CHEM 116 Electrochemistry at Non-Standard Conditions, and Intro to Thermodynamics

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1 CHEM 116 Electrchemistry at Nn-Standard Cnditins, and Intr t Thermdynamics Imprtant annuncement: If yu brrwed a clicker frm me this semester, return it t me at the end f next lecture r at the final exam If yu d nt return it, yu will receive an INC fr yur grade Lecture 23 Prf. Sevian Tday s agenda Big picture f electrchemistry Redx reactins and xidatin numbers (last lecture) Charge flw in electrchemical cells and diagramming a cell Using the mathematical mdel t predict current and vltage under standard and nn-standard cnditins Imprtant pints f thermdynamics fr general chemistry Enthalpy change (+endthermic, exthermic) Entrpy change (+mre disrder, mre rder) Gibbs free energy (+nn-spntaneus, spntaneus) Cnnectin t equilibrium Cnnectin t electrchemistry Annuncements Final exam is Tuesday, Dec 16, 3:00-6:00pm in S-1-006

2 Predicting vltage under standard cnditins Vltage = cell ptential (E cell ) = related t ΔG, which is related t ΔH, T, and ΔS Table f reference vltages, all referenced t the hydrgen half-cell All reference vltages are reductin ptentials, s if yu need an xidatin ptential yu just take the ppsite See table f standard reductin ptentials Example f using standard reductin ptentials t predict E cell Nn-standard cnditins: Nernst equatin Cncentratins f slutins nt at standard 1.0 M Ecell = Ecell lnq n = Ecell lgq n Temperature nt at standard 25 ºC E cell = E cell RT lnq ni Reactin qutient Least cmmn multiple f electrns exchanged in the redx reactin where F is the Faraday cnstant: F = 96,500 C/ml /vltaiccellemf.html set up Cu Cu 2+ (0.001M) Ag + (2.0M) Ag cell

3 Electrlysis: electrchemical cell frced t run backwards (against its will) Nte: sectins 20.7 and 20.8 in the text bk are fascinating reading, but they are nt required reading. Hwever, sectin 20.9 is required reading. Electrplating: The lnger yu run the cell, the mre metal electrplate builds up Current means hw many electrns pass by per secnd If yu knw hw much metal electrplate yu want t make, then stichimetry tells yu hw many electrns are required Cu 2+ (aq) + 2 e Cu (s) Au 3+ (aq) + 3 e Au (s) Ag + (aq) + 1 e Ag (s) If yu knw what current is being applied (e.g., amperes = Culmbs/secnd), then yu can figure ut hw much time yu must run the cell fr in rder t build the amunt f electrplated metal that yu want Electrlysis example Similar t Sample Exercise 20.14, pp Calculate the mass f O 2 prduced in the electrlysis f water, using a current f A fr a perid f 45 minutes.

4 Thermdynamics Reactin directin given by Free energy change, ΔG can be predicts Overview f thermdynamics Reactin extent given by Equilibrium cnstant, K ΔG < 0 ΔG = 0 ΔG > 0 Equilibrium achieved at a particular T given by Nnspntaneus ΔG = ΔH TΔS = 0 Calculated using ΔG = -RT ln K Spntaneus driven by Entrpy change and/r Enthalpy change Adapted frm Key Cncept Summary in McMurray & Fay, Chemistry (3 rd edn) Three laws f thermdynamics 1. The ttal energy f the universe is cnstant. Energy is cnserved in all prcesses If a system gains/lses heat energy, then the surrundings must d the ppsite 2. In prcesses that ccur spntaneusly, disrder in the universe increases. Disrder (called entrpy ) is a measure f hw spread ut matter is If a system gains/lses disrder, then the surrundings must d s in a way such that bth system and surrundings tgether net an increase in the universe s disrder 3. Zer disrder is defined as a perfect crystal at zer abslute temperature. Zer abslute temperature is impssible t achieve

