enthalpies of formation for a few thousand compounds can be used for thermochemical calculations for millions of different chemical reactions

Transcription

1 hater 4. hermchemistry Summary thermchemistry: branch f thermdynamics dealing with energy changes f chemical reactins, w, U, and are calculated fr chemical reactin rcesses enthalies f frmatin are intrduced because enthaly is a state functin: enthalies f frmatin fr a few thusand cmunds can be used fr thermchemical calculatins fr millins f different chemical reactins thermchemistry can be investigated withut actually carrying ut reactins (imrtant fr slw r nn-sntaneus reactins

2 Sectins 4. t 4.3 Internal Energy and Enthaly hanges f hemical Reactins revius haters: hysical rcesses, such as heating, cling, exanding, r cmressing a system What abut systems with chemical reactins?, Examle: Fe 3 O 4 (s + 4 (g 3 Fe(s + 4 O(l One mle f slid Fe 3 O 4 and fur mles f gas cnverted t three mles f slid irn and fur mles f liuid water at a secified temerature and ressure. All cmunds assumed t be ure.

3 hermdynamics f hemical Reactins At nstant Pressure 98 K, bar Fe 3 O 4 (s + 4 (g 3 Fe(s + 4 O(l n g = 4 ml he heat absrbed by the reacting system can be determined using a calrimeter. Measure = 4,800 J w he wrk dne (at cnstant ressure is. Details: f i externald f i d ( f [ 3 m(fe,s 4 m( O, l m (Fe3O4,s 4 m(, g ] negligible 4 (, g ] 4 (, g 4R [ m m negligible i negligible n g R 4 (8.34 J K ml (98 K 990 J ml w

4 Fe 3 O 4 (s + 4 (g 3 Fe(s + 4 O(l (cnt. = (U + = U + (cnstant ressure = + w + = + = 98 K, bar = 4,800 J U = + w = 4,800 J + 9,90 J = 4,890 J chemical reactins at cnstant ressure: = w = = Rn g U = Rn g

5 hemical Reactins at nstant lume Bmb alrimeter In a strng steel cntainer at cnstant vlume: w = 0 U = = (U + = + Rn g = is calculated frm the measured temerature change and the calrimeter heat caacity determined by calibratin.

6 hermchemical Algebra Reactin: Fe 3 O 4 (s + 4 (g 3 Fe(s + 4 O(l = f i = (rducts (reactants = 3 m (Fe, s + 4 m ( O, l m (Fe 3 O 4, s 4 m (, g cncise ntatin: vi m( i i v i = stichimetry cefficient f cmund i (sitive fr rducts, negative fr reactants Examle: v Fe3O4,s = (reactant v,g = 4 (reactant v Fe,s = 3 (rduct v O,l = 4 (rduct

7 hermchemical Algebra similarly: U vu i m( i i v i m( i i vi m( i i subscrit m refers t mlar uantities

8 Reactins as Standard Pressure ( = bar vi m( i i U vu i m( i i v i m ( i i vi m( i i standard uantities dented by suerscrit

9 Enthaly is a State Functin Imrtant nseuence: fr chemical reactins can be calculated withut carrying ut reactins! Examle. alculate fr the reactin 5, bar (grahite (diamnd Big Prblem: he reactin is immeasurably slw. (in fact, nnsntaneus at 5, bar

10 (grahite (diamnd at 5 and bar (cnt. Direct thermchemical measurement f imssible. N rblem. Enthaly is a state functin. can be measured fr any ath cnnecting grahite and diamnd. A cnvenient tw-ste indirect ath is: Ste Ste (grahite + O (g O (g (diamnd + O (g Why cnvenient? fr Ste and Ste are easily measured: ste = heat f cmbustin f grahite = kj ste = (heat f cmbustin f diamnd = kj (grahite diamnd = =.89 kj

