Lecture 10: Chemistry PDF

Lecture #10, p. 1 Lecture 10: Announcements Today: Brown Ch. 14 Chemical Kinetics I 14.1 Factors That Affect Reaction Rates 14.2 Reaction Rates 14.3 Concentration and Rate L...

Lecture #10, p. 1 Lecture 10: Announcements Today: Brown Ch. 14 Chemical Kinetics I 14.1 Factors That Affect Reaction Rates 14.2 Reaction Rates 14.3 Concentration and Rate Laws 14.4 The Change of Concentration with Time Problem Set 9: Due before Exercise #10 tomorrow; upload on Moodle link Problem Set 10: Posted on Moodle; due before Exercise #11 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 #10, p. 2 Lecture 11 Next Week: Brown Ch. 14 Chemical Kinetics II 14.5 Temperature and Rate 14.6 Reaction Mechanisms 14.7 Catalysis Chemistry  Red Thread Where are we going? Acid-Base Catalysis Properties Christmas! Kinetics Batteries Equilibrium Chemistry  Lecture #10, p. 3 Review In Lecture 9, we discussed solutions Thermodynamics of solutions: ∆"!"#$ , ∆#!"#$ , and ∆$!"#$ Solubility, miscible, immiscible, saturated solutions Factors affecting solubility: polarity, temperature, pressure Henry’s law: solubility of gases in liquids Expressions for concentration Colligative properties: Boiling-point elevation Vapor-pressure lowering Ideal solutions, Raoult’s law Freezing-point depression Osmosis and osmotic pressure Chemistry  Lecture #10, p. 4 Antifreeze Proteins (AFPs) “A class of polypeptides produced by certain animals, plants, fungi, and bacteria that permit their survival in temperatures below the freezing point of water.” —wikipedia.org Insect antifreeze protein, Tenebrio-type Unlike the widely used automotive antifreeze, ethylene glycol, AFPs do not lower freezing point in proportion to concentration. Rather, they work in a non-colligative manner. This phenomenon allows them to act as an antifreeze at concentrations 1/300th to 1/500th of those of other dissolved solutes. Their low concentration minimizes their effect on osmotic pressure. The unusual properties of AFPs are attributed to their selective affinity for specific crystalline ice forms and the resulting blockade of the ice-nucleation process.” —wikipedia.org Chemistry Uses kinetics instead of thermodynamics  Lecture #10, p. 5 Today: Chemical Kinetics Why is this topic important? Thermodyamics tells us if “driving force” exists for a reaction or process Does the reaction/process lower the Gibbs free energy? But thermodynamics doesn’t say how fast the reaction or process is Too slow: takes billions of years! Too fast: explodes! Chemical kinetics describes speed of a reaction or process Obviously important if we are trying to make something Key parameters: concentration, time, temperature Kinetics also gives us information bout how reaction occurs Tells us about the “reaction mechanism” Insights gained can teach us how to optimize the reaction or process Chemistry  Lecture #10, p. 6 Reaction Rate Chemical kinetics provides tools for describing a “reaction rate” So what is a reaction rate? Quantifies speed of a reaction Units: change in concentration of reactants or products M - 7 Reaction rate ≡ time interval s By convention, reaction rates are positive Consider: rate of appearance rate of disappearance reaction rate ≡ ≡ A B of B of A generic ∆[B] −∆[A] reaction = = ∆t ∆t Brackets denote concentrations in molarity, i.e. moles per liter Chemistry  Lecture #10, p. 7 Average versus Instantaneous Reaction Rates A B We can consider two types of rates generic reaction Average reaction ∆[B] [B]t2 − [B]t1 Concentration of B at t2 minus at t1 t t rate over time = = interval t1 to t2 ∆t t2 − t1 If we let ∆t = t2 − t1 ⟶ 0, then we get: Instantaneous ∆[B] d[B] Using definition of the derivative reaction rate at = = time t ∆t ∆t ⟶ 0 dt Average and instantaneous reaction rates not typically the same! Chemistry  Lecture #10, p. 8 Plot Concentrations versus Time A B Consider appearance of B Average [0.9] − M