5 Additinal imprtant implicatins If a chemical r physical change written in ne directin is nnspntaneus, then written in the ppsite directin it is spntaneus Spntaneus means that nce a prcess begins (after activatin barrier is surmunted) it cntinues withut interventin Spntaneus and nn-spntaneus are ppsites Whether a given change is spntaneus depends n the experimental cnditins (e.g., temperature, pressure) A change that is spntaneus under ne set f cnditins may be nnspntaneus under a different set f cnditins Spntaneus change always prgresses tward a cnditin f equilibrium Enthalpy: what yu have already learned Heat flw Endthermic = int the system (at cnstant p, ΔH is +) Exthermic = ut f the system (at cnstant p, ΔH is ) System vs. surrundings Tgether, system + surrundings = universe Heat flws frm ne t the ther If heat flws ut f system (exthermic), then it ges int surrundings If heat flws int system (endthermic), it is because it cmes frm the surrundings Ttal energy f the universe remains cnstant Clsed system Heat can g in and ut f system, but matter cannt Can be measured by calrimetry Using equatin q = mcδt At cnstant pressure, q = ΔH When heat flws int the system, the temperature ges up When heat flws ut f the system, the temperature ges dwn

6 Using Hess s law t calculate ΔH sys Hess s law: enthalpy is a state functin and as such its value des nt depend n the path taken t get frm initial t final state Reference state has enthalpy change f zer reference state defined t be elements in the states they exist in naturally at standard cnditins (e.g., hydrgen is H 2 (g), carbn is C (s), irn is Fe (s)) initial state final state ΔH = ΔH frmatin final cmpnents Example ΔH fr H 2 O (l) H 2 O (g) can be predicted frm tabulated values (see Appendix C, pp in text bk) ΔH H O ( l) H O ( g) 2 = 2 ΔH f final cmpnents = ΔH frmatin initial cmpnents ( H O ( g) ) ΔH ( H O ( l) ) kj ml f initial cmpnents kj ml 2 = kj ml Abslute entrpy (S) Entrpy means disrder, r spreadedness The mre disrdered r spread ut a material is, the greater the abslute entrpy (S) The mre rdered a material is, the lwer the entrpy Must always be a cmparisn Ultimate cmparisn is t abslute rder, which is a perfect crystal lattice structure with n mtin (zer abslute temperature) Impssible fr abslute entrpy t be zer (except at reference state f abslute rder, which is unachievable) Examples (cmparisn per mle f the chemical) Water in different states Hmlgus series f alkanes Eek! Chas!

7 Cmparing abslute entrpy f water in different physical states State S (J/ml K) Slid * Liquid Gas *N value because Sº by definitin means at standard cnditins f 25 ºC and 1 atm and slid water des nt exist under these cnditins Frm Chemistry & Chemical Reactivity 5 th editin by Ktz / Treichel. C Reprinted with permissin f Brks/Cle, a divisin f Thmsn Learning: Cmparing abslute entrpy f different alkanes under standard cnditins The mre cmplex the mlecular structure, the higher the abslute entrpy f the substance Mre cmplicated mlecules have mre ptins fr cnfiguratins, rtatins, vibratins, etc. (This is the same as Fig in yur text bk, but the ne here is a slightly nicer drawing.) Frm Chemistry & Chemical Reactivity 5 th editin by Ktz / Treichel. C Reprinted with permissin f Brks/Cle, a divisin f Thmsn Learning: Fax

8 Mlecular interpretatin f entrpy (S) S = k ln W W is the number f micrstates available, k is a cnstant S, as W increases, the abslute entrpy (S) increases Factrs that influence W (fr making qualitative cmparisns) Temperature Vlume Number f independently mving particles Cmpare abslute entrpies Arrange in rder frm lwest t highest abslute standard entrpy (Sº nt ΔSº): O J/ml K O a) O 2 (g) vs. O 3 (g) b) NH 4 Cl (s) vs. NH 4 Cl (aq) c) F 2 (g), Cl 2 (g), Br 2 (l), I 2 (s) d) NaCl (s) vs. MgO (s) NH 4 Cl (s) J/ml K NH 4 Cl (aq) I 2 (s) J/ml K Br 2 (l) F 2 (g) Cl 2 (g) MgO (s) J/ml K NaCl (s) 72.11