11 anther useful result Standard Enthalies f Frmatin fr any chemical reactin is the enthaly change fr the frmatin f the rducts frm the elements less the enthaly change fr the frmatin f the reactants frm the elements cnstituent elements f (reactants f (rducts reactant cmunds rduct cmunds = f (rducts f (reactants

12 Examle: standard enthaly f frmatin f methane at 5 (s, grahite + (g 4 (g f = 74.8 kj ml (use grahite, the mst stable frm f carbn at 5, bar Examle: calculate at 5 fr the reactin 4 (g + O (g O (g + O(l = f (rducts f (reactants = fm (O, g + fm ( O, l fm ( 4, g fm (O, g = kj ml + (85.8 kj ml (74.8 kj ml (0 = kj ml

13 Sectins 4.4 emerature Deendence f Anther useful result f enthaly being a state functin: If fr a reactin is knwn at a given temerature (e.g., 5, can be calculated at ther temeratures. ( Reactants at Prducts at (react.d (rd.d ( Reactants at Prducts at

14 ( = (cl reactants frm t + ( + (heat rducts frm t (rductsd ( (reactantsd ( (reactants]d (rducts [ ( ( d ( ( emerature Deendence f i i i v ( m eating r cling at cnstant ressure ( = : d = d

15 emerature Deendence f ( ( d S what? Significance: If heat caacity data are available, fr chemical reactins measured by calrimetry at a single temerature can be used t calculate ver a range f temeratures, in sme cases u t extremely high temeratures where calrimetry is difficult. In ractice, heat caacity measurements are easier than reactin measurements. Als, heat caacities can be calculated using mlecular energy levels redicted by uantum mechanics (hem 33.

16 data fr reactins at standard ressure ( = bar are widely available. What abut fr reactins at ther ressures? (, = (de-ressurize reactants frm t + (, + (ressurize rducts frm t (rductsd, ( (reactantsd, ( d, (, ( Pressure Deendence f i i i v m ( fr ressure changes at cnstant temerature: d = d

17 Isthermal Reactins Examle: 4 (g + O (g O (g + O(l w can the cmbustin f methane ccur at 5? = = = kj ml eat is lst t the surrundings (exthermic reactin. Warning! Many chemical reactins are nt isthermal: raid reactins (n time fr heat transfer systems thermally insulated frm the surrundings

18 Adiabatic Flame emerature Fr the reactin rducts t reach maximum temerature, n heat is allwed t escae (adiabatic reactin. Prducts at f feed heat back in Reactants at i Prducts at i

19 Adiabatic Flame emerature Ste react Ste heat Reactants at i Prducts at i Prducts at f = ( i = ( i ( f i (rductsd (rducts( f assuming cnstant (rducts i httest flames: f i ( i (rducts large negative ( i (exthermic small (rducts (e.g., diatmics large i (re-heat reactants

20 Adiabatic Flame emerature f yangen (NN N (g + O (g O(g + N (g Data at i = 98 K: (98 K = 096 kj ml O and N heat caacities (assume n vibratin: m = m + R = m (trans. + m (rt. + R = (3/R + R + R = (7/ R f f i 98 K ( i (rducts,096 kj ml 7 3 ml 8.34 J K ml Nte: nstant (rducts assumed. Nt an accurate arximatin fr large ( 3,000 K f 98 K +,600 K =,900 K O!!!

21 Adiabatic Flame emeratures Mlecules start vibrating when they get ht, increasing m Fr accurate flame temerature calculatins, include vibratinal heat caacities: N in O 4800 K 4 N * in O 560 K** in O 3470 K*** in air 480 K*** (acetylene in O 3750 K (acetylene in air 770 K *** Why are flame temeratures lwer fr burning fuel in air instead f xygen? 4 in air 0 K 3 8 (rane in air 50 K * dicyanacetylene (N ** almst as ht as the surface f the sun (5600 K

22 Sectin 4.6 Differential Scanning alrimetry (DS ractical frm f calrimetry imrtant techniue fr characterizing materials relatively inexensive measurements are raid and cnvenient DS units cmmercially available

