Physical chemistry formulary - the laws of thermodynamics hold

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Physical chemistry formulary - the laws of thermodynamics hold

  1. 1. Dr. Lauth, University of Applied Sciences, Jülich Campus Physical Chemistry Formulary The Laws of thermodynamics hold William Thomson (Lord Kelvin; 1824 – 1907) “when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind” E=E°+RT/F ln([Ox]/[Red]) k=Aexp(E/RT) G=-RTln(K) pV=nRT r=k[A]a [B]b pi=xip* dn/dt=-ADdc/dx a=a[A]/([A]+K)
  2. 2. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 1 Basic Concepts System  A system is a particular segment of the world (with definite boundaries); outside the system are the surroundings (system & surroundings = universe)  A system may be open (boundary permeable to matter and heat), closed (boundary permeable to heat) or isolated (boundary impermeable)  The condition or state of a system is determined by a number of properties - intensives properties do not change with the quantity of matter present (p, T, , xi, Vm, Um…) - extensive properties do change with the quantity of matter (m, n, V, U, S, G…)  These properties are state functions: they depend only on the current state of the system, not on the way in which the system got to that state. Mathematically: State functions form exact differentials. GIBBS´ Phase Rule  F: "degrees of freedom" ; number of intensive variables (T, p, c, ...) that must be fixed in order for the condition of a system at equilibrium to be completely specified  C: number of (independent) components  P: number of phases Phase Diagram for a One-Component System A plot representing the phases of a substance as a function of temperature and pressure, showing  one phase regions (s, l, g)  two phase regions (s/l, l/g, s/g)  critical point (above which vapor cannot be liquefied by pressure)  triple point (three states of a substance are present)
  3. 3. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 2 Thermodynamic Process / Work and Heat Process  A thermodynamic process is defined as a system preceeding from an initial state to a final state.  Work and Heat are no state functions but process quantities because they describe the transition between states Work W [J]  Convention: positive sign of W (W>0) indicates that the system´s energy is increasing  The work accompanying a change in volume is called „pV work“ = WVol WVol = - p dVex (pex[Pa]: external pressure) Heat Q [J]  Convention: positive sign of Q = endothermic process negative sign of Q = exothermic process Heat Capacity C [J/K]  Heat capacity is the heat required to raise the temperature of a substance by 1 K  Index „p“: process occuring at constant pressure  Index „V“: process occuring at constant volume Td Q =C; Td Q =C V Vp p  Specific and Molar Heat Capacity c [J/(kg K)] , Cm [J/(mol K)] c = C m c = C m p p V V C = C n C = C n p,m p V,m V (m[kg]: mass; n[mol]: moles) Examples (25°C / 1 bar): Substance H2 N2 H2O C2H5OH Ag Fe Si SiO2 CDia (g) (g) (l) (l) (s) (s) (s) (s) (s) Cp,m [JK-1 mol-1 ] 28,82 29,12 75,29 111,5 25,35 25,1 28,09 44,4 6,113 Standard State (index °) definitions: - For a gas the standard state is a pressure of 1 bar (p°) - For a substance present in a solution, the standard state is a concentration of 1 mol/L (c°) - For a liquid or solid substance, the standard state is a molar fraction of 1 (pure substance) nitial state Final state Ti pi Vi Tf pf Vf Work Heat
  4. 4. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 3 Ideal Gases Equation of State of an Ideal Gas TRn=Vp (p [Pa]: pressure; V[m³] volume; T [K] temperature; n[mol] moles; R = 8,314 J/(mol K) universal gas constant) GAY-LUSSAC´s Law (CHARLES´s Law) The volume of a given sample of gas at constant pressure is directly proportional to the temperature in Kelvins T K273,15 V =V 0 BOYLE-MARIOTTE´s Law The volume of a given sample of gas at constant temperature varies inversely with the pressure AVOGADRO´s Hypotheses Equal volumes of gases at the same temperature and pressure contain the same number of particles Examples (273 K; 101325 Pa = 1 atm): Gas (ideal) N2 H2 O2 He CO2 NH3 C2H6 (g) (g) (g) (g) (g) (g) (g) Vm [10-3 m3 mol-1 ] 22,414 22,40 22,43 22,39 22,43 22,26 22,40 22,17 DALTON´s Law of Partial Pressures  For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone py=pp=p total i total iii (y [mol/mol]: molar fraction of component „i) Composition of dry air (mean molar mass M = 28,96 g/mol): N2 O2 Ar CO2 Vol.-% (Weight %) 78,09 (75,52) 20,95 (23,14) 0,93 (1,29) 0,03 (0,05) const.=Vp const.)=p(T,const.=V= n V m
  5. 5. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 4 Kinetic-Molecular Theory I Postulates of the kinetic molecular theory of ideal gases:  The volume of the individual particles can be assumed to be negligible  The particles are assumed to exert no forces on each other Pressure p [Pa] and Temperature T [K] of a Gas The collisions of the particles with the walls of the container are the cause for the pressure exerted by the gas p = 1 3 N V m v1 2 (N [] : number of molecules; m1 [kg] : mass of a molecule; v² [m²/s] : mean-square velocity) The average kinetic translational energy of a collection of gas is assumed to be directly proportional to the Kelvin temperature of the gas trans Atransm,B N=UTk 2 3 =trans EE (kB = 1,38110-23 J/K : BOLTZMANN constant; R = 8,314 J/(mol K): gas constant ; NA = 6,022 1023 1/mol : Avogadro´s number; N []: number of particles; Utrans [J] internal translational kinetic enrergy ; Um [J/mol] : molar translational kinetic energy) MAXWELL-BOLTZMANN Distribution Law d N N d v = 2 M R T v exp - M v 2 R T 2 2              3 2 M R = m k 1 B (N [] : number of particles; M [kg/mol]: molar mass; R = 8,314 J/(mol K): gas constant; v [m/s] : velocity) average velocity v = 8 R T M most probable velocity v = 2 R T M h square root of the mean square velocity v = 3 R T M 2 Examples: Gas N2 He H2 Cl2 CO2 NH3 O2 Hg Ar v [m s-1 ] (298 K) 475 1256 1770 298 379 609 444 177 398
  6. 6. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 5 Kinetic-Molecular Theory II Cross Section of Collision  [m²]  = 4 r2 Mean Free Path ̅ [m]  The average distance a molecule in a given gas sample travels between collisions with other molecules ̅ √ (r [m] : (mean) radius of particle, C = N/V [1/m³]: concentration of particles; p[Pa] : pressure; T [K] : temperature; kB = 1,38110-23 J/K : BOLTZMANN constant) Collision Frequency zt [1/s] of Intermolecular Collisions ̅ ̅ (v [m/s] mean velocity, ̅ [m] mean free path) Collisions of Gas Particles with the Container Wall zW [1/(m²s)] z = 1 4 C vW (v [m/s] mean velocity, C [1/m³] = N/V concentration of particles ) Examples (293 K, 1 bar): Gas N2 H2 CO2 O2 Ar m [10-10 m] 600 1123 397 647 635 zt [109 s-1 ] 5,07 10,0 6,1 4,4 4,0 BOLTZMANN Distribution and Barometric Distribution Law  The ratio of the populations in two energy states E1 and E2 (distribution of thermal energy on energy states) N N E E E2 1        exp k TB  Applied to gas molecules in earth atmosphere p ph        0 exp M g h R T (M [kg/mol]: (mean) molar mass; h [m]: height; g = 9,81 m/s² : gravitational acceleration; R = 8,314 J/(mol K): gas constant)
  7. 7. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 6 Real Gases I Compression Factor Z [] Z = p V R T = p V n R T m Virial Equation p V = A + B p + C p + D p + ...m 2 3 2. Virial Coefficient B [m³/mol] and Boyle- temperature TB [K] B b RT a   a T = R b B Examples : Gas N2 CO2 Ar H2 O2 B[10-6 m3 mol-1 ](273K) -10,5 -149,7 -21,7 13,7 -22,0 B[10-6 m3 mol-1 ](373K) 6,2 -72,2 -4,2 15,6 -3,7 VAN-DER-WAALS Equation of State  p + V V - b = R T m 2 m a        Covolume b [m³/mol] b = 4 N 4 3 rA 3  Simplified VAN-DER-WAALS Equation p V = RT + - R T pm b a      (a/V²m [Pa]: internal pressure; Vm [m³/mol]: molar volume; b [m³/mol]: covolume; R = 8,314 J/(mol K): Gas constant) ,b [m³/mol]: covolume; NA = 6,022 1023 1/mol : Avogadro´s number; r [m] radius of gas particle) Examples: Substance Ar N2 CO2 H2O CH4 C2H6 a [m6 Pa mol-2 ] 0,1363 0,1408 0,364 0,5536 0,23 0,5562 b [10-5 m3 mol-1 ] 3,219 3,913 4,267 3,049 42,9 6,38 repulsion attraction repulsion attraction repulsion attraction repulsion attraction
  8. 8. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 7 Real Gases II Critical Constants pk, [Pa], Tk [K], Vm,k [m³/mol] b3=V km, 2 27 =pk b a R27 8 =Tk b a )Z=( 8 3= TR V k k km,kp Examples: Substance N2 H2 CO2 H2O CH4 C2H6 C5H12 Tk [K] 126,2 33,3 304,2 647,4 190,7 305,4 425,2 pk [M Pa] 3,394 1,297 7,387 22,119 4,63 4,884 3,8 Vm,k [10-6 m3 mol-1 ] 90,1 65,0 94,0 56,0 98,7 148,0 255 JOULE-THOMSON Coefficient J-T [K/Pa] and Inversion Temperature Ti [K]  When a non-ideal gas is forced through a membrane or porous plug, its temperature changes  A gas cools on expansion at temperatures below Ti , above Ti a gas warms on expansion  = 2 R T - CJ-T p,m a b T = 2 Ri a b Examples: Gas N2 He CO2 N2 H2 J-T [K bar-1 ] (300 K) 0,25 -0,059 1,1 0,25 Ti [K] 621 40 1500 621 202
