Lecture 5 Chemistry PDF

Lecture #5, p. 1 Lecture 5: Announcements Today: Brown 19.1 Spontaneous Processes 19.2 Entropy and the Second Law of Thermodynamics 19.3 The Molecular Interpretation of Entropy and the Third Law...

Lecture #5, p. 1 Lecture 5: Announcements Today: Brown 19.1 Spontaneous Processes 19.2 Entropy and the Second Law of Thermodynamics 19.3 The Molecular Interpretation of Entropy and the Third Law of Thermodynamics 19.4 Entropy Changes in Chemical Reactions 19.5 Gibbs Free Energy 19.6 Free Energy and Temperature Problem Set 4: Due before Exercise #5 tomorrow; upload on Moodle link Problem Set 5: Posted on Moodle; due before Exercise #6 next week Study Center: Wednesdays 18:00–20:00 in ETA F 5 Office Hours: Prof. Norris and Brisby, Thursdays 17:00–18:00 in LEE P 210 Chemistry  Lecture #5, p. 2 Lecture 6 Next Week: Brown 6.1 The Wave Nature of Light 6.2 Quantized Energy and Photons 6.3 Line Spectra and the Bohr Model 6.4 The Wave Behavior of Matter 6.5 Quantum Mechanics and Atomic Orbitals 6.6 Representation of Orbitals 6.7 Multi-Electron Atoms 6.8 Electron Configurations 6.9 Electron Configurations and the Periodic Table 7.2 Effective Nuclear Charge 7.3 Sizes of Atoms and Ions 7.4 Ionization Energy 7.5 Electron Affinity Chemistry  Lecture #5, p. 3 Review In Lecture 4, we started thermodynamics 1st Law of Thermodynamics System and surroundings Internal energy, ! State functions: ", $, ! Energy diagrams Endothermic and exothermic Enthalpy, % = ! + "$ Pressure–volume work ∆% = )! , calorimetry, heat capacity Hess’s law, heats of reaction, heats of formation Chemistry  Lecture #5, p. 4 Heat and Work: Sign Convention Chemistry  Lecture #5, p. 5 Enthalpy Diagram for Propane Combustion Chemistry  Lecture #5, p. 6 Thermodynamics II Last time we discussed energy conservation Today: which processes will occur “spontaneously” ? Spontaneous process? Process that occurs without assistance Criterion? Spontaneous processes seem to favor lowering their energy Ex: at constant P, is process spontaneous if ∆" < 0 ? (exothermic) Cannot be complete answer! Many spontaneous processes do have ∆" < 0 But others have ∆" > 0 (endothermic) Ex: ice melting is spontaneous ∆" = +6.0 kJ/mol Something is missing in our description... What? Chemistry  Lecture #5, p. 7 Spontaneous versus Nonspontaneous Processes Before answering that question, let’s describe characteristics of spontaneous processes If process is spontaneous, reverse process in nonspontaneous Ball does not spontaneously roll up hill Basedon our Experimental conditions (e.g., T, P) are important for determining spontaneity experience Ex: ice melts at +1 °C, but not at − 1 °C Spontaneous does not mean fast! Just means process will occur How fast? Answered by kinetics: Lectures 10–11 Ex Ha combustion Nonspontaneous does not mean impossible! May be possible process if we add energy Nonspontaneous just means it will not occur without our help We also need to define... Chemistry  Lecture #5, p. 8 If Heo isnotthecriterionforspontaneitythenwhich First we need to define someterms Reversible versus Irreversible Processes Reversible process? Process can be reversed with no change to surroundings I “Reversed” means system is returned to its initial state Irreversible process? Surroundings are changed when process is reversed Let’s discuss these definitions with example of heat flow... We know from everyday life, hot-to-cold heat transfer is spontaneous Not cold-to-hot heat transfer Energy tends to spread from concentrated to less concentrated Chemistry  Lecture #5, p. 9 Example: Heat Transfer Heat flows spontaneously from hot to cold Reversible heat transfer is ideal case !!"# = ! + $! !$"%& = ! !" ≡ infinitesimal temperature To reverse process, change !!"