Entropy and reaction spontaneity

Transcription

1 A quote of the week (o camel of the week): Minds ae like paachutes they only function when open Thomas Dewa 1 Entopy and eaction spontaneity Back to the II law ot themodynamics A spontaneous change is accompanied by an incease in the total entopy of the system and its suoundings. tot s tot s sys s su s sys h T s s s tot su tot spontaneous equilibium extenally diven Is a given chemical eaction spontaneous? (1) Given is eaction: S(s,homb) + O (g) = SO (g) Can it occu spontaneously at standad conditions? H f,98 kj/mol S 98 J/(K mol) S(s,homb.) 31,8 O (g) 5,14 SO (g) -96,83 48, Si. s. Ssys Ssu H, J S sys S, 98 (48,) (31,8 5,14) 11,8 J/K S S i. s. 11, J/K ot H T ukł J/K 98 YES, IT IS!!! 3 1

2 Gibbs fee enegy (1) Si. s. Ssys Ssu H Si. s. S T T Si. s. TS H TSi. s. H TS if : TS i. s. then theeaction isspontaneous Josiah Willad Gibbs G H TS G H TS Chem. Fiz. TCH II/4 4 Gibbs fee enegy () H S tot S TS tot H TS T G H TS G G G spontaneous equilibium extenally diven foced spontaneous in evesed diection 5 Gibbs fee enegy (3) Citeia of eaction spontaneity: exothemic H < endothemic H > S > S < S > S < always spontaneous spontaneous, if H > T S spontaneous, if H < T S neve spontaneous G H TS Always is spontaneous when G T,P < 6

3 Gibbs fee enegy (4) The standad eaction fee enegy G is the diffeence between the fee enegies of fomation of the poducts and the eactants (all in thei standad states). n n G, 98 nigi, f, p,98 nigi, f, e,98 i1 i1 The standad fee enegy of fomation, G f, of a compound is the standad eaction fee enegy pe mole fo its synthesis fom elements in thei most stable foms. Standad fee enegies of elements in thei most stable foms ae equal to zeo at 98K. 7 Gibbs fee enegy (5) 8 Gibbs fee enegy (6) 9 3

4 Gibbs fee enegy (7) 1 Fee Helmholtz enegy Fo isochoic/isothemic conditions anothe state function was defined, known as fee Helmholtz enegy: F U TS F U TS Hemann Ludwig Fedinand von Helmholtz Citeion of spontaneity of pocesses (chemical eactions) occuing at such conditions is: F V,T < 11 Is a given chemical eaction spontaneous? () Given is eaction: S(s,omb) + O (g) = SO (g) Can it occu spontaneously at standad conditions? G f,98 kj/mol S(s,homb.) O (g) SO (g) -3,19 G G, 98 twso,98 3,19 kj YES, IT CAN!!! G TS u. i. H TS We check calculations fom pat (1). Left side: TS i. s. (9817,35)/1 3,19 kj Right side: H TS 96,83 (9811,8)/1 3,19 kj 1 4

5 Is a given chemical eaction spontaneous? (3) Given is eaction: NaHCO 3 (s) = NaOH(s) + CO (g) Can it occu spontaneously at standad conditions? G f,98 kj/mol NaHCO 3 (s) -851,9 NaOH(s) -379,7 CO (g) -394,38 G,98 G G f, NaCO3,98 f, CO,98 G 773,45 851,9 78,45 kj f, NaOH,98 NO, IT CAN NOT!!! CONCLUSION: Sodium hydocabonate is themodynamically stable at standad conditions. 13 Gases Seveal following slides contain shee epetition o a eminde. Pefect (ideal) gas (an example of a model) Gas molecules emain in pepetual, chaotic movement. They do not inteact, neithe with the walls of the containe, no with each othe, except pefectly elastic collisions (bouncing). The molecules do not occupy any space (thei mass is concentated in points), at least thei size is negligible, when compaed with thei path between collisions. 14 Gases () Gases occupy any volume unifomly. Basic paametes: Volume, V units: m 3, dm 3 (l), cm 3 (all SI) Pessue, P units: Pa (N/m ), hpa, kpa, MPa, Ba (1 Ba=1kPa), Atm (1 Atm= Pa), To (1 mmhg). Tempeatue, T units: K (1 K=1 o C, as T) T = t + 73,15 whee: t is tempeatue in Celsius scale. 15 5