  9. 9. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 8 Transport Properties I - Diffusion and Heat Transfer Diffusion (FICK´s first and second Law)  The rate of diffusion (the diffusive flux dn/dt) is proportional to the concentration gradient dc/dx  The rate of accumulation (or depletion) of concentration is proportional to the local curvature of the concentration gradient d²c/dx². dx² d²c D dt dc xd cd -= A n D  for a perfect gas (self-diffusion) (A[m²]: area; D [m²/s]: diffusion coefficient) Examples: hydrogen ethanol Sugar chloride-ion sodium-ion silver in (T) air(301K) H2O(298 K) H2O (298 K) H2O (298 K) H2O (298 K) copper(900 K) D[m2 /s] 710-5 1,08. 10-9 5,21. 10-10 2,03. 10-9 1,33. 10-9 1,38. 10-15 Randow-walk Equation (EINSTEIN-SMOLUCHOWSKI Equation)  x² is the mean square distance traversed by a molecule in time t x² = 2 D t Heat Transfer by Conduction (FOURIER´s Law)  The rate of flow of heat dQ/dt is proportional to the temperature gradient dT/dtx xd Td -= A Q W   cCv:gasdiatomicafor mV,mW   [A [m²]: area; w [W/(Km)] : thermal conductivity] Examples (273 K): Substance N2 H2 Xe H2O H2O Cu glas wood soil concrete (g) (g) (g) (l) (s) (s) (s) (s) (s) (s) w [WK-1 m-1 ] 0,024 0,1682 0,0052 0,600 0,592 393 ~0,7 ~0,1 ~0,35 ~1,3
  10. 10. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 9 Transport Properties II - Viscosity Viscosity (NEWTON´s Law of Viscous Flow)  The frictional force F (resisting the relative layers in the fluid) is proportional to the area A and to the velocity gradient dvy/dx (applies only to laminar flow) xd vd -= A Y V  F  Application: rotating-plate viscosimeter  v 2 1 =:gasperfectafor mV (F [Pa]: frictional force; A [m²]: area;  = F/A [Pa]: shear stress; dvy/dx [1/s]: shear rate) Examples: Substance N2 (g) H2 (g) Ar(g) H2O (l) EtOH (l) Hg (l) H2SO4 (l) 298K 298K 273 K 293K 273K 298K 298K 293 K 298 K V [mPas] 0,018 0,0087 0,021 0,0223 1,8 1,009 1,19 1,55 21,6 HAGEN-POISEUILLE Equation  The viscosity V can be calculated from measurements of the rate of flow dV/dt in a tube of known dimensions (l, r), if the pressure difference p is known d V d t = r l p 4 V  8   Application: extrusion viscosimeter STOKES´s Law  The frictional force Fd opposing the motion of a large spherical particle of radius r moving at speed v through a solvent of viscosity V is given by STOKES´s law F = 6 r vR V   Application: falling ball viscosimeter
  11. 11. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 10 The First Law of Thermodynamics Internal Energy U [J], including  The kinetic energy of motion of the individual molecules (rotation, vibration, translation)  The potential energy that arises from interactions between molecules  The kinetic and potential energy of the electrons within the individual molecules (chemical bonds, etc.) U = + E )kin pot (E First Law of Thermodynamics  The energy of the universe is constant  Applied to closed systems: change of internal energy = heat absorbed by the system + work done on the system Enthalpy H [J] H = U + p V Processes at Constant Volume  Increase of internal energy U of a system at constant volume is equal to the heat QV that is supplied to it V V T T T U C         TdC=U=Q 2 1 21 T VTV   Processes at Constant Pressure  Increase of enthalpy H of a system at constant pressure is equal to the heat Qp that is supplied to it p p T T T CH         H TdC==Q 2 1 21 T pTp   Phase Transitions (at constant pressure)  The enthalpy change that occurs to melt a solid at its melting point = Molar enthalpy of fusion: fH = Qp,sl / n  Molar enthalpy of vaporization:vH = Qp,lg / n Examples: Substance Ar H2O C6H6 Ag fH [kJ/mol] (at TE) 1,188 (83,8 K) 6,008 (273,1 K) 10,59 (278,6 K)) 11,3 (1234 K vH [kJ/mol] (at TS) 6,51 (87,3 K) 40,656 (373,1 K) 30,8 (353,2 K) 250,6 (2436 K)
  12. 12. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 11 Thermochemistry I - Basics Stoichiometric Equation of a Chemical Reaction    A B C DA + B C + D A, B: reactants C, D: products Stoichiometric Coefficients i reactants < 0 products > 0  i i = 0 Extent of Reaction  [mol] d  = d ni / i ( = 0: reactants only; =1 products only) Enthalpies of Formation H°f,i [J/mol]  Change in enthalpy („Heat“) that accompanies the formation of 1 mole of a compound from its elements (with all substances in their standard state) Examples (298 K, 1 bar): compound N2 H2O H2O CO2 CO NH3 NO C2H4 C6H6 (g) (l) (g) (g) (g) (g) (g) (g) (l) H0 B [kJ mol-1 ] 0 - 285,84 -241,83 -393,51 -110,52 -46,19 90,37 52,3 49,03 more examples see appendix Enthalpy of Reaction RH° [J/mol]  Heat associated with a chemical reaction at constant pressure rH can be calculated from the enthalpies of formation of the reactants and products  Enthalpy and energy changes are considered with reference to the extent of reaction; stoichiometric equation must be specified  i if, o i o H=H r  0 reactantsf, 0 productsf, H-H=  Energy of Reaction RU [J/mol]  Heat associated with a chemical reaction at constant volume; rU can be calculated from rH      r r r r r rH = U + (p V) H = U + R T ngaseous (R = 8,314 J/(mol K) : gas constant Rngaseous: change in moles of gaseous products and reactants) HESS´s Law  The enthalpy of reaction is not dependent on the reaction pathway RH = 0 d H = 0  
  13. 13. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 12 Thermochemistry II - Calorimetry Enthalpy of Combustion cH [J/mol]  Amount of heat produced for the complete combustion of a substance (at constant pressure) Examples : compound H2 CH4 C2H4 C4H10 CH3OH C8H18 C12H22O11 (g) (g) (g) (g) methanol(l) i-octan(l) saccharose(s) cH [kJ mol-1 ] - 286 -890 -1411 - 2877 -726 -5461 -5645 Measurement of Enthalpy Changes (Calorimetry)  Direct measurement of rH or indirect calorimetry (application of Heß´s law)  Indirect calorimetry: determination of enthalpies of formation HB,i from enthalpies of combustion cH   icproductscombustionf,, H-H=ifH KIRCHHOFF´s Law  Temperature dependence of enthalpies of reaction can be calculated from the heat capacities of the reactants and products     H T = C H = H + C dT i p,i i T T T T i p,i i 2 1 1 2    R R R    Enthalpy of Atomization - Hf,at [J/mol]  Heat to be supplied at constant pressure in order do dissociate all the molecules into gaseous atoms  atomsfgifiatf HHH ,)(,,, Bond Enthalpy Hbond  The bond enthalpie or bond strenth is an average quantity  bondiatf HH ,, Examples: Bond O-H C-H C-C C=C CC C-O C-N C=O N-H (ketone) Hbond [kJ mol-1 ] -463 -416 -340 -615 -815 -340 -296 -750 -390
  14. 14. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 13 Second Law of Thermodynamics - Entropy Second Law of Thermodynamics  The entropy of the universe tends towards a maximum (while the energy of the universe is a constsant) Suniverse  0  In any spontanous irreversible process (occuring without outside intervention) there is always an increase in the entropy of the universe Suniv., irrev. > 0  In reversible processes the entropy of the universe remains constant Suniv., rev. = 0 Entropy S [J/K]  measure of randomness or disorder; increase in entropy means an increase in disorder Microscopic Definition of Entropy (BOLTZMANN´s Equation)  entropy is related to thermodynamic probabiltiy W, the number of microstates corresponding to a given state (including both position and energy) S = k ln(W)B (kB = 1,38110-23 J/K: BOLTZMANN constant; W []: thermodynamic probability) Macroscopic Definition of Entropy Change S (CLAUSIUS)  S = Q T d S = Q T rev rev (Qrev [J] heat absorbed or released during a reversible process; T [K] temperture) Third Law of Thermodynamics (NERNST´s Heat Theorem)  The entropies of a perfect crystal at 0 K is zero S = 0crystalline, pure, 0 K Absolute Entropies S°i [J/(mol K)]  The more complex the molecule, the higher the standard entropy value Examples: (1 bar, 298 K) Substance Si N2 N2O4 H2O H2O SiCl4 SiF4 CO2 C6H6 (s) (g) (g) (l) (g) (l) (g) (g) (l) S0 i [J K-1 mol-1 ] 18,82 191,5 304,3 69,94 188,72 239,32 282,14 213,64 172,8 more examples see appendix
