the gas gives back the atmosphere and therefore The amount of H2 produced

Physical Chemistry Chapter 2 Example: • 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. • The reaction is • 1 mole H2 is generated when 1 mole Fe is consumed The system does 2.2 kJ of work driving back the atmosphere Molar mass of Fe

(2.74) (2.75) Physical Chemistry Chapter 2 A perfect gas Reversible isothermal process in a perfect gas Reversible adiabatic process in a perfect gas

(2.76) (2.75) Physical Chemistry Chapter 2 A perfect gas If CV,m is constant (independent of T over a wide temperature range) Reversible adiabatic process, CV is constant

(2.76) Physical Chemistry Chapter 2 A perfect gas An alternative equation can be obtained by using

(2.77) CP,m - CV,m = R (2.72)* (2.76) (2.78) Physical Chemistry Chapter 2 A perfect gas Heat capacity ratio

final initial cyclic Physical Chemistry Chapter 2 Thermodynamic Processes Key Notes • Cyclic process: the system’s final state is the same as the initial state. • Reversible 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=0 • Isochoric (isobaric) process: volume (pressure) is held constant throughout the process.

Physical Chemistry Chapter 2 Calculation of First-Law Quantities • Reversible phase change at constant T and P: • 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.

Physical Chemistry Chapter 2 Calculation of First-Law Quantities • Reversible phase change at constant T and P:

Physical Chemistry Chapter 2 Calculation of First-Law Quantities • Reversible phase change at constant T and P: • Constant-pressure heating with no phase change: • 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.

(2.79) Physical Chemistry Chapter 2 Calculation of First-Law Quantities • Reversible phase change at constant T and P: • Constant-pressure heating with no phase change:

Physical Chemistry Chapter 2 Calculation of First-Law Quantities • Reversible phase change at constant T and P: • Constant-pressure heating with no phase change: • Constant-volume heating with no phase change: • 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.

Physical Chemistry