6 Gas laws Boyle s law Chales law Gay-Lussac s law PV= const at constant T isothemal pocess V 1 T =V T 1 at constant P isobaic pocess P 1 T =P T 1 at constant V isochoic pocess The laws wee discoveed expeimentally. They ae obeyed when gases ae aefied. (not too high P o T, not to small V) 16 Clapeyon equation Genealization of the 3 gas laws is equation of state of the pefect gas, also known as Clapeyon equation: PV nrt whee: n is numbe of moles of gas, R is univesal gas constant equal to J/(Kmol). R k B N Av whee: k B is Boltzman s constant, N Av is Avogado s numbe. 17 Avogado s law The same volumes of diffeent gases contain the same numbe of molecules (moles). V const n whee: const is mola volume. V m =.4 dm 3 /mol at nomal pessue ( Pa) and 73,15 K (calculated fom Clapeyon equation). Physical ChemistyGTM/4 18 6

7 Patial pessues and Dalton s law Patial pessue of a component of a gaseous mixtue is pessue of this component occupying alone the same volume as does the mixtue. Total pessue of a gas mixtue is the sum of patial pessues of all components. ni xi n n n i i x 1 i i P total P i i Pi xi P Whee x is mola faction and (appoximately) volume faction. 19 total Real gases vs pefect gas The pefect gas can not be liquefied (no inteactions). Real gases follow the pefect gas behavio (obey the pefect gas law) when P (gases ae aefied). Mola volumes of eal gases diffe fom the afoementioned value of.4 dm 3 /mol. Detailed study of eal gases evealed deviations fom the gas laws. Let s see some isothems of a eal gas (CO ). Real gas isothems The isothems ae no moe hypeboles (inflection points may bee seen). The ed isothem is know as the citical isothem and coesponding tempeatue as the citical tempeatue. The coodinates of the inflection point of this isothem ae: citical pessue and citical mola volume. 1 7

8 Van de Waals equation P RT Pe 1 mole of gas, V m mola volume: Vm b V m whee: b is coection fo the molecules own volume, a is a coection allowing fo molecula inteactions (attactive). Citical paametes: a 8a T c 7 br V mc 3b a P c 7b No eal gas can be liquefied above its citical tempeatue. Real gas isothems () P, V m, T paametes ae given hee as the educed paametes: T T c V V m mc P P c Viial Equation of State This equation was intoduced by Kamelingh Onnes (in two foms): 3 PV m RT(1 B' P C' P D' P...) B C D PVm RT Vm Vm Vm Coefficients B, C, D (B, C, D ) ae known as viial coefficients (they depend on tempeatue). Fequently only second viial coefficient is used: PV m RT B" P 4 8

9 The Pinciple of Coesponding States Real gases at the same educed tempeatue and educed volume have also the same educed pessue and the same educed Z (compessibility) It oiginates fom the educed Van de Waals equation (gas specific factos a and b disappea). Othe equations of state (educed) also include this pinciple. The pinciple cannot be applied when gas molecules ae pola ao non-spheical. 5 Maxwell distibution M is mola mass of the gas v is velocity M f ( v) 4 RT 3/ Mv /(RT) v e 6 Maxwell distibution () Some featues of the gas molecules may be calculated, on the basis of this distibution, like: 1/ Mean velocity: 8RT c M Mean fee path: c kt z P whee: z is collision fequency, (in Hz o s -1 ); is active coss-section (m ). Impotant popeties of the gases (viscosity, diffusion, efusion and themal conductivity coefficients, etc.) may be deived fom the kinetic model. 7 9