  15. 15. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 14 Entropy and Energy Conversion Temperature Dependence of Entropy  S = C T d TT T p T T 1 2 1 2   (Cp [J/(mol K)] : molar heat capacity) Entropy Changes Associated with Changes of Aggregation State entropy of fusion:   f H S = T f .E ; entropy of vaporization:  v v S S = T H Examples: Substance Ar N2 O2 Cl2 H2O CH3OH C6H6 CH3COOH fS [J/(K mol)] (at TE) 14,17 11,39 8,17 37,22 22,00 18,03 38,00 40,4 vS [J/(K mol)] (at TS) 74,53 75,22 75,63 85,38 109,0 104,6 87,19 61,9 Concentration Dependence of Entropy (Expansion; Dillution)  S = n R ln V V V V 2 1 1 2       (n [mol] :moles; R = 8,314 J/(K mol): gas constant)  Entropy Changes in Chemical Reactions RS° [J/(K mol)]  rS can be calculated from the absolute entropies of the reactants and products  Stoichiometric equation must be specified    RS = S = S -0 i i 0 i product 0 reactant 0  CARNOT Cycle  The efficiency C of the reversible CARNOT engine can be defined as the work done by the system during the cycle Wrev, divided by the heat absorbed at the higher temperature Q1 Q W = 1 rev C T T-T = Q W 1 12 1 rev 0WQQ rev21 
  16. 16. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 15 Free Enthalpy and Equilibrium Free Enthalpy (GIBBS Energy) G [J]  At constant temperature and pressure, systems tend to move toward a state of minimum GIBBS energy G  H - TS (= second law of thermodynamics for constant T and p)  rG = G/ is a measure for the tendency of a reaction to occur; the more negative the value of rG, the further a reaction will go to the right to reach equilibrium  rG can be calculated from standard reaction free enthalpy rG° and reaction ratio Qr   R R RQG = G + RT ln0  i iR a= ][Reactants [Products] =Q i Reactants Products     The standard reaction free enthalpy rG° can be calculated from standard reaction enthalpy rH° and standard reaction entropy rS° (sometimes called GIBBS-HELMHOLTZ equation)   R R RG = H - T S    Equilibrium of a reaction is established when rG = 0 (minimum GIBBS energy); the reaction ratio has a particular value - the thermodynamic equilibrium constant KGG  i i GG GG a= ][Reactants [Products] =K i Reactants Products    GG  The equilibrium constant K can be calculated from the standard reaction free enthalpy rG°  R G = - R T ln Ko  K = exp - G R T o R      Examples: (298 K) reaction N2 + 3 H2  2 NH3 H2O  H+ + OH - K 6,8105 bar-2 1,010-14 mol²/l² reaction CH3COOH  CH3COO- + H+ AgCl  Ag+ + Cl - K 1,810-5 mol²/l² 1.610-10 mol²/l²
  17. 17. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 16 Shifts of Equilibrium Exergonic Reations Endergonic Reactions  RG° < 0 RG° > 0  KGG > 1 KGG < 1 Temperature Dependence of Equilibrium Constants  ULICH´s approximation : rG° for temperatures other than 298 K can be calculated from rH°- and rS°- values for 298 K   R R R G (T) = H (298 K) - T S K)o o o (298 Possible Combinations of H° and S° for a Process RH° < 0 RS° > 0  exergonic (spontaneous) at all temperatures RH° < 0 RS° < 0  exergonic at T < RH°/RS° RH° > 0 RS° > 0  exergonic at T > RH°/RS° RH° > 0 RS° < 0  not exergonic at any temperature VAN´T HOFF´s Equation  A plot of ln{K} against 1/T will have a slope equal to H°/R  ln K = - H R 1 T + S R o o  R R (T [K]: temperature; R = 8,314 J/(K mol) : gas constant) Examples: Reaction N2 + 3 H2  2 NH3 N2 + O2  2 NO T 298 K 400 K 500 K 1000 K 3000 K K 6,8105 bar-2 41 bar-2 3,510-2 bar-2 6,810-9 0,017 LE CHATELIER/BRAUN Principle  If a change in conditions (a „stress“) is imposed on a system at equilibrium, the equilibrium position will shift in a direction that tends to reduce that change in conditions process „stress“ shift RH > 0 increase in temperature product yield higher RH < 0 increase in temperature product yield lower RV < 0 increase in pressure product yield higher RV > 0 increase in pressure product yield lower
  18. 18. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 17 Phase Equilibria of One-Component Systems Vapor Pressure [Pa]  Vapor pressure = the pressure of the vapor over a liquid at equilibrium  At equilibrium, the rates of condensation and evaporation are equal (dynamic equilibrium) Examples: Substance H2O(s) (s/l) H2O(l) (vH = 41 kJ/mol ) | Hg(l) (vH = 59 kJ/mol) T [°C] -10 0,0 10 25 100 150 200 | -10 25 100 p [mbar] 2,5 6,0 12,3 31,7 1 013 4 760 15 551 | 8,810-5 110-3 0,35 ANTOINE´s Equation  Empirical equation for vapor pressure change with temperature (p [bar] : vapor pressure in bar; 1 bar = 100 000 Pa; T [°C] temperature in °C ; A, B, C ANTOINE constants) examples: Substance benzene ethanol toluol water A 4,2144 3,9251 4,0899 4,9513 B 1314,90 912,01 1348,21 1575,61 C 232,40 154,35 219,55 218,62 CLAUSIUS-CLAPEYRON Equation  The CLAUSIUS-CLAPEYRON equation represents the vapor pressure change with temperature  Enthalpy (“heat”) of vaporization vH is assumed to be independent of temperature  A “CLAUSIUS-CLAPEYRON-plot” (ln(p) versus 1/T) results in a straight line with a (-vH /R) - slope [ ( )] (T1 / T2 [K] temperature corresopoding to vapor pressure p1 / p2; vH [J/mol]: enthalpy of vaporization; R = 8,314 J/(mol K): gas constant)
  19. 19. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 18 Surface Tension Definition of Surface Tension  [J/m² = N/m]  Surface Tension : the work dW necessary to increase the surface area by dA Ad Wd = L F = Examples (20 °C) Substance H2O (l) Ethanol (l) glycerol (l) Hg (l)  [mN m-1 ] 72,8 22,3 63,0 480 YOUNG Equation and Meniscus Angle  LG SL- =)(cos   SG  ([°]: meniscus angle ; SG [N/m] surface tension between solid phase and gas) Examples (20 °C) (l) C6H6 H2O H2O Hg Hg (s) glas glas wax steel glas  6° 0° 105° 154° 140° LAPLACE Equation  The pressure on the inside of a bubble (radius r) must be higher than on the outside r 2=p   convexconcave p-p=p ( [N/m] surface tension; p [Pa] Pressure difference; r [m] radius of the surface curvature) Capillarity  Spontaneous rising of a wetting liquid in a narrow tube to the height h rg )(cos2 =h   (: meniscus angle;  [kg/m³] density; g = 9,81 m/s² : gravitattional acceleration; r [m]: radius of the capillary)
  20. 20. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 19 Two-Component Systems - Ideal Solutions Ideal Solutions  Mixture of component (A) = solvent and component (B) = solute  Ideal solution: Inter molecular attractions of (A) for (A) and of (B) for (B) are the same as the attraction of (A) for (B) { interaction (A  B)  interactions (AA / BB) } RAOULT´s Law  Vapor pressure of solvent p is equal to its mole fraction in the solution x multiplied by the vapor pressure of the pure solvent p° (ideal solutions). (p A [Pa] : vapor pressure of component A in sulution; p A * [Pa] : vapor pressure of pure component A; x 1 []: mole fraction of component 1) HENRY´s Law  The molar fraction of a gas dissolved by a given volume of solvent at constant temperature, is propotional to the pressure of the gas in equilibrium with the solution. (pB [Pa]: vapor pressure of component B (gas) in solution; kH [Pa] : Henry´s constant; x2 []: molare fraction of component 2) Examples (25 °C) Component „2“ (gas) N2 O2 CO2 H2 CH4 N2 CO2 H2 CH4 Solvent „1“ H2O H2O H2O H2O H2O C6H6 C6H6 C6H6 C6H6 kH [GPa] 8,68 4,4 0,167 7,12 0,0419 0,239 0,0114 0,367 0,0569 Vapor Pressure and Boiling Point of two Liquids obeying Raoult´s Law  The total vapor pressure in a binary solution will be intermediate between the vapor pressures of the two pure components (no maximum or minimum in p-x-diagram)  The boiling points of all the mixtures are inter- mediate between the boiling points of the pure components
  21. 21. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 20 Colligative Properties A colligative propery is a property of dilute solutions that depends on only the number of solute molecules and not on the type of species present Boiling Point Elevation  Boiling point elevation is a colligative propery  The molality b is the number of moles of solute per kilogram of solvent in a solution (bB [mol/kg] : molality ; i[]: VAN´T HOFF factor; Keb [K kg/mol]: ebullioscopic constant) Freezing Point Depression  Freezing point depression is a colligative property (RAOULT´s second law) (bB [mol/kg] = nB/mA: molality ; i []: VAN´T HOFF factor; kkr [K kg/mol]: cryoscopic constant) Examples : Solvent H2O C6H6 cyclohexane camphen acetic acid CS2 CCl4 keb [K kg/mol] 0,514 2,64 2,75 6,09 3,07 2,37 4,95 Kkr [K kg/mol] 1,86 5,07 20,2 40,0 3,90 3,8 30 Osmotic Pressure  [Pa] (VAN´T HOFF Equation)  Osmosis: the flow of solvent into a solution through a semipermeable membrane (permeable for solvent molecules only)  Osmotic pressure : the pressure that must be applied to stop osmosis  Molarity c: moles of solute / volume of solution (i[] : van´t Hoff factor; cB [mol/m³]: molarity; R = 8,314 J/(mol K) : gas constant) Examples: Solution 0,4 mol sugar in 1 kg water/ 20° human blood at 37 °C  [bar] 10,3 bar 7,7 bar Dissociation (VAN´T HOFF Factor i) van´t Hoff Factor i: the number of particles in solution formed from one molecule ( ) (+,- []: number of cations/anions formed from one molecule; z+,- []: charge of cation / anion;  []: degree of dissociation.)