# → ! − $! Heat flow reverses without changing surroundings Reversible process? Process that reverses direction after infinitesimal change to property of system In above example, T was changed from ! + #! to ! − #! Chemistry  Lecture #5, p. 10 Another Example: Isothermal Expansion Expand ideal gas into vacuum at constant temperature spontaneous irreversible How could we reverse by some infinitesimal change? To return system to initial state, surroundings need to do work on gas to compress it Thus, surroundings have changed spontaneous reversible If we increase ! to ! + #! at any time, process is reversed Reversible process is idealized process Chemistry  Lecture #5, p. 11 Real Processes We can never achieve idealized reversible processes in practice All real processes are irreversible All spontaneous processes are real processes ∴ All spontaneous processes are irreversible To return system to initial state Requires work (" > 0) While ! is conserved during spontaneous process, 1st Law ! tends to spread out and become less useful The spreading of energy makes some of it unavailable to do work Chemistry  Lecture #5, p. 12 Entropy, S A measure of the tendency for E to spread, which reduces system’s ability to do work Also related to randomness or disorder in system S is another state function ∆" = "$%&'( − "%&%)%'( $!"# $!"# ≡ heat flow for For isothermal process: ∆" = % reversible process (constant T) %≡ absolute temperature Chemistry  Lecture #5, p. 13 However ideal reversible processes are helpful fordefininganotherstatefunctionthat quantifiesthistendency of energy to spreadand become lessuseful Ofsystem _Path Note Onlyonepathis associated with grew unique Even if process is irreversible because S is a statefunction we can use idealized reversible process to determine s  Lecture #5, p. 14 S for Phase Changes Melting and boiling are isothermal srocesses Ex What is 5 if ice melts at T O C and O 3 Pa 6.0 103 moot at constant fifting fus of fus Imagine melting slowly a Tarr Oc at Process is reversible grew fus 6.0 103Jmo frev 6.0 103Jmol g 273 22 m Needtouseabsolutetemperature  Lecture #5, p. 15 SoS is astatefunctionlike E butis it conservedlike E Inotherwordswhatisthe1stlawequivalentfor s Conservation of 5 Consider ice cube meting in yourhand Says 6.0 103Tmo 22 m.TK is 273 6 0 1035m01 19 moTK 37C 310 Findings Ssurr 310 hand Thus ota S for universe cue to this irreversible srocess Suniv Ssys Ssurr 3.0 motk Suniv hasincreased Note Itaptiiess.ttFersibiethen Suni  Lecture #5, p. 16 Thus a thermodynamic lawexistsforentropy butentropy isnotconserved ingeneral Entropy: Molecular Interpretation 2nd Law of Thermodynamics Kinetic-Molecular Theory of Gases Molecules moving with statistical distribution Reversible process Suniv Says Surr O Explains spontaneous expansion of gas into vacuum for It Irreversible process Suniv Says Ssurr O Statistical thermodynamics Since all rea processes Connects are irreversize macroscopic state of system t to microscopic arrangement of molecules ndLaw Entropy of universe increases for soon aneous process any Microstate Notation Says S because One particular care about wearrangement Ssys of the molecules Chemistry  Lecture #5, p. 17 Boltzmann’s Equation ! = #! ln ' ln ≡ natural logarithm Lecture 2 # ≡ number of microstates consistent with specific macroscopic state !! ≡ Boltzmann constant = 1.38 × 10−23 J/K Depffete Entropy measures number of microstates consistent with macroscopic state Entropy of system increases with number of microstates '"#$%& wifi ∆! = #! ln '"#$%& − #! ln '#$#'#%& = #! ln '#$#'#%& Chemistry itit Fili si  Lecture #5, p. 18 Iiii ms Implications? In general, ! and " increase with... system’s $ system’s #... increases in number of molecules complexity of molecules melting of solids Entropy... and also with Measure of spread in energy or vaporizing of liquids randomness/disorder in system Chemistry Note in I t.fi iaiiiiiimti.ts.s t.am PE  Lecture #5, p. 19 Engineers: Entropy Warriors Logopolis Engineers spend large amounts of energy to fight the 2nd Law of Thermodynamics We make highly ordered, useful materials Otherwise, universe increases in disorder While ordering our small part of the universe, we must increase disorder somewhere else by more! Iiii Chemistry Increasing complexity in moleculeincreases its degreesoffreedom orformsofmotion for each molecule Moredegreesoffreedom means more possible microstates  Lecture #5, p. 20 3rd Law of Thermodynamics As we cool any system, it has less energy, less degrees of freedom, and less microstates 3rd Law: A pure, perfect crystalline solid substance at T = 0 K has S = 0 It has only one microstate, i.e., W = 1 Chemistry  Lecture #5, p. 21 Finally Determining ∆" for Chemical Reactions Last lecture a 1 R1 + a 2 R2 + a 3 R3 + ⋯ b 1 P1 + b 2 P2 + b 3 P3 + ⋯ ai , bj are stoichiometric coefficients where Ri , Pj are reactants and products, respectively We showed ° ∆"!"