Lecture 12: Chemistry Announcements PDF

Lecture #12, p. 1 Lecture 12: Announcements Today: Brown Ch. 15 Chemical Equilibrium 15.1 The Concept of Equilibrium 15.2 The Equilibrium Constant 15.3 Understan...

Lecture #12, p. 1 Lecture 12: Announcements Today: Brown Ch. 15 Chemical Equilibrium 15.1 The Concept of Equilibrium 15.2 The Equilibrium Constant 15.3 Understanding and Working with Equilibrium Constants 15.4 Calculating Equilibrium Constants 15.5 Le Châtelier’s Principle 19.7 Free Energy and the Equilibrium Constant Problem Set 11: Due before Exercise #12 tomorrow; upload on Moodle link Problem Set 12: Posted on Moodle; due before Exercise #13 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 Final Exam: Monday, February 3, 2025, at 8:30–10:30 Chemistry  Course Feedback Email: Thursday Nov. 28 Ends at 8:20 on Monday Dec. 9 Thank you in advance! Chemistry  Lecture #12, p. 2 Lecture 13 Next Week: Brown Ch. 16 Acid–Base Equilibria 16.1 Acid–Base Equilibria 16.2 The Autoionization of Water 16.3 The pH Scale 16.4 Strong Acids and Bases 16.5 Weak Acids 16.6 Weak Bases Ch. 17 Additional Aspects of Aqueous Equilibria 17.1 The Common-Ion Effect 17.2 Buffers Chemistry  Lecture #12, p. 3 Red Thread Last three weeks? Acid-Base Catalysis Properties Christmas! Kinetics Batteries Equilibrium Chemistry  Lecture #12, p. 4 Review In Lecture 11, we finished our discussion of kinetics What role does temperature play in kinetics? ! " = $ exp(−,! ⁄-") Arrhenius equation ,! ≡ Activation energy Given two spontaneous reactions, why can one be fast and one slow? ,! can be large or small Independent of whether Δ, is exothermic or endothermic Given: Rate = ![A]" [B]# [C]$ ⋯ , what do 8, 9, : mean? Rate laws complicated for multistep reactions Defined elementary reactions and molecularity Rate laws easily written down for elementary reactions: Rate = ! [A]% B & C ' ⋯ Chemistry  Lecture #12, p. 5 Questionfromendof last lecture Why Is High Pressure Needed to Make NH3? Haber–Bosch process N2 + 3H2 ⇌ 2NH3 Reaction is spontaneous at room temperature But kinetics makes it SLOW Large activation energy Catalysts lower Ea But they still require high T to get reasonable rates But increasing T shifts reaction toward reactants ! Increasing pressure is needed to shift back toward products Haber and Bosch used knowledge to solve problem! Chemistry  Lecture #12, p. 6 Today: Equilibrium We have already seen several examples of “dynamic equilibrium” Examples: saturated solutions, Henry’s Law, and vapor pressure Vapor pressure: molecules leaving/entering gas phase are balanced s More generally, dynamic equilibrium occurs when 2+ processes balance System reaches “steady state” Processes still occurring, but they balance Some property we care about is constant So far, we have ignored dynamic equilibrium in chemical reactions We assumed that reactions can run forward OR reverse, but not both simultaneously Reaction goes in both directions, and dynamic equilibrium can be established Chemistry  Lecture #12, p. 7 Chemical Equilibrium Occurs when forward and reverse rates are equal Consider: Define forward and reverse rate constants, !! and !" !! Assume forward and reverse reactions are elementary A ⇌ B !" generic reactionrates reaction At equilibrium, these two rates are equal (i.e. they balance) For reverserat Known as the equilibrium constant Chemistry  Lecture #12, p. 8 Equilibrium Constant ≡ # ∴ At given T, at equilibrium, concentration ratio of products to reactants is constant Notes Equilibrium requires closed system I At equilibrium, concentration of reactants and products do not change in time Reactions still occurring—just forward and reverse rates are balanced Does not matter if we start with pure reactants or pure products Iiiii System moves to same equilibrium concentrations for a given T Chemistry  Lecture #12, p. 9 Equilibrium Constant "! A ⇌ B ≡ # "" Starting from pure reactant Starting from pure product Chemistry  Lecture #12, p. 10 How Can We Determine Equilibrium Constant? Law of Mass Action 1864: Goldberg and Waage postulated this law Discovered empirically but can be proven with thermodynamics Kc ≡ equilibrium constant for molarity concentrations Equilibrium-constant expression Expresses relation between concentrations of reactants and products at equilibrium Chemistry we usingis cint  Lecture #12, p. 11 Equilibrium Constant in Terms of Pressure Erases Kp ≡ equilibrium constant in terms of partial pressures Expresses relation between pressures of reactants and products at equilibrium Iiiii Note! In general, Kc ≠ Kp ∆" ≡ "!"