  22. 22. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 21 Binary Phase Diagrams / Boiling and Melting Negative Deviations from RAOULT´s Law (example: acetone-chloroform)  Interaction (A B) > interactions (AA / BB)  Solution „more stable“ than components  Negative sign of mH and mV  In case of large deviations: Maximum in boiling point curve (azeotrope) Positive Deviations from RAOULT´s law (example: ethylene chloride - ethanol)  Interaction (AB) < interactions (AA / BB)  Solution „less stable“ than components  Positive sign of mH and mV  In case of large deviations: Minimum in boiling point curve (azeotrope) Azeotrope (minimum or maximum in boiling point curve)  Liquid and vapor are of the same composition; separation by direct distillation impossible Examples: boiling point of (1) boiling point of (2) boiling point of azeotrope TS(H2O): 100 °C TS(HNO3) 87°C TS (69 % HNO3): 120 °C TS(H2O): 100 °C TS(EtOH): 78,4°C TS (96 % ethanol): 78,2 °C Eutectic (minimum in liquidus curve)  Composition which has the lowest melting point  Mixture of eutectic composition (heterogeneous !) will melt sharply at the eutectic temperature to form a homogeneous liquid phase of the same composition  Invariant point: A(s) + B(s)  A/B (l)  (Other invariant points:  Peritectic / eutectoid / peritectoid) Examples: melting point of (1) melting point of (2) melting point of eutectic TE (Si): 1685 °C TE(Al): 930 °C TE(xSi = 0,11): 851°C TE (Sn): 232 °C TE(Pb): 327,5 °C TE(33% Pb): 183°C TE (H2O): 0 °C TE(NaCl): 801 °C TE(23% NaCl): -21°C
  23. 23. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 22 Ternary Phase Diagrams / Triangle Diagram General Remarks on Phase Diagrams  Phase Diagrams are are descriptions of the state of a system on a graph of temperature versus composition  Binodal Curve: Boundary between homogeneous and heterogeneous regions in a phase diagram (Examples: boiling , liquidus curve, solidus curve)  Conodal Curve (tie line in 2-phase regions): connection line between equibilibrium phase  Using the lever rule one can determine quantitatively the relative composition of a mixture in a two-phase region  ln=ln GIBBS´s Triangle Diagram  In ternary phase diagrams the composition of a phase containing up to three components is represented on triangular axes.  Within the two-phase regions only specific compositions can be in equilibrium; the lines joining these compositions are known as tie lines . Triangle Diagram and NERNST Distribution Law  If two liquids A (raffinate R) and B (extractant E) are partially immiscible and if there is a third component C present in both phases (which behaves individually as an ideal solute), the ratio of its concentrations is constant K= c c NernstR GGC, E GGC,
  24. 24. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 23 Adsorption  Adsorption: the collection of one substance on the surface of another Surface Concentration a [mol/g] and Fraction of Surface covered  [ ] adsorbent speciesadsorbed m n =a layermomoa a  LANGMUIR Adsorption Isotherm  Formation of a unimolecular layer at saturation [ ] [ ] (K [Pa or M]: Langmuir constant; [A] [Pa] Pressure or [M] : molarity)  Surface areas of the sorbent can be calculated from a (spec. area = a . NA . Aadsorbed molecule)  In order to test the Langmuir isotherm it is best to use a reciprocal plot (1/a versus 1/c or 1/p) BET Adsorption Isotherm  Extension of the Langmuir treatment (by BRUNAUER, EMMETT AND TELLER) to allow for the physisorption of additional layers of adsorbed molecules monad, * monad,ad * * VK p/p1)-(K + VK 1 = V)p/p-1( p/p (K []: BET-constante; p* :saturation vapor pressure; Vmon: volumen that can be adsorbed as a monolayer) FREUNDLICH Adsorption Isotherm [ ]  In order to test the Freundlich isotherm it is best to use a logarithmic plot (ln(a) versus ln(c)) )ln()ln(ln(a) c 
  25. 25. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 24 Chemical Kinetics Rate of Consumption and Formation ri [mol/(s m³)]  The change in concentration of a reactant or product per unit time [ ] Rate of Reaction r [mol/(s m³)] Rate Law, Rate Constant and Half Life  Rate law: an expression, which shows how the rate depends on the concentrations of reactants r = k f(c ,c ,c ...)A B C often ( ) [ ] [ ] [ ]  The proportionality constant k is called the rate constant; the exponents a,b,c.. are called the order of the reactant  The form of the rate law (the values for k, a, b, c ...) must be determined by experiment  The integrated rate law relates concentration to reaction time: cA = f(t)  The time required for a reactant to reach half of its original concentration is called the half life of a reaction and is designated by the symbol t½ 0st order reaction
  26. 26. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 25 Simple-Order Reactions First-Order Reaction (A  P)  Doubling the concentration of A doubles the reaction rate  Half-life does not depend on concentration  A plot of ln(cA) versus t is a straight line A1 A ck= td cd -=r  tk-expc=c 1A,0A tk-cln=cln 1A,0A t1 2 1 = ln 2 k Second-Order Reaction (A  P)  Doubling the concentration of A quadruples the reaction rate  Half-life is dependent of cA,0  A plot of 1/cA versus t is linear 2 A2 A ck= td cd -=r c k t A = c 1+ c A,0 A,0 2 1 c = 1 c + k t A A,0 2 t1 2 2 A,0 = 1 k c Examples: Reaction 2 N2O5  2NO2 + O2 Cyclopropane  Propene C2H6  2 CH3 2 NO2  2 NO + O2 H+ + OH-  H2O 25 °C (gas phase) 500 °C (gas phase) 700 °C (gas phase) 300°C (gas phase) 25 °C (in water) k 3,1410-5 1/s 6,7110-4 1/s 5,46 10-4 1/s 0,54 dm³/(mol s) 1,5. 1011 dm³/(mol s) Kinetics of simple order reactions Reaction Rate Law Integrated Rate Law Half Life A  P r = k0 k0  t = cA,0 – cA t½ = cA,0/(2k0) A  P r = k1  cA k1  t = ln(cA,0) - ln(cA) t½ = ln(2)/k1 A  P r = k2  cA² k2  t = 1/cA – 1/cA,0 t½ = 1/(cA,0k2) A + B  P (cA,0 = cB,0) r = k2  cA  cB k2  t = 1/cA – 1/cA,0 t½ = 1/(cA,0k2) A + B  P (cA,0  cB,0) r = k2  cA  cB k2t = 1/(cA,0 – cB,0)ln(cB,0cA/cA,0cB)
  27. 27. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 26 More Complicated Mechanisms Equilibrium Reaction ( A  P) A reversible chemical reaction will be at dynamic equilibrium when the rate of forward reaction is equal to the rate of the reverse reaction. GGA GGp c c , , k k =K   AA EEH  R Consecutive Reaction (A  I  P)  The steady-state approximation (SSA) assumes that, after an initial induction period the rates of change of concentrations of all unstable intermediates are negligibly small, i.e.: unstable intermediate  The rate-determining step approximation states that in a series of consecutive elementary rections the rate of production of the final products depends only the rate coefficient for the slowest step in the sequence stable intermediate Competitive Reaction ( P´  A  P) Reaction 1 (-----) has a more stable transition state and therefore a lower activation barrier. So diamond is the kinetic product. Reaction 2 (_____ ) generates the more stable product since graphite it is at lower energy than diamnond. So graphite is the thermodynamic product. Kinetic control is favoured with mild and low temperature conditions. Thermodynamic reaction control takes place with vigorous reaction conditions or when the reaction is allowed to continue over a long time