rate = = 0.09 over 10 s 10 s s Instantaneous d[B] rate = = local at time t dt slope t t In this case, instantaneous reaction rate is initially faster than slows Reaction rate slows as A disappears: less product produced with less A Chemistry makessense on howmuchreactant A is present If I In.laftasBwitesE.d  Lecture #10, p. 9 But Curve Shape Depends on Specific Reaction C D Another example: Consider appearance of D Average [1.0] − M rate = = 0.1 over 10 s 10 s s Instantaneous d[D] local rate = = at time t dt slope t t For line, local slope is constant ∴ In this case, average reaction rate = instantaneous reaction rate What does this mean? Chemistry  Lecture #10, p. 10 What Does This Mean? C D Reaction rate does not depend on [C] Clearly, this tells us something about this reaction! This is a reason for looking at such plots factory supplies cookies Analogy: cookie factory Black C Box D reaction How can cookie production not depend on supplies? Chemistry Reaction rate can also be independent of reactants T EE E t siti  Lecture #10, p. 11 What Do Reaction Rates Tell Us? Reaction rates don’t just tell us how fast we can make products Also, teach us about how the reaction works! reaction Chemical reactions are initially “black box” C Black D Box Kinetics teaches us about what happens inside Knowledge is empowering! We can use this knowledge to make the reaction work better Or apply the reaction in a different way Chemistry in  Lecture #10, p. 12 Abovewe introduced averageandinstantaneousreactionrates buttypically we justtalkaboutrate Whichdowemean Our Terminology Rate ≡ instantaneous rate at time t Initial rate ≡ instantaneous rate at t = 0 with stoichiometric For general reaction: $A + 'B → *C + ,D iii iii coefficients: !, #, $, and % Because of the stoichiometric coefficients, we need a convention: ! #$ ! #' ! #) ! #[$] Rate = − = −& = ( #% = " #% #% * #% ! #.! ! #." Ex: 2 O3 (g) 3 O2 (g) Rate = − - #% = / #% Chemistry Ii iii IE If fi EEi Eis  Lecture #10, p. 13 Animportantaspect ofchemical kinetics is thatrelatereactionrates to reactant determining expressions concentrations Theseexpressions are called Rate Laws Expressions that predict reaction rates from concentrations For general reaction: (A + *B → ,C +.D The general rate law is then: Rate = # [A]0 B 1 Iii ! is the rate constant where ", # are the reaction orders # ", # can be 0, $, 1, 2, ⋯ ", # are not necessarily equal to %, &, respectively Chemistry The it is ii mechanism Eat sing ftp.t.tierepa.it Wewilldiscussmorenextlecture  Lecture #10, p. 14 Rate Laws Note 1 If more reactants: *A + ,B + γC + ⋯ → products Then rate law has more terms: Rate = # [A]! B " C #⋯ Overall reaction order = / + 0 + 1 + ⋯ (i.e., sum of exponents) Note 2 Units of # depend on overall reaction order! Units Units Units of !+#+$+⋯ Units # = ⋅ ⇒ = of rate of ! concentration of ! s #!"#"$"⋯ M T.IE Chemistry it iii it  Lecture #10, p. 15 Units of Rate Constant Overall Reaction Order Units of ! 0 ! " s !" 1/2 ! #.% " s !" 1 s !" 2 ! !" " s !" 3 ! !& " s !" ⋮ ⋮ Chemistry  Lecture #10, p. 16 Determining Rate Laws Experimental measurements give rate law Ex: A+B C Rate = # [A]! B " What are (, )? Experimental data for initial rates: Compare experiments 2 and 1: t.FI III Exp. [A] (M) [B] (M) Initial Rate (M/s) Rate 2 4.0 × 10#$ //s 1 0.1 0.1 4.0 × 10 !" = = 1 Rate 1 4.0 × 10 #$ //s Enchentiation 2 0.1 0.2 4.0 × 10!" b ! " iiii 3 0.2 0.1 16.0 × 10!" # 0.1 / 0.2 / = = 1 ! " # 0.1 / 0.1 / ⇒ 2" = 1 ⇒ ) = 0 ⇒ Rate = # [A]! B % Chemistry  Lecture #10, p. 17 Determining Rate Laws Experimental measurements give rate law Ex: A+B C Rate = # [A]! B " What are (, )? Experimental data for initial rates: Compare experiments 3 and 1: Exp. [A] (M) [B] (M) Initial Rate (M/s) f it Rate 3 16.0 × 10#$ //s 1 0.1 0.1 4.0 × 10 !" = = 4 p Rate 1 4.0 × 10 #$ //s isdoubled 2 0.1 0.2 4.0 × 10!" 