#$%&# ()%*&+,# − "!"#$%&# )$"+,"-,# Chemistry  Lecture #12, p. 12 But Wait! Don’t we need to know whether the reaction is elementary to use stoichiometric coefficients as exponents ? [C]$ [D]% Rate = %[A]![B]" versus ## = [A]& [B]' In rate laws, we said exponents come from experiment Unless we are told that reaction is elementary Then, we can write down rate law with stoichiometric coefficients as exponents One can prove: all reactions are elementary near equilibrium Thus, unlike rate laws, for ! we don’t need to know reaction mechanism Chemistry  Lecture #12, p. 13 !! , !" are Unitless Why? !! , !" are actually related to “activities” Activity for any substance ≡ Ratio of its concentration or pressure to in an ideal mixture a reference concentration or pressure IM Activity of species j: Iar [%] !( = Thermodynamics gives: if 1M !) $ !* % or Unitless! ) = ideal & ' *( !+ !, mixture !( = So also, unitless 1 bar Pure liquids and pure solids have activities of 1 a 1 Chemistry Inastehi.ly rsfikpays Activity is a moregeneral thermodynamic concept ies it.it  Lecture #12, p. 14 Magnitude of !! , !" ? Products Reactants ⇌ Products !- = Reactants If ! ≫ 1 Equilibrium lies to the right ⇒ products dominate If ! ≪ 1 Equilibrium lies to the left ⇒ reactants dominate mostlyreact Remember: Ratef = Rater at equilibrium NOT Reactants = Products Chemistry  Lecture #12, p. 15 Pit Reaction Quotient, ! Calculate equilibrium expression away from equilibrium [C]$ [D]% Same expression used for equilibrium constant - = [A]& [B]' but calculated with non-equilibrium concentrations -# ⇒ reverse reaction forms more reactants Thus, # predicts direction of reaction, given a specific set of concentrations away from equilibrium Chemistry  Lecture #12, p. 16 Therearemanypossibleproblemswe cansolveusingtheseconcepts Morein Exercise 12 Herelet's discusssomegeneralrules Equilibrium Math ! for reaction written in reverse is inverted Ex: If A ⇌ B has !( ⇒ B ⇌ A has !) = 1⁄!( " i If reaction is multiplied by constant ', then ! = !*+,-,./0 1 Ex: If A ⇌ B has !*+,-,./0 ⇒ 3A ⇌ 3B has ! = !*+,-,./0 ! for multistep reaction is product of !’s for individual steps Ex: If A ⇌ B has !( and B ⇌ C has !) ⇒ A ⇌ C has ! = !( 4 !) Chemistry  Lecture #12, p. 17 Notes chetmist Same reaction can be written in different ways ⇒ " will be different! ⇒ But equilibrium concentrations are same! Thus, we must always write our reaction with our ! ButK'swo bediffere Homogeneous equilibria: All substances in same phase rminology Heterogeneous equilibria: Substances in different phases phases Saturated NaCl solution Ex: NaCl (s) ⇌ Na+ (aq) + Cl− (aq) in equilibrium In such cases, how do we treat solids and solvent? Chemistry  Lecture #12, p. 18 Pure Solids and Pure Liquids In heterogeneous equilibria: exclude pure solids and pure liquids from ! Ex: PbCl2 (s) ⇌ Pb2+ (aq) + 2Cl− (aq) !! = [Pb2+] [Cl−] Concentration of pure solids and pure liquids is constant Why? Pure solids and pure liquids have activities of 1 Air For saturated solutions of low-solubility ionic solids, !! has special name: Product of concentrations of !"# ≡ solubility product dissolved ions at equilibrium Chemistry gin iii app 5  Lecture #12, p. 19 Implications of Equilibria Product “yield” can be limited in closed system Different if system is open and we are taking product as it forms Equilibrium sets maximum amount of product we can obtain What can we do? How can we exploit equilibria? We are engineers! We use our knowledge to solve problems! Chemistry  Lecture #12, p. 20 Le Châtelier’s Principle Freemanintern Very important concept! If a system at equilibrium is disturbed by a change in T, P, or concentration... Henry Louis Le Châtelier,1850–1936 (wikipedia.org)... the system shifts its equilibrium to counteract the disturbance. What does this mean in practice? Chemistry  Lecture #12, p. 21 Concentration Changes Consider: A+B⇌D Initially at equilibrium seep15 Chemistry  Lecture #12, p. 22 Soconcentrationchangesmakesense Whatabouttemperaturechanges Temperature Changes Define: ∆ ≡ heat Treat heat (∆) as reactant or product Then works just like a change in concentration Endothermic rxn: A+∆⇌B Exothermic rxn: A⇌B+∆ Increase T (+∆): rxn moves right Increase T (+∆): rxn moves left Decrease T (−∆): rxn moves left Decrease T (−∆): rxn moves right Why? Chemistry  Lecture #12, p. 23 Consider Exothermic Case Think about the activation energy, !a !a is in an exponential, exp(−!!