  28. 28. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 27 Influence of Temperature and Catalyst on Reaction Rates ARRHENIUS Equation  The rate constant k shows an exponential increase with temperature k = A exp E R T A       (A: frequency factor; EA [J/mol] activation energy; R = 8,314 J/(mol K) gas constant)  A plot of ln(k) against (1/T) gives a straight line („ARRHENIUS plot“); the value of the activation energy can be obtained from the slope of the line, which equals -EA/R; the intercept can be used to determine A. ln( )k = ln(A) - E R 1 T A  Activation energy EA : for a reaction , mole- cules must come together with at least EA in order to surmount the energy barrier (threshold energy)  Frequency factor A (preexponential factor): rate constant at very high temperture Examples: Reaction 2 N2O5 2NO2 + O2 cyclopropane propene sucrose  fructose + glucose 1. order, gas phase 1. order, gas phase 2. order; aqueous solution EA 88 kJ/mol 272 kJ/mol 107,9 kJ/mol A 6,311014 1/s 1,581015 1/s 1,5 1015 dm³/(mol s) Collision Theory and Activated Complex  Molecules must collide to react (reaction rate = number of successfull collisons)  The relative orientation of the reactants must allow formation of any new bonds necessary to produce products (steric factor = fraction of collisions with effective orientation)  The collision must involve enogh energy to form the activated complex (transition state) Catalysis  A catalyst is a substance that increases the rate of reaction without being consumed itself  A catalyst does not modify the overall thermodynamics (H, G, S) of the reaction  A catalyst provides a new pathway with lower activation energy for the reaction Reaction 2 HI H2 + I2 catalyst (none) Au(s) Pt(s) EA [kJ/mol] 184 105 59
  29. 29. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 28 Electrochemistry - Solutions of Electrolytes Dissociation of Electrolytes  Strong electrolytes occur almost entirely as ions in solution; degree of dissociation   1  Weak electrolytes are present only partially as ions;  << 1 K A K + A+ - + - + z - z     n = z = - ze + + - -  ( [] dissociation number of cation / anion; z [] : charge number of cation / anion; ne [] : elektrochemical number) Conductivity E [S/m]  Product from conductance (G [S] = 1/R) and cell constant (C = d/A) A d R 1 =E E i=1= E ( [m] : specific resistance; E [V/m]: electric field ; R [] resistance, d[m] distance between electrodes; A[m²] area of electrode) Molar Conductivity m and Equi- valent Conductivity  [Sm²/mol] m = c E   = c n E e  (c [mol/L]: molarity; ne []: electrochemical number) Examples (25 °C, unless otherwise stated): Substance Cu Fe NaCl (l) KCl 1M KCl 0,1 M ZrO2/Y(s) H2O 850 °C 750 °C E [S/cm] 580000 96100 3,66 0,098 0,00112 0,01 4,41. 10-8 KOHLRAUSCH´s Law of Independent Migration of Ions - Ion Conductivities  [Sm²/mol]  Each ion is assumed to make its own contribution to the molar conductivity, irrespecitve of the nature of the other ion with which it is associated Examples (infinite dilution): Ion H+ Na+ K+ Ca2+ OH- Cl- NO3 - SO4 2- CH3COO-  [cm²/( mol)] 349,7 50,1 73,5 59,5 197,0 76,4 71,5 80,0 40,9
  30. 30. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 29 DEBYE-HÜCKEL-Theory Ionic Strength I and Ionic Cloud  The ionic strength I of a solution is a function of the concentration of all ions present in a solution. i i 2 i cz 2 1 I   Solutions that contain ionic solutes do not behave ideally even at very low concentrations. DEBYE AND HÜCKEL introduce the concept of an ionic cloud: Each ion attempts to surround itself with oppositely charged ions. The radius of the ionic cloud depends on the ionic strength of the solution I 1 nm0,304=rI  Activity a and DEBYE-HÜCKEL limiting law  The effective concentration – the activity a - is proportional to the concentration by the activity coefficient  c= iiia  The DEBYE-HÜCKEL limiting law enables one to determine the activity coefficient of an ion in a dilute solution of known ionic strength. Izz5091,0)log( -+ 
  31. 31. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 30 Electrochemistry - Conductivity Ionic Velocity v [m/s] and Ionic Mobility u [m²/V s]  The mobility u of an ion is defined as the speed with which the ion moves under a unit potential gradient.  The mobility can be calculated from ion conductivities v = u E v = u E+ + - - = F u = F u+ -   (E [V/m]: electric field) Examples (infinite dilution): Ion H+ Na+ K+ Ca2+ OH- Cl- NO3 - SO4 2- CH3COO- u [10-4 cm²/(Vs) 36,23 5,19 7,62 6,17 20,64 7,91 7,4 8,29 4,34 Variation of Equivalent Conductivity  with Concentration a) Strong Electrolytes (KOHLRAUSCH´s Law)  Electrophoretic effect: the ion and its ionic atmosphere move in different directions  Asymmetry effect: the ionic atmosphere around a moving ion is not symmetrical  = - const. c b) Weak Electrolyte (OSTWALD´s Dilution Law)  conductivity is proportional to the degree of dissociation   =   K = c 2  ( )1     1 c 1 = 1 2 K ( []: degree of diss.;  [Sm²/mol] : equivalent conductivity at molarity c [M];  [Sm²/mol] : equivalent conductivity at infinite dilution)
  32. 32. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 31 Electrochemistry - Electrodes Electron Transfer Reaction Half-reactions occuring at the interface between an electrode and the solution:  Oxidation (transfer of electrons to the metal) occurs at the anode [Ox]anode + e e-  [Red] anode  Reduction (transfer of electrons to the electrolyte) occurs at the cathode [Ox]cathode + e e-  [Red] cath NERNST Equation - Electrode Potential at Zero Current  The potential of a single electrode Eredox is dependent on concentration    red ox red ox e o redox a a ln F TR +E=   redoxE (R=8,314 J/(mol K) : gas constant; e []: number of electrons in electron transfer reaction; F= 96 485 C/mol : Faraday constant) Standard Electrode Potentials E° React. Cl2+2e- 2Cl- Ag+ +e- Ag Fe3+ +e- Fe2+ Cu2+ +2e- Cu Zn2+ +2e- Zn E°redox 1,36 V 0,80 V 0,77 V 0,34 V - 0,76 V Combinations of Electrodes - Cell Potential E [V] („EMF“)  The cell potential at zero current (electromotive force „emf“ E) is the potential difference beween the cathode and the anode  The galvanic cell runs spontaneously in the direction that give a positive value for E  The process of electrolysis involves forcing a current throgh a cell to produce chemical change for which the cell potential E is negative E = E - Eredox,cathode redox, anode  S, H and G values can be calculated, if emf measurements are made over a range of temperature R G = - F Ee  R S = F E T e          R H = - F E - T E T e          (RH [J/mol] : enthalpy of reaction; RS [J/(K mol)] : entropy of reaction; RG [J/mol] : free enthalpy of reaction; E [V]: electromotive force emf; e []: number of electrons transferred for every unit of reaction; F= 96 485 C/mol : Faraday constant) Reference Electrodes and Potentials: electrode Diagram potential standard hydrogen electrode (SHE); Pt/H2(1 bar), H+ (a= 1mol/l) E = 0,00 V calomel electrode, saturated; Hg/Hg2Cl2, KCl (sat.) E = 0,241 V silver chloride electrode, saturated; Ag/AgCl, KCl (sat.) E = 0,197 V Galvanic Cell