23 w des Differential Scanning alrimetry Wrk? a small samle (< g and an inert reference material* are heated at a steady rate in an insulated enclsure a sensitive thermcule thermmeter mnitrs the temerature difference between the samle and reference *such as slid alumina (Al O 3

24 w des Differential Scanning alrimetry Wrk? he difference in the heat caacities f the samle and reference generates a steady temerature difference = samle reference an exthermic samle reactin (warming the samle rduces a sitive eak an endthermic samle reactin (cling the samle rduces a negative eak the eak area is rrtinal t Exthermic DS Peak samle > 0

25 What s a hermcule junctin between tw different electrnic cnductrs (usually metals a temerature difference rduces a vltage difference used t measure temeratures run in reverse, an alied vltage rduces a temerature difference (slid-state refrigeratr! ref + vltage vltage = cnstant ( ref

26 Anther Alicatin: Gas Shut-Off alve If the gas suly t the burner is temrarily interruted and the ilt light ges ut, the thermcule cls, dring the vltage t zer and clsing a gas suly valve.

27 hater 5. Entry and the Secnd Law f hermdynamics Summary the First Law f hermdynamics describes energy changes fr hysical and chemical rcesses n excetins t the First Law and the cnservatin f energy have been discvered But many rcesses beying the First Law never ccur. Why? the Secnd Law f hermdynamics and the entry are intrduced t redict sntaneus rcesses cmbining the First and Secnd Laws unleashes the full wer f thermdynamics

28 First Law f hermdynamics he change in internal energy f a system (U euals the heat absrbed frm the surrundings ( lus the wrk dne n the system (w by the surrundings. U = + w he energy f an islated system (n cntact with the surrundings, ( = w = 0 is cnstant. U = 0 (islated system (cnservatin f energy

29 Sectin 5. Sntaneus Prcesses First Law calculatins: U w fr hysical and chemical rcesses. But frm everyday exerience, many rcesses cnsistent with the First Law never ccur. Others ccur sntaneusly. Why?

30 Mystery: Sme heat flw rcesses beying the First Law never ccur, thers ccur sntaneusly islated system (U = 0: ml cer ml cer haens sntaneusly ml cer 0 30 X never haens 5 the frward and reverse rcesses bth bey the First Law the frward rcess ccurs sntaneusly ( by itself the reverse rcess is never bserved (fr an islated system

31 Mystery: Sme mechanical rcesses beying the First Law never ccur, thers ccur sntaneusly islated system (U = 0: L air.0 bar L vacuum haens sntaneusly L air.0 bar 300 K (0 bar X never haens 300 K the frward and reverse rcesses bth bey the First Law the frward exansin rcess ccurs sntaneusly the reverse rcess is never bserved fr an islated system

32 Mystery: Sme mixing rcesses beying the First Law never ccur, thers ccur sntaneusly islated system (U = 0: ml ure N (g ml ure O (g haens sntaneusly mixture f ml N (g + ml O (g 300 K 300 K X never haens 300 K the frward and reverse rcesses bth bey the First Law the frward mixing rcess ccurs sntaneusly the de-mixing rcess is never bserved fr an islated system

33 Mystery: Sme chemical reactins beying the First Law never ccur, thers ccur sntaneusly islated system (U = 0: ml ure (g / ml ure O (g haens sntaneusly ml O(g 5 5 X never haens 300 the frward and reverse rcesses bth bey the First Law the frward reactin rcess ccurs sntaneusly the reverse reactin is never bserved fr an islated system

34 Big Mysteries: Many hysical and chemical rcesses bey the First Law f hermdynamics (cnservatin f energy but never haen, thers ccur sntaneusly. Why? Smething imrtant must be missing frm thermdynamics based n the First First Law. hese cncerns led t the discvery f entry and the Secnd Law f hermdynamics, ne f the mst imrtant advances in the histry f science.