/()) Larger !a affected more strongly by increase in T See example numbers in Exothermic case: reverse reaction is affected more footnote Reaction shifts left with increase in T Chemistry withEatRT and Ta 2T wedoubletemperature Ents k a exp if Epf a j Rfpexp 0.61 kgαexp 1 0.37 Forward rate increasesbyfactor 1.6 kn exp E exp2,7 kraxexp f exp 5 kraxexp 1 0.37 krxexp 2 0.14 Reverserateincreases byfactor 2  Lecture #12, p. 24 Pressure Changes System shifts its equilibrium to counteract pressure changes Higher pressure: system shifts to side of reaction with fewer moles Lower pressure: system shifts to side of reaction with more moles Justification? ∆" = −2 According to Le Châtelier: For higher pressure, rxn should shift right Double pressure Reaction initially at equilibrium out of equilibrium shifts right Chemistry  Lecture #12, p. 25 Why Is High Pressure Needed to Make NH3? Haber–Bosch process N2 + 3H2 ⇌ 2NH3 Reaction is spontaneous at room temperature But kinetics makes it SLOW Large activation energy Catalysts lower Ea But they still require high T to get reasonable rates But increasing T shifts reaction toward reactants ! Increasing pressure is needed to shift back toward products Haber and Bosch used knowledge to solve problem! Chemistry  Lecture #12, p. 26 Catalysts: Affect on Equilibria? − f + − + With catalyst: Equilibrium constant K unchanged! Chemistry Note result tested itinericat  Lecture #12, p. 27 But Catalyzed Reactions Reach Equilibrium Faster! Due to faster forward and reverse rates with catalyst Chemistry i e forward andreverse ratesarefas  Lecture #12, p. 28 Equilibria: Relation to Thermodynamics? Note: Equilibrium connects both to kinetic rates and thermodynamic energies − Let’s be more precise: Which ∆" do we mean? Rxns spontaneous when: ∆# < 0 Spontaneous from pure reactants or pure products At equilibrium: ∆# = 0 Chemistry  Lecture #12, p. 29 Gibbs Free Energy Recall from Lecture 5: ∆"!° = Free energy to form substance from its elements at standard state 1 bar ∆" ° = Free energy change for any reaction $%&'()*+ =∑# $# ∆"!° − ∑%-.)*./*+ , ', ∆"!° But ∆" ° is for standard state at 25°C: ( ≡ Gas constant What is ∆" for other conditions ? 1 ≡ Absolute temperature ∆" = ∆" ° + %& ln * : ≡ Reaction quotient Chemistry  Lecture #12, p. 30 Relationship Between ∆" and #? At equilibrium: ∆" = 0 and : = @: Thus: ∆" = ∆" ° + (1 ln : Becomes: 0 = ∆" ° + (1 ln @ Rearranging: ∆" ° = −(1 ln @ Or: @ = exp(−∆" ° ⁄(1) Important equation relating equilibrium to thermodynamics Note: If ∆" ° < 0, @ > 1 (equilibrium favors products) If ∆" ° > 0, @ < 1 (equilibrium favors reactants) Makes sense: consistent with spontaneity Chemistry  Lecture #12, p. 31 Relationship Between ∆" and #? At equilibrium: ∆" = 0 and % = &: Thus: ∆" = ∆" ° + () ln % Becomes: 0 = ∆" ° + () ln & Rearranging: ∆" ° = −() ln & Consistent with: − Or: xp °⁄ & = exp(−∆" ()) Important equation relating equilibrium to thermodynamics Note: If ∆" ° < 0, & > 1 (equilibrium favors products) If ∆" ° > 0, & < 1 (equilibrium favors reactants) Makes sense: consistent with spontaneity Chemistry NEXT TIME ACID BASE EQUILIBRIA  Lecture #12, p. 32 What We Learned Chemical rxns experience dynamic equilibria between reactants and product At equilibrium, the forward and reverse rxn rates balance Quantified by equilibrium constant, !) or !0 Equilibrium constant given by Law of Mass Action Equilibrium constants are unitless Reaction quotient, ": equilibrium-constant expression away from equilibrium Meaning of ", math with !’s, solubility product, !+$ Le Châtelier’s Principle: response to changes in concentrations, #, and $ Catalysts and equilibria: equilibrium achieved faster, but ! is same Relationship between ∆' and ! Chemistry