  33. 33. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 32 Electrochemistry - Electrolysis FARADAY´s Law of Electrolysis  The mass of an element produced at an electrode is proportional to the quantitiy of electricity passed through the liquid and proportional to the equivalent weight of the element m = I t M F e (m [kg]: mass; I [A] : current; t [s] : time; M [kg/mol] : molar mass; F = 96 495 C/mol: FARADAY constant; e []: number of electrons in electron transfer reaction) Liquid Junction (Diffusion) Potential and Membrane Potential At the liquid junction of two different electrolytes the ions have different mobilities t+ and t-. The movement of the ions across this boundary generates a current flow and hence a potential (junction or diffusion potential diff; membrane potential mem, if the junction is permeable only to one kind of ion)         2 1 + c c ln)(t Fz TR -= tdiff        2 1 c c ln Fz TR -=mem
  34. 34. Physical Chemistry / EquationS and Data / Prof. Dr. G. J. Lauth / university of applied sciences Standard Enthalpies and Entropies (1 bar; 25 °C) M Cp,m HB,i S°i g/mol J/(mol K)) kJ/mol J/(molK Ag (s) Silver 107,87 25,351 0 42,69 Ag+ (aq) Silverion107,87 105,90 73,93 AgCl (s) Silver chloride 143,32 50,79 - 127,03 96,10 AgBr (s) Silver bromide 187,78 52,38 - 99,5 107,1 AgI (s) Silver iodide 234,77 54,43 - 62,4 114,2 Ag2S (s) Silver sulfide 247,80 76,40 - 29,3 150,2 Al (s) Aluminium26,98 24,35 0 28,31 Al3+ (aq)Aluminiumion 26,98 - 524,7 - 313,4 Al2O3 (s,) Al. oxide 101,96 79,04 - 1675 50,94 Ba (s) Barium137,34 28,07 0 64,85 Ba2+ (aq) Bariumion 137,34 - 538,4 11 BaSO4 (s) Barium sulfate 233,40 101,75 - 1465 131,8 Br2 (l) Bromine159,82 75,689 0 152,3 Br2 (g) Bromine159,82 36,02 30,7 245,4 Br (g) Bromine atom 79,91 20,786 96,44 174,9 Br- (aq) Bromide ion 79,91 - 120,9 80,7 Cgraphite (s) Carbon12,011 8,527 0 5,694 Cdiamond (s) Carbon12,011 6,113 1,896 2,378 C (g) Carbon atom12,011 20,838 718,38 157,99 CCl2O (g) Phosgen98,92 - 223 289 CHO3 - (aq) Hydrogencarbonat 2 61,02 - 691,1 95 CH2O (g) Formaldehyde 30,03 35,40 - 116 219 CH4 (g) Methane16,04 35,31 - 74,8 186,2 CH3OH (l) Methanol 32,04 81,6 - 238,6 126,8 CH3OH (g) Methanol 32,04 43,89 - 201,2 237,7 CH3NH2 (g) Methylamine 31,06 53,1 - 28 242 CO (g) Carbon monoxide 28,011 29,14 - 110,52 197,91 CO2 (g) Carbon dioxide 44,010 37,11 - 393,51 213,64 CO3 2- (aq) Carbonate Ion 60,01 - 676,3 - 53 C2Ca (s) Carbide64,10 62,3 - 62,8 70,3 C2H2 (g) Ethyne (=acetylen) 26,04 43,93 226,7 200,8 CH3CN (g) Acetonitril 41,05 88,91 87,7 243 C2H4 (g) Ethene (= Ethylen) 28,05 43,56 52,30 219,5 CH3CHO (g) Acetaldehyde 44,05 57,3 - 166,35 265,7 C2H6 (g) Ethane30,07 52,63 - 84,68 229,5 C2H5OH (l) Ethanol 46,07 111,46 - 278 161 C2H5OH (g) 46,07 65,44 - 235 282 Ethanol CH3OCH3 (g) Dimethyl ether 46,07 170,7 - 185 267 CH3COOH (l) Acetic acid 60,05 124,3 - 484,5 159,8 CH3COOH (aq) Acetic acid 60,05 - 485,76 178,7 CH3COO- (aq) Acetate 59,05 - 486,01 86,6 CH3COCH3 (l) Acetone 58,08 124,7 - 248 200 CH3COCH3 (g) Acetone 58,08 - 216 295 C3H8 (g) Propane44,10 73,5 - 103,85 269,9 (CH3)3N (g) Trimethylamine 59,11 - 46,0 289 M Cp,m HB,i S°i g/mol J/(mol K) kJ/mol J/(molK) C4H8 (g) 1-Butene56,11 85,65 1,17 301,4 C4H8 (g) cis-2- Butene 6,11 78,91 - 5,70 300,8 C4H8 (g) trans-2- Butene 56,11 87,82 - 10,06 296,5 C4H10 (g) n-Butane58,13 97,45 - 124,73 310,0 C4H10 (g) Isobutane 58,13 - 131,60 294,6 C5H12 (g) n- Pentane 72,15 120,2 - 146,4 348,4 C6H6 (l) Benzene78,12 136,1 49,03 172,8 C6H6 (g) Benzene78,12 81,67 82,93 269,2 C6H12 (g) Cyclohexane 84,16 156,5 - 123,1 298,2 C6H12 (g) 1- Hexene 84,16 - 41,7 386,0 C6H14 (l) Hexane86,18 - 199,2 285,8 C6H14 (g) Hexane86,18 143,1 - 167,2 386,8 C6H12O6 (s) -D- Glucose 180,16 - 1274 C6H5COOH (s) Benzoic acid 122,13 146,8 - 385,1 167,6 C8H18 (l) n-Octane114,23 -249,9 361,1 C10H8 (s) Naphthalene 128,18 165,5 78,53 C12H22O11 (s) Saccharose 342,3 - 2222 360,2 Ca (s) Calcium0,08 25,31 0 41,62 Ca2+ (aq) Calcium ion 40,08 - 543,0 - 55 CaO (s) Calcium oxide 56,08 42,80 - 635,5 39,7 CaCO3 (s)Calcit - carbonat 100,09 81,88 - 1206,9 92,9 Ca(OH)2 (s) Ca- hydroxide 74,09 84,5 - 986,2 83,4 Cl2 (g) Chlorine70,91 33,91 0 223,0 Cl (g) Chlorine atom 35,45 21,840 121,1 165.09 Cl- (aq) Chloride ion 35,45 - 167,4 55,1 HCl (g) Hydrogen chloride 6,46 29,12 - 92,31 186,7 Cu (s) Copper63,54 24,44 0 33,30 Cu2+ (aq) Copper (II) ion 63,54 64,4 - 98,7 Cu+ (aq) Copper63,54 52 - 26
  35. 35. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 34 (I) ion CuI (s) Copper(I) iodide) 190,44 54,1 68,2 96,6 CuSO4 (s) Copper sulfate 159,60 100,0 - 771,36 109 CuSO45 H2O(s) - hydrate 249,68 280 - 2279,7 300,4 F2 (g) Fluorine38,00 31,3 0 202,7 F (g) Fluorine atom 19,00 22,74 79,09 158,6 F- (aq) Fluoride ion 19,00 - 329,1 - 9,6 HF (g) Hydrogen fluoride) 20,01 29,13 - 268,5 173,7 Fe (s) Iron 55,85 25,10 0 27,15 Fe2+ (aq) Iron(II) ion 55,85 - 88 - 113 Fe3+ (aq) Iron(III) ion 55,85 - 48 - 293 M Cp,m HB,i S°i g/mol J/(mol K) kJ/mol J/(molK) H2 (g) Hydrogen2,016 28,824 0 130,6 H (g) Hydrogen atom 1,008 20,784 217,94 114,6 H+ (aq) Hydrogen ion 1,008 0 0 H2O (l) Water18,015 75,291 - 285,84 69,94 H2O (g) Water18,015 33,58 - 241,83 188,72 Hg (l) Mercury200,59 27,983 0 76,09 Hg (g) Mercury200,59 20,786 60,8 174,9 Hg2 2+ (aq) Mercury ion 401,18 169 74 Hg2Cl2 (s) Hg chloride 472,09 102 - 264,8 195,7 I2 (s) Iodine253,81 54,44 0 116,14 I2 (g) Iodine253,81 36,90 62,24 260,6 I (g) Iodine atom126,90 20,786 106,6 180,7 I- (aq) Iodide ion126,90 - 55,9 109,4 HI (g) Hydrogen iodide 127,91 29,158 25,94 206,3 K (s) Potassium39,10 29,58 0 64,35 K (g) Potassium39,10 90,04 160,2 K+ (aq) Potassium ion 39,10 - 251,2 102,5 Mg (s) Magnesium 24,31 24,89 0 32,55 Mg2+ (aq) Magnesium ion 24,31 - 462,0 - 118 MgO (s) Magnesium oxide 40,31 37,15 - 601,2 26,8 Mn (s) Manganese54,938 26,32 0 31,76 Mn2+ (aq) Manganese ion 54,938 - 219 - 83 MnO (s) Manganese(II)oxid e 70,94 42,97 - 348,8 59,71 Mn3O4 (s) Mn- (II,III)oxide 228,81 139,7 - 1386 149,5 MnO2 (s) Mn- (IV)oxide 86,94 57,2 - 519,7 53,1 MnO4 - (aq) Permanganate 118,94 - 518 190 N2 (g) Nitrogen28,013 29,125 0 191,5 N(g) Nitrogen14,007 20,786 470,6 153,1 atom N2O (g) Din- monoxide 44,01 38,45 81,55 220,0 NO (g) Nitrogen monoxide 30,01 29,844 90,37 210,6 