16.0 × 10!" ! " 3 0.2 0.1 # 0.2 / 0.1 / = = 4 ! " # 0.1 / 0.1 / ⇒ 2! = 4 ⇒ ( = 2 ⇒ Rate = # [A]& B % Chemistry  Lecture #10, p. 18 Theratelaw is useful Using Rate Laws Assuming we now have rate law for a given reaction... We can determine how concentrations change with time Take A B and consider three cases: generic reaction #$ − = Rate = $ [A]0 #% !=0 zeroth with !=1 first order reaction !=2 second Chemistry  Lecture #10, p. 19 Let'sstartwith mel ratelaw First-Order Reactions !" Solve this differential A B Rate = − = $ A equation to get [A]! A co !# Iiii !" !" Integrate [#]" 'A & − !# = $[A] ⇒ = −$ )* ⇒ & = − * & '+ " both sides A [#]! % in [A]! τ ⇒ ln A [A]" = −$* 0 ⇒ ln[A]$ − ln[A]% = −$- I ln [A]& [A]% = −$- Take exponent ⇒ of both sides [A]$ = [A]% exp −$- II Iiii Chemistry IEiiii i I ie i  Lecture #10, p. 20 I iii in Plots for First-Order Reactions I Relabel ! → # A B I ln[A]# = −() + ln[A]% II [A]# = [A]% exp −() ! = $% + ' (line) Dec stan iiii ∴ If we plot ln[A]! versus # and get line ⇒ First-order kinetics Chemistry  Lecture #10, p. 21 Next m 2 Second-Order Reactions !" Solve this differential A B Rate = − = $[A]& equation to get [A]! !# Integrate [#]" %A & !" !" − !# = $[A]& ⇒ = −$ )* ⇒ & = − ( & %) ["]' both sides [#]! [A]( % 1 [A]! τ Relabel 1 1 ) ) ⇒ − [A] [A]" = −#$ ⇒ − = #+ ⇒ [A]! = #$ + [A]% 0 ["]) ["]* !→# ! = $% + ' (line) + ∴ If we plot versus ) and get line ⇒ Second-order kinetics [#]# Chemistry Slope of linegives k y interceptgives  Lecture #10, p. 22 Finally m 0 Zero-Order Reactions !" Solve this differential A B Rate = − = $[A]% equation to get [A]! !# Integrate [#]" & !" − !# = $ ⇒ ) A = −$ )* ⇒ & % A = − ( & %) both sides [#]! % [A]! τ Relabel ⇒ A [A]" = −#$ 0 ⇒ [A]& −[A]% = −#+ ⇒ [A]! = −#$ + [A]% Note A !→# islinear ! = $% + ' (line) in t ∴ If we plot [A]! versus ) and get line ⇒ Zeroth-order kinetics Chemistry S q.int eptgive ii  Lecture #10, p. 23 Summary of Plots A B First Order Second Order Zero Order Chemistry Wewillprantinewiththis in Exercise 10andon PS 10  Lecture #10, p. 24 Reaction Half-Life, t1/2 t1/2 = time needed for half of [A] to disappear A B ⇒ A = # A !"⁄# $ " re I It First Order Second Order Zero Order [A]! 1 1 ln = −)* = )* + [A]! = −)* + [A]" P.IE [A]" [A]! [A]" # $ A" 2 1 [A]" ln = −)*#⁄$ − = #$$⁄% − [A]" = −#$$⁄% [A]" [A]" [A]" 2 1 ln = −)*#⁄$ 2 0.693 1 [A]" *#⁄$ = *#⁄$ = *#⁄$ = ) ) [A]" 2) Chemistry In 0.693  Lecture #10, p. 25 Reaction Half-Life, t1/2 t1/2 = time needed for half of [A] to disappear A B ⇒ A !"⁄# = # $ A " First Order Second Order Zero Order 0.693 1 [A]" !#⁄$ = !#⁄$ = !#⁄$ = ( ( [A]" 2( Does not depend on Inversely proportional Proportional to initial concentration to initial concentration initial concentration of reactant, [A]0 of reactant, [A]0 of reactant, [A]0 Ii it.it In all cases, half-life is inversely proportional to k II Chemistry Makessense Bigger k means fasterreation fem total 2 which toshorterhalflife s I  Lecture #10, p. 26 Important Open Questions Given: Rate = ([A]& [B]' [C]( ⋯ , what do 4, 5, 6 mean? Given two spontaneous reactions, why can one be fast and one slow? Why do we often heat our reactions? What role does temperature play in kinetics? Chemistry  Lecture #10, p. 27 Speed of Ants versus Temperature Ants are “cold blooded” Body temperature changes with ambient Cool experiment a century ago! If ∆" = +10°C, ant speed doubles! Related to chemistry? Can we explain/understand? Next time: we will see! H. Shapley, PNAS 6, 204 (1920). Chemistry  Lecture #10, p. 28 What We Learned Chemical kinetics tells us about the speed of reactions/processes Speed quantified by reaction rate Rate depends on reactant concentrations according to rate law: Rate = )[A]% [B]& [C]' ⋯ / + 0 + 1 ⋯ = reaction order Rate law and reaction order determined by experiment! Rate law can give concentrations versus time Result depends on reaction order (zero-, first-, second-, etc.) Half-life, 3"/# , is when half of the initial reactant is gone Chemistry