# = $ ∘ %- Δ".,- − $ )3 Δ".,∘ 3 Get %!&'()*+,- !01)*1#*+, 3 Δ".∘ and # ∘ values from ∆* ° = %- *-∘ − )3 *3∘ tables Similarly $ $ %!&'()*+,- !01)*1#*+, 3 * ∘ ≡ standard molar entropies * for substance in its standard state Chemistry  Lecture #5, p. 22 Determining ∆" for Chemical Reactions? Ex: N2 (g) + 3 H2 (g) 2 NH3 (g) ∆" ° 298 K = ? ∆" ° = 2 " ° NH" − [" ° (N# ) + 3 " ° (H# )] = 2⋅193 J/mol⋅K − 192 J/mol⋅K − 3⋅131 J/mol⋅K = −199 J/mol⋅K Note: ∆" ° is negative This is consistent with our discussion above Namely, as the number of gas species is reduced by the reaction, the number of microstates, and hence !, also decreases Chemistry Deficient in  Lecture #5, p. 23 What Does This Mean for Spontaneity of a Reaction? Ex: N2 (g) + 3 H2 (g) 2 NH3 (g) ∆"!'! = −199 J/mol⋅K ∆"!"## = ? ;%&!! *;%'% *∆,%'% ° *∆,!"# ∆"!"## = - = - = - = - k iii it ° *∆,!"#./.1 34/678 ° ∆,#($ = −92.4 kJ/mol ∆"!"## = - = /.9 : = +310 kJ/mol⋅K ∆""$%& = ∆"!'! + ∆"!"## = −199 + 310 J/mol⋅K = +111 J/mol⋅K spontaneous! But this criterion for spontaneity, ∆""$%& > 0, is complicated! Must analyze both system and surroundings and combine to get ∆""$%& Does a better criterion exist to predict spontaneity of process? Chemistry  Lecture #5, p. 24 Whatdoesthismeanforspontaneity Is thereaction Nat3H 2MHz spontaneous Wejustdetermined Ssys 199E 5 is p I iiiiii Turnsout yes  Lecture #5, p. 25 To findthis bettercriterion weneed to introduce anotherkeystatefunction GisssFreeEnergySoon anei y driven by lowering or increasing s fi i Let's combine G 5 where G is GisssFree Energy Why Suniv Says Ssurr Ssys Is a constant_ Multiply by Suniv Ssys sys Compare A constant Gsys sys Ssys Spontaneous process requires Suniv 0 huqi.to Note Wecall Gsy simply G E me it ineering1isos  Lecture #5, p. 26 At constant T P Standard Free Energy of Formation G!∘ , weO Like Δ" process can define Δ#!∘ : is soon aneous Moreconvenient G Δ# ∘ ≡ O ! process free energy is nonsson aneous criterion change to form a substance from its elements he under standard conditions (1 atm and 25 °C) Also if G O process is irreversize atyptan Δ#!∘ = 0 for0elements in their standard state G process is reversize Other values forCan Δ#! found showin 1ha tables ∘ WhyFree Energy ma imum(Appendix amountC inofBrown) work we Eitan can extract from process is We can use the Δ#!∘ values to determine ° ∆##$% G for any reaction reaction eg a chemical G Wmax Chemistry Soreactionswithlarge negative G are useful  Lecture #5, p. 27 Summary of ∆"()* ° , ∆# ° , and ∆$ ° ()* For reaction a 1 R1 + a 2 R2 + a 3 R3 + ⋯ b 1 P1 + b 2 P2 + b 3 P3 + ⋯ ∘ Enthalpy ° ∆&$%& = - */ Δ&!,/ − - -3 Δ&!,∘ 3 '$()*+,-,/ $01+,1&,-, 3 Get Δ"!∘, # °, Δ$!∘ Entropy ∆. ° = - */./∘ − - -3.3∘ values from '$()*+,-,/ $01+,1&,-, 3 tables Gibbs free energy ° ∆/$%& = - */ ∆/!,° / − - -3 ∆/!,° 3 '$()*+,-,/ $01+,1&,-, 3 Chemistry  Lecture #5, p. 28 Importance of Temperature ∆" = ∆$ − &∆' Spontaneous for ∆" < 0 ∆" depends on temperature, so how does # affect spontaneity of reaction? 1 2 3 4 Ex 1: 2 O3 (g) 3 O2 (g) Spontaneity favored by both enthalpy and entropy Ex 2: 3 O2 (g) 2 O3 (g) Spontaneity favored by neither enthalpy and entropy Ex 3: H2O (l) H2O (s) Spontaneity favored only by enthalpy Ex 4: H2O (s) H2O (l) Spontaneity favored only by entropy Chemistry  Lecture #5, p. 29 What We Learned Spontaneous versus nonspontaneous processes Reversible, irreversible processes Isothermal processes Entropy, 2nd Law of Thermodynamics Boltzmann’s equation, microstates 3rd Law of Thermodynamics Gibbs free energy, G Standard free energies Chemistry The t s termbecomes increasingly negative as t goesup Eventually a temperature isreachedwhere T s compensates for it o NEXT TIME Electronic structure and That'swhentheicemelts Its all thermodynamics the periodic table