NO2 (g) Nitrogen dioxide 46,01 37,20 33,32 239,8 N2O4 (g) Din- tetroxide 92,01 77,28 9,368 304,3 NO3 - (aq) Nitrate ion 62,01 - 206,6 146 NH3 (g) Ammonia17,03 35,06 - 46,19 192,5 NH4 + (aq) Ammonium ion 18,04 - 132,8 112,8 NH4Cl (s) A- chloride 53,49 84,1 - 315,39 94,6 HNO3 (l) Nitric acid 63,01 109,87 - 173,0 156,1 M Cp,m HB,i S°i g/mol J/(mol K) kJ/mol J/(molK) Na (s) Sodium22,99 28,24 0 51,42 Na (g) Sodium atom 22,99 108,7 153,62 Na+ (aq) Sodium ion 22,99 - 239,7 60 NaCl (s) Sodium chloride 58,44 49,71 - 411,1 72,12 Na2SO4 (s) Sodium sulfate 142,04 127,82 -1384,5 149,5 O2 (g) Oxygen31,999 29,355 0 205,0 O3 (g) Ozone47,997 142,67 238,82 O (g) Oxygen atom15,999 21,912 247,52 160,9 OH- (aq) Hydroxide ion 17,007 -148,5 - 230 - 10,54 Pb (s) Lead 207,19 26,44 0 64,91 Pb2+ (aq) Lead ion207,19 1,6 21,4 PbO2 (s) Lead(IV) oxide 239,19 64,64 - 276,6 76,44 PbCl2 (s) Lead(II) chloride 278,10 76,8 - 359,1 136,4 PbI2 (s) Lead(II) iodide 461,00 81,7 - 175,1 176,9 PbS (s) Lead(II) sulfide 239,25 49,5 - 94,28 91,2 PbSO4 (s) Lead(II) sulfate 303,25 104,3 - 918,1 147,2 Srhombisch (s) Sulfur32,06 22,64 0 31,8 Smonoklin (s) Sulfur32,06 23,6 0,29 32,6 S2- (aq) Sulfide ion32,06 42 22 SO2 (g) Sulfur dioxide 64,06 39,87 - 296,9 248,1 SO3 (g) Sulfur trioxide 80,06 50,67 - 395,2 256,0 H2SO4 (l) Sulfuric acid 98,08 138,9 - 811,7 156,9 HSO4 - (aq) Hydrogensulfate 97,07 - 885,75 126,9 SO4 2- (aq) Sulfate ion 96,06 - 907,5 17,2 H2S (g) Hydrogen sulfide 34,08 34,23 - 20,15 205,6 Si (s) Silicium28,09 20,00 0 18,82 SiO (g) Silicium monoxide 44,09 -100,42 211,47 SiO2 -Quartz(s) Si- dioxide 60,09 44,43 -910,86 44,59 SiH4 (g) 32,12 40,67 32,64 204,13
  36. 36. Physical chemistry formulary Dr. Lauth, University of Applied Sciences, Jülich Campus 35 Monosilane SiF4 (g) Si- tetrafluoride 104,08 73,6 -1614,9 282,14 SiCl4 (l) Si- tetrachloride ( 169,90 145,2 -640,15 239,32 SiCl4 (g) Si- tetrachloride 169,90 -657,31 330,83 Snweiß (s) Tin118,69 26,99 0 51,5 Sngrau (s) Tin118,69 - 2,19 44,1 Sn2+ (aq) Tin ion118,69 - 10 - 20,5 Zn (s) Zink 65,37 25,40 0 41,59 Zn2+ (aq) Zink ion65,37 46 - 152,4 - 106,5 AVOGADRO number NA = 6,0221023 1/mol Universal gas constant R = 8,3145 J/(mol K) BOLTZMANN constant kB = 1,38110-23 J/K Charge of a proton e = 1,6021810-19 C FARADAY constant F = 96485,3 C/mol Permittivity of vacuum 0 = 8,85410-12 C2 /(Jm) Speed of light c = 2, 9979 108 m/s PLANCK constant h = 6,6261 10-34 Js Mass of an electron me = 9,10938 10-31 kg Mass of a proton mp = 1,672610-27 kg Acceleration of gravity g = 9,81 m/s2 Electrochemical Reduction Potentials (p = p0 = 1 bar; c = c0 = 1 mol/L ; T = 298 K; aqueous solution) [Ox] + e e-  [Red] E0 redox [V] F2 (g) + 2 e-  2 F- + 2,85 S2O8 2- + 2 e-  2 SO4 2- + 2,0 PbO2(s) + SO4 2- + 4 H+ + 2 e-  PbSO4 (s) + 2 H2O + 1,685 MnO4 - + 8 H+ + 5 e-  Mn2+ + 4 H2O + 1,491 PbO2 (s) + 4 H+ + 2 e-  Pb2+ + 2 H2O + 1,455 Ce4+ + e-  Ce3+ + 1,443 Au3+ + 3 e-  Au (s) + 1,42 Cl2(g) + 2 e-  2 Cl- + 1,358 O2 (g) + 4 H+ + 4 e-  2 H2O + 1,229 HCrO4 - + 7 H+ + 3 e-  Cr3+ + 4 H2O + 1,195 Br2 (l) + 2 e-  2 Br- + 1,065 AuCl4 - + 3 e-  Au (s) + 4 Cl- + 0,994 NO3 - + 4 H+ + 3 e-  NO (g) + 2 H2O + 0,96 Ag+ + e-  Ag (s) + 0,7996 Hg2 2+ + 2 e-  2 Hg (l) + 0,798 Fe3+ + e-  Fe2+ + 0,770 C6H4O2 + 2 H+ + 2 e-  C6H4(OH)2 + 0,6995 I2 (s) + 2 e-  2 I- + 0,535 Cu+ + e-  Cu (s) + 0,522 O2 (g) + 2 H2O + 4 e-  4 OH- + 0,401 Cu2+ + 2 e-  Cu (s) + 0,340 AgCl (s) + e-  Ag (s) + Cl- + 0,2223 [Ox] + e e-  [Red] E0 redox [V] SO4 2- + 4 H+ + 2 e-  H2SO3 (aq) + H2O + 0,20 Sn4+ + 2 e-  Sn2+ + 0,15 S(s) + 2 H+ + 2 e-  H2S (aq) + 0,141 CuI2 - + e-  Cu (s) + 2 I- + 0,00 2 H+ + 2 e-  H2 (g) 0 Fe3+ + 3 e-  Fe (s) - 0,036 Pb2+ + 2 e-  Pb (s) - 0,126 Sn2+ + 2 e-  Sn (s) - 0,136 Ni2+ + 2 e-  Ni (s) - 0,23 PbSO4 (s) + 2 e-  Pb (s) + SO4 2- - 0,356 Cd2+ + 2 e-  Cd (s) - 0,4026 Fe2+ + 2 e-  Fe (s) - 0,440 S(s) + 2 e-  S2- - 0,508 Zn2+ + 2 e-  Zn (s) - 0,7628 Al3+ + 3 e-  Al (s) - 1,66 Ce3+ + 3 e-  Ce (s) - 2,335 Na+ + e-  Na (Hg) (l) - 2,711 Li+ + e-  Li (Hg) (l) - 3,045 Conversion factors Force (= mass x acceleration) 1 N = 1 kg m/s² 1 dyn = 10-5 N 1 kp = 9,806 N Pressure (= force / area) 1 Pa = 1 N/m² = 10-5 bar 101325 Pa = 1 atm = 760 Torr 760 mmHg = 10,33 mWS 1 psi = 6 895 Pa Energy (= force x distance; el. work = charge x voltage) 1 J = 1 N m = 1 m³ Pa 1 erg = 10-7 J 1 eV = 1,602110-19 J 1 eV = 96 494 J/mol 1 cal = 4,184 J Power (= work / time) 1 W = 1 J/s 1 kWh = 3600000 J/s 1 hp = 745,7 W
  37. 37. Index (D = Data, Examples) 1. Ficksches Gesetz Fick´s first Law 8 1. Hauptsatz der Thermodynamik 1. Law of Thermodyn. 16 2. Hauptsatz der Thermodynamik 2. Law of Thermodyn. 19 2. Raoultsches Gesetz Raoult´s Second Law 13 2. Virialkoeffizient 2. Virial Coefficient (D) 6 3. Hauptsatz der Thermodynamik 3. Law of Thermodyn. 19 A Absorption Absorption 31 Adsorption Adsorption 15 Aktivierungsenergie Activation Energy EA 26 Anode Anode 29 Antoine Gleichung Antoine Equation (D) 10 Äquivalent Leitfähigkeit Equivalent Cond.  27 Arbeit Work 2 Arrhenius-Gleichung Arrhenius Equation (D) 26 Asymmetrieeffekt Asymmetry Effect 28 atom. Bildungsenthalpie Enth. of Atomization 18 Azeotrop Azeotrope 14 B barometrische Höhenformel Barometric Distrib. Law 5 Bedeckungsgrad Fraction of Surface Cov. 15 BET-Isotherme BET Adsorption Isoth. 15 Beweglichkeit Ionic Mobility u (D) 28 Bildungsenthalpie Enth. of Formation HB 17 Bindungsenthalpie Bond Enthalpy 18 Binnendruck Internal Pressure 7 BOLTZMANN Verteilung BOLTZMANN Distribution 5 BOLTZMANNsche Entropieformel BOLTZMANN´s Equation 19 Boyle-Mariottesches Gesetz Bolye-Mariotte´s Law 3 Boyle-Temperatur Bolye-Temperature 6 Brechungsindex Refraction Index n (D) 31 C Carnotscher Kreisprozess Carnot Cycle 20 chemische Kinetik Chemical Kinetics 24 Clausius-Clapeyronsche Gleichung Clausius-Clapeyron E. 10 Couette Viskosimeter Couette Viscosimeter 9 Daltonsches Gesetz Dalton´s Law 3 Dampfdruck Vapor Pressure 10 D Dichte Densitry 1 Diffusion Diffusion 8 Diffusionskoeffizient Diffusion Coefficient 8 Dissoziation Dissociation 13 Driftgeschwindigkeit Ionic Velocity 28 Druck Pressure 1 Durchlässigkeit Transmittance T 31 Durchtrittsreaktion Electron Transfer Reac. 29 E Einstein-Smoluchowski-Gleichung Einstein-Smoluchowski 8 elektrische Leitfähigkeit Electrolytic Cond.  27 Elektrochemie Electrochemistry 27 Elektroden Electrodes (D) 29 Elektrodenpotential Electrode Potential (D) 29 Elektrolyse Electrolysis 29 elektrolytische Dissoziation Dissociation of Electrol. 