9 Entrpy change (Nw we re talking abut ΔSº, nt Sº) The change frm ne state t anther state (can be psitive r negative) Difference between the final and initial entrpy states Symblized ΔS When ΔS > 0 it means disrder ( spreadedness ) f the system increases during the change Hess s law applies because entrpy is als a state functin Example H2O ( l) H2O ( g) Entrpy change is als a state functin, s ΔS = S ( H g ) S ( ΔS fr l ) H 2 O (l) 2O ( ) H2O ( ) H 2 O (g) can be predicted finalfrm tabulated initial values (see Appendix C in text bk) = J ml K J ml = K kj ml Gibbs free energy Derives frm the idea that the entrpy change t the universe resulting frm a change in a system and its surrundings, under cnditins f cnstant temperature and pressure, is ΔS universe = ΔS surrundings + ΔS system (see pp in yur text bk) Measures abslute entrpy change t the entire universe, which always increases fr any change that ccurs spntaneusly Results in an equatin in terms f the system f interest (at cnst. p): ΔG = ΔH - T ΔS Gibbs free energy Enthalpy change Abslute temperature Entrpy change Depends n bth enthalpy change term (ΔH) and entrpy change term (TΔS) Either term, r bth, culd drive the change t be spntaneus (spntaneus when ΔG is negative)

10 Example: H 2 O (l) H 2 O (g) is a physical change Enthalpy: The change, in the frward directin written, is endthermic (ΔH = 44 kj/ml > 0, the system requires energy input frm the surrundings fr the change t prceed) Entrpy: The change, in the frward directin written, represents an increase in the system s disrder (ΔS = J/ml K> 0, gases are mre disrdered r spread ut than liquids) ΔG = ΔH TΔS Cnditins: T = 90 ºC, p = 1 atm ΔG = ΔH TΔS = 44 ( )(0.119) = kj / ml Nn-spntaneus in directin written Cnditins: T = 100 ºC, p = 1 atm ΔG = ΔH TΔS = 44 ( )(0.119) = 0 kj / ml At equilibrium Cnditins: T = 110 ºC, p = 1 atm ΔG = ΔH TΔS = 44 ( )(0.119) = 1.6 kj / ml Spntaneus in directin written Summarizing the example f water s physical change frm H 2 O (l) t H 2 O (g) The spntaneity f the change depends n what temperature the change ccurs at ΔG = ΔH T ΔS Belw nrmal b.p kj/ml = (nnspntaneus) 44 kj/ml (endthermic) ( K) (0.119 kj/ml K) (increasing disrder) At nrmal biling pint 0 = (at equilibrium) same ( K) same Abve nrmal b.p. 1.6 kj/ml = (spntaneus) same ( K) same

11 Magnitudes and signs f terms in free energy Abut the mathematical terms in this table: ΔH is the change f enthalpy. When ΔH > 0 (i.e., ΔH is psitive), the change is endthermic. When ΔH < 0 (i.e., ΔH is negative), the change is exthermic. ΔS is the change f entrpy. When ΔS > 0 (i.e., ΔS is psitive), the entrpy increases during the prcess (the system becmes mre disrdered). And vice versa. T is the abslute temperature (i.e., Kelvin scale). It is always a number larger than zer. Therefre, the term TΔS has the ppsite sign f ΔS. Effect f temperature n spntaneity Similar t Exercise 19.8, p. 829 Metallic irn is prduced in a blast furnace by reducing irn xide (mined frm the earth) using carbn. Fr the reactin, 2 Fe 2 O 3 (s) + 3 C (s, graphite) 4 Fe (s) + 3 CO 2 (g) the fllwing infrmatin is available: ΔH = kj ΔS = J/K Shw that it is necessary that this reactin be carried ut at a high temperature. rxn rxn

12 Relatinship between ΔG and K eq At a temperature (T) ther than standard temperature (25ºC = 298K), the Gibbs free energy is given by ΔG = ΔG + RT ln Q At equilibrium, ΔG = 0 Als at equilibrium, Q = K eq Substituting int the expressin abve, at equilibrium 0 = ΔG + RT ln K eq Therefre (rearranging): ΔG = RT ln K eq Hw ΔG indicates reactin extent Similar t Exercise 19.11, p. 834 Determine the standard free energy change fr the reactin C (s) + CO 2 (g) 2 CO (g) frm the fllwing thermdynamic data. C (s) ΔG f = 0 kj/ml CO 2 (g) ΔG f = kj/ml CO (g) ΔG f = kj/ml Then, use this result t calculate the equilibrium cnstant at 25 ºC.

13 What s left t cver this semester? Relating ΔG, E cell and K eq Predicting free energy changes under nn-standard cnditins Next class (last lecture this semester) we will d this in the cntext f ging ver selected prblems frm Assignment 13 Re-read chapter 19, and sectin 20.5, and attempt the hmewrk befre yu cme t the next lecture Ding thermchemistry prblems brings tgether nearly all f the tpics yu have learned this semester, and is in this sense a review f the semester

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