10 Viscosity of Gases(1) Coefficient of intenal fiction,, o viscosity, one can discuss in cathegoies of the kinetic theoy of gases, as exchange of momentum between the molecules in neighbouing layes of flowing gas. 4 dv ΔP F A; (1) v ; () 8l v+ dv/ dv One molecule momentum: p1 m v dv If in V=A thee ae N molecules: p t 1 3 Nm dv only 1 / 3 exchange the momentum along x; N=N A A/V m p t 1 3 A 8 Viscosity of Gases() All this happen in time =1/z: And because /=ĉ: dv 1 1 F 3 A F Compaing the last equation with the Poiseuille s one: c dv c A That we can futhe complicate intoducing values fom the Maxwell distibution. Conclusions: (expeimentally veifiable) viscosity does not depend on pessue, viscosity does depend on the squae oot of tempeatue (how is it in liquids?) Wzó Suthelanda: T 1 c T 9 Heat Conductivity of Gases Heat flow depends on tempeatue gadient dt/. Amount of heat cossing a pependiculat to the gadient suface of aea A in time d amounts to: dt dq Ad Heat conductivity of this gas,, means tansfe of kinetic enegy by molecules in neighbouing layes. Reasoning the same way as in the case of viscosity one can obtain: 1 3 cc V c V Heat condutivity of gases is vey impotant in gas analysis and in GC detectos. 3 1

11 Diffusion Diffusion depends on concentation gadient dc/. Mass of substance cossing a suface nomal to the gadient of aea A, in time d amounts to (II Fick law): dc dm D Ad Diffusion coefficient, D, is substance specific and depends on tempeatue. Repeating the same of easoning as in last cases, one can get the authodiffusion coefficient accoding to the kinetic model: 1 D 3 c 31 Efusion Efusion is flow of gas fom a containe though a hole (o holes) of size smalle than the mean fee path of gas molecules. Steam of gasflowing though such a hole (mass pe 1 cm pe 1 second) is equal to: M P 1 4 c P RT And volumetically (cm 3 /(cm s)): v P Efusion may be pactically used in desciption of flow though poous stuctues (sepaation of isotopes). 3 C p and C v of gases Equipatition of enegy Each degee of feedom of motion of a molecule coesponds to enegy equal to ½kT. When we talk about a mole of a gas, each degee of feedom means ½RT. If, as it esults fom the kinetic (Maxwell) model, enegy of tanslation was the only kind of enegy of gas molecules, then: du CV 3 R and fom Meye equation CP CV R 5 R dt V This is tue only fo helium and othe monoatomic gases. The molecules of othe gases must, theefoe, possess also enegy of othe kinds

12 C p and C v of gases () Gas molecules can also otate (otational motion o otation aound thei axes of symmety). Monoatomic molecules have no enegy of otation and no degees of feedom of otation because all thei moments of inetia J (vs. the thee axes) ae negligible. Diatomic and othe linea molecules have two degees of feedom of otation (one moment of inetia is negligible). Fo such molecules: E ot 1 J RT Fo non-linea molecules (possessing thee dimensions) 1 J RT 3 E ot 3 34 C p and C v of gases (3) Hence, fo linea molecules of gases: 5 C V R 7 C P R and fo non-linea (3D ones): C V 3R C P 4R It was obseved, howeve, that at sufficiently high tempeatues, heating cuves of polyatomic gases indicate yet highe heat capacities. This is explained by vibational excitation. 35 C p and C v of gases (4) Numbe of nomal vibations amounts to: fo non-linea molecules fo linea molecules 3N 5 3N 6 Each nomal vibation means two degees of feedom of vibation (fo both potential and kinetic enegy). Hence, at sufficiently high tempeatues, fo diatomic gases: 7 C V R 9 C P R Thee ae following contibutions to the intenal enegy of gases: U E E E E 3 RT RT RT const t ot osc el., nucl. 36 1

13 Mola Heat Capacities of Liquids and Solids Cystals oscillations only (Einstein, 197): Mola heat capacity of simple cystal substances inceases with tempeatue fom zeo to 3R (a set of hamonic oscillatos vibating in thee dimensions). Dulong-Petit ule: Mola heat capacities of the elements, especially the metals, ae appoximately equal to 3R at K 5 J/(K mol) Thee ae no ules fo liquids as thee is no geneal theoy of the liquid state. 37 Compessibility of Gases (1) PVm Z RT Coefficient of compessibility of gases is given by the equation: Fo the pefect gas it is always equal to 1 and the deivative: Fo eal gases: dz dz B' C'... lim B' dp dp P dz dp Howeve B does not have to be equal to, moeove, it depends on T. Thee is cetain tempeatue, known as Boyle s tempeatue, at which B = fo P, o eal gases behave like the pefect one (at low pessues). 38 Compessibility of Gases() The eason of the fact is a balance of epulsive inteactions (shot distance) and attactive inteactions (long distance). Pefect gas 39 13