27 elektrolytische Lösungen Solutions of Electrolytes 27 Elektromagnetisches Spektrum Electromagnetic Sp. 31 Elektromotorische Kraft Electromotive Force E 29 elektrophoretischer Effekt Electrophoretic Effect 28 EMK EMF 29 endergonische Reaktionen Endergonic Reactions 22 Enthalpie Enthalpy H 16 Enthalpiemessungen Enthalpy Measurements 18 Entropie Entropy S 19 Eutektikum Eutectic 14 exergonsiche Reaktionen Exergonic Reactions 22 Extinktion Absorbance E 31 Extinktion Extinction E 31 F Faradaysches Gesetz Faraday´s Law 30 Fouriersches Gesetz Fourier´s Law 8 Freie Energie Free Energy A 21 Freie Enthalpie Free Enthalpy G 21 Freiheitsgrad Degree of Freedom 1 Frequenzfaktor Frequency Factor A (D) 26 G Galvanische Zellen Galvanic Cell 29 Gay-Lussacsches Gesetz Gay-Lussac´s Law 3 Gefrierpunktserniedrigung Freezing Point Depr. 13 Gesamtdampfdruck Total Vapor Pressure 12 Geschwindigkeitsgesetz Rate Law 24 Geschwindigkeitskonstante Rate Constant 24 Gesetz von Charles Charles´s Law 3 Gibbs Energie Gibbs Energy G 21 Gibbs-Helmholtz-Gleichung Gibbs-Helmholtz Equ. 21 Gibbssche Phasenregel Gibbs´ Phase Rule 1 Gleichgewicht Equilibrium 21 Gleichgewichtskonstante Equilibrium Constant K 21 H Hagen-Poiseuillesches Gesetz Hagen-Poiseuille Equ. 9 Halbwertszeit Half-life 24 Helmholtz Energie Helmholtz Energy A 21 Henrysches Gesetz Henry´s Law (D) 12 Heßscher Satz Heß´s Law 17 I ideale Lösungen Ideal Solutions 12 ideales Gas Ideal Gas 3 individuelle Reaktionsgeschw. Rate of Consumtion ri 24 individuelle Reaktionsgeschw. Rate of Formation ri 24 Innere Energie Internal Energy U 16 Inversionstemperatur Inversion Temperature 7 Ionenleitfähigkeit Ion Conductivity  (D) 27 isobare Prozesse Process at const. Press. 16 isochore Prozesse Process at const. Vol. 16 J Joule-Thomson-Koeffizient Joule-Thomson Coef. 7 K Kalorimetrie Calorimetry 17 Kapillarität Capillarity 11 Kapillarviskosimeter Capillary Viscosimeter 9 Katalysator Catalyst (D) 26 Katalyse Catalysis (D) 26 Kathode Cathode 29 Kelvin Gleichung Kelvin Equation 11 kinetische Energie Kinetic Energy 4 kinetische Gastheorie Kinetic-Molecular The. 4 Kirchhoffsches Gesetz Kirchhoff´s Law 18 Kohlrauschsches -Gesetz Kohlrausch´s  Law 28 Kohlrauschsches Gesetz Kohlrausch´s Law 27 Kolligative Eigenschaft Colligative Property 13 Kombination von Elektroden Comb. of Electrodes 29 Komponente Component 1 Kompressionsfaktor Compression Factor 6 Konduktion Conduction 8 Konjugierte Base Conjugate Base (D) 23 Konvektion Convection 8 Konz.-abhängigkeit der Entropie Entropy; Conc.-Dep. 20 Kovolumen Colvolume (D) 6 kritische Daten Critical Constants (D) 7 kritischer Punkt Critical Point 1 Kugelfallviskosimeter Falling-ball Viscosim. 9 L Lambert-Beersches Gesetz Lambert-Beer Law 31 Langmuir-Isotherme Langmuir´s Ads. Isoth. 15 Laplacesche Gleichung Laplace Equation 11 Le Chateliersches Prinzip Le Chatelier Principle 22 Lichtstreuung Light Scattering 31 Liquiduslinie Liquidus Curve 14 Löslichkeit Solubility cs 23 Löslichkeitsprodukt Solubility Product KL 23 Luft Air (D) 3 M Maxwell-Boltzmann-Verteilung Maxwell-Boltzmann D. 4 mittlere freie Weglänge Mean Free Path  (D) 5 mittlere Geschwindigkeit Average Velocity (D) 4 mittleres Geschwindigkeitsquadrat Mean-Square Velocity 4 mittleres Verschiebungsquadrat Mean Square Dist. x² 8 Molalität Molality b 13 molare Leitfähigkeit Molar Conductivity m 27 molare Wärmekapazität Molar Heat Capacity 2 neg. Abweichungen v. Raoult Neg. Deviations Raoult 14
  38. 38. N Nernstsche Gleichung Nernst Equation 29 Nernstscher Wärmesatz Nernst´s Heat Theorem 19 Newtonsches Gesetz Newton´s Law (visc.) 9 Normalentropien Absolute Entropies S° 19 O Oberfläche Surface Area 15 Oberflächenspannung Surface Tension 11 Osmose Osmosis 13 osmotischer Druck Osmotic Pressure  (D) 13 Ostwald Viskosimeter Ostwald Viscosimeter 9 Ostwaldsches Verdünnungsgesetz Ostwald´s Dilution Law 28 P Partialdruck Partial Pressure 3 Phase Phase 1 Phasendiagramm Phase Diagramm 1 Phasenumwandlungen Phase Transitions (D) 16 Phasenumwandlungsentropien Entropy; Phase Trans. 20 Polarimetrie Polarimetry 31 Polarisiertes Licht Polarized Light 31 Pos. Abweichungen v. Raoult Pos. Deviations Raolt 14 Präexponentieller Faktor Preexp. Factor A (D) 26 R Random-walk Gleichung Random-walk Equation 8 Randwinkel Meniscus Angle 11 Raoultsches Gesetz Raoult´s Law 12 Rayleighsches Gesetz Rayleigh´s Law 31 Reaktionen 1. Ordnung First-Order Reaction (D) 25 Reaktionen 2. Ordnung Second-Order Reac. (D) 25 Reaktionen einfacher Kinetik Simple-Order Reactions 25 Reaktionsenergie Energy of Reaction rU 17 Reaktionsenthalpie Enthalpy of React. rH 17 Reaktionsgeschwindigkeit Rate of Reaction r 24 Reaktionsordnung Reaction Order 24 Reaktionsquotient Reaction Ratio QR 21 Reaktionsstand Extent of Reaction  17 reale Gase Real Gas 6 reale Lösungen Real Solutions 14 Reatkionsentropie Reaction Entropy 20 Referenzpotential Reference Potentials (D) 30 S Satz von Avogadro Avogadro´s Hypotheses 3 Säurekonstante Acid Diss. Constant 23 Schergeschwindigkeit Shear Rate 9 Schubspannung Shear Stress 9 schwache Elektrolyte Weak Electrolytes 27 Siedelinie Boiling Point Curve 14 Siedepunktserhöhung Boiling Point Elevation 13 spez. Wärmekapazität Specific Heat Capacity 2 spezifische Leitfähigkeit Specific Cond.  (D) 27 Standardzustand Standard State (°) 2 starke Elektrolyte Strong Electrolytes 27 Stefan-Boltzmannsches Gesetz Stefan-Boltzmann´ Law 8 stöchiometrische Gleichung Stoichometric Equation 17 stöchiometrische Umsatzzahlen Stoichiometric Coeff. 17 Stoffmengenkonzentration Molarity c Stokesches Gesetz Stokes´s Law 9 Stoßfrequenz Collision Frequency (D) 5 Stoßquerschnitt Cross Section of Coll. 5 Stoßtheorie Collision Model (D) 26 Strahlung und Materie Radiation and Matter 31 System System 1 T Temp.-abhängigkeit der Entropie Entropy; Temp.-Dep. 20 Temp.-Abhängigkeit von K Temperature Dep. of K 22 Thermochemie Thermochemistry 17 thermodyn. Wahrscheinlichkeit Thermodynamic Prob. 19 Translationsenergie Translational Energy 4 Transporteigenschaften Transport Properties 8 Tripelpunkt Triple Point (D) 1 U Ubbelohde Viskosimeter Ubbelohde Viscosimeter 9 Ulichsche Näherung Ulich´s Approximation 22 Umgebung Surroundings 1 unabhängige Ionenwanderung Independent Migration 27 V van´t Hoffsche Gleichung van´t Hoff´s Equation 22 van´t Hoffscher Faktor van´t Hoff´s Factor i 13 van-der-Waalssche Gleichung van-der-Waals Equ. (D) 6 Verbrennungsenthalpie Enth. of Combustion 18 Verdampfungsenthalpie Enth. of Vaporization 10 Verschiebung von Gleichgewichten Shifts of Equilibrium 22 Viralgleichung Virial Equation 6 Viskosität Viscosity (D) 9 W Waldensche Regel Walden´s Rule 28 Wärme Heat 2 Wärmekapazität Heat Capacity 2 Wärmeleitfähigkeit Thermal Conductivity 8 Wärmestrahlung Radiation (heat transfer) 8 Wärmetransport Heat Transfer 8 Wellenlänge Wavelength 31 Wellenzahl Wave number 31 Wiensches Verschiebungsgesetz Wien´s Law 8 Wirkungsgrad Efficiency  20 Y Young Gleichung Young Equation (D) 11 Z Zellspannung Cell Potential E 29 Zustand Condition 1 Zustand State 1 Zustandsgröße Property 1 Rudolf Clausius (1822 – 1888) The energy of the universe is constant. The entropy of the universe tends toward a maximum. Heat death of the universe is inevitable!

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