35 Sectins 5. eat Engines and the Secnd Law Analysis f the efficiency f heat engines (hw much wrk can be dne er tn f cal burned? was used t devel the Secnd Law f thermdynamics, useful fr redicting sntaneus rcesses. he steam engine has dne mre fr science than science has ever dne fr the steam engine.

36 eat Engine eat Surce (emerature absrb heat eat Engine wrk w dne n the surrundings reject heat eat Sink (emerature > 0 < 0 w < 0 First Law : + + w = 0 (cnservatin f energy

37 Reversible arnt Engine ycle Ste I Isthermal Exansin at absrb heat Ste II Adiabatic Exansin 3 = 0 Ste III Isthermal mressin at 3 4 reject heat Ste I Adiabatic mressin 4 = 0

38 Reversible arnt ycle Stes I, II, III, I I t 4 I ld III 3 II Istherm Istherm

39 Reversible arnt Engine ycle the details system: n mles f ideal gas (the wrking fluid in the engine Ste I Isthermal Exansin at w I = nr ln( / U I = 0 I = w I Ste II Adiabatic Exansin 3 w II = ( = U II II = 0 Ste III Isthermal mressin at 3 4 w III = nr ln( 4 / 3 U III = 0 III = w III Ste I Adiabatic mressin 4 w I = ( = U I I = 0

40 Relatin between vlumes,, 3, 4 ( will be useful later : 3 4 ln ln d d d d d d 3 4 nr nr d nr d nr Stes II and I [reversible ( = external and adiabatic ( = 0 ] du = dw + d d = d / 4 = / 3 / = 3 / 4 0

41 Reversible arnt Engine ycle First Law Analysis 0 ( 0 ( 0 d cycle I I I III II I U U U U U U U U Internal Energy hange fr One ycle (I II III I I

42 Reversible arnt Engine ycle First Law Analysis cycle 3 4 I III II I ln ( 0 ln 0 ln ( ln ( ln d nr w nr nr nr nr w w w w w Wrk Dne fr One ycle (I II III I I use 4 / 3 = /

43 Reversible arnt Engine ycle First Law Analysis eat Absrbed fr One ycle (I II III I I d cycle I nr nr( II ln III 0 ln I nr ln use 3 / 4 = / heck: c an yu verify that cycle + w cycle = 0 (= U cycle?

44 Efficiency f a Reversible* arnt Engine wrk dne n the surrundings heat absrbed frm the ht reservir w cycle nr( ln( nr ln( / / S What? his result is a big deal! It laces a fundamental limit n heat engine efficiency. *reversible heat engine: infinitesimal temerature and ressure differences between the gas and the surrundings

45 Efficiency f a Reversible* arnt Engine Examle: alculate the efficiency f a reversible steam engine erating between = 373 K (the biling int f water at bar and = 93 K. w much wrk is dne if 0.0 MJ f heat is absrbed at 373 K? K K % w 0.4 w 0.0 MJ w = MJ =.4 MJ wrk dne n the surrundings* *this is the maximum amunt f wrk that can be dne real engines are less efficient than reversible engines

46 Sectin 5.3 Imrtant nseuences f the arnt ycle / ln( / ln( / ln( / ln( / ln( / ln( 0 0 d d d d d rev nr nr nr nr nr nr Fr ne cmlete cycle, all stes reversible, it was nticed that: = 0 S what?

47 Imrtant nseuences frm the arnt ycle A. he Entry S ( A New State Functin! he result d rev 0 can be generalized t any reversible cycle fr any system.

48 Imrtant nseuences frm the arnt ycle A. he Entry S ( A New State Functin nclusin: he entry S defined by ds d rev is a functin f the state f the system (like the internal energy U and the enthaly state functins.

49 Imrtant nseuences frm the arnt ycle B. lausius Ineuality the breakthrugh! Fr a reversible arnt cycle, frm the First Law U cycle = + + w = 0 s w = + w multily by divide by 0 reversible 0 d rev generalizes t