Chemistry XXI Unit 5 How do we predict chemical change? M3. Measuring Rates Analyzing the factors that affect reaction rate. M2. Comparing Free Energies Determining the directionality and extent of a chemical reaction. M1. Analyzing Structure Comparing the relative stability of different substances M4. Understanding Mechanism Identifying the steps that determine reaction rates. The central goal of this unit is to help you identify and apply the different factors that help predict the likelihood of chemical reactions.

Chemistry XXI Unit 5 How do we predict chemical change? Module 3: Measuring Rates Central goal: To analyze the effect of concentration and temperature on the rate of chemical reactions.

Chemistry XXI The Challenge Imagine that you were interested in comparing the rates at which different substances appeared or were decomposed on the primitive Earth. How could we evaluate the kinetic stability of a substance? How could we determine the effect of concentration and temperature on reaction rates? Transformation How do I change it?

Chemistry XXI Determining  G o rxn or K for a chemical reaction allows us to predict the directionality and extent of the process, but tell us nothing about how long it will take to happen. Time Issues Consider these two possible routes for the synthesis of glycine, the simplest amino acid, on the primitive Earth: CH 2 O(g) + HCN(g) + H 2 O(l)  C 2 H 5 NO 2 (s)  G o rxn = kJ 2 CH 4 (g) + NH 3 (g) + 5/2 O 2 (g)  C 2 H 5 NO 2 (s) + 3 H 2 O(l)  G o rxn = kJ

Chemistry XXI Thermo vs. Kinetics GG 2 CH 4 (g) + NH 3 (g) + 5/2 O 2 (g) C 2 H 5 NO 2 (s) + 3 H 2 O(l) Reaction Coordinate CH 2 O(g) + HCN(g) + H 2 O(l) C 2 H 5 NO 2 (s) Themodynamically favored, but does not occur for all practical purposes (High E a ) Occurs readily at 25 o C (Low E a ) Activation Energy E a

Chemistry XXI Analyzing chemical systems from both the thermodynamic and kinetic point of view is crucial in making decisions about the actual “stability” of substances. Analyzing Stability For example, the decomposition or transformation of a substance may be favored thermodynamically, but can take millions of years to occur. How stable is it then? C(diamond)  C(graphite)  G o tr = -2.9 kJ/mol E a ~ 728 kJ/mol

Chemistry XXI Kinetic Stability The analysis of the kinetic stability of biomolecules has been crucial in the analysis of different theories about the origin of life. How stable are amino acids under such conditions? For example, it has been proposed that amino acid synthesis could have occurred deep in the Earth's crust and that these amino acids were subsequently shot up along with hydrothermal fluids into cooler waters. CH 4 and NH 3 are abundant in hydrothermal vent regions ( o C).

Chemistry XXI Unstable? Many aqueous solutions of amino acids are “thermodinamically unstable.” Let’s consider the case of alanine: Decarboxylation  G o rxn < 0 The kinetics of this reaction has been thoroughly explored by measuring the concentration of alanine [Ala] as a function of time (t) in aqueous solutions at various temperatures. Alanine (Ala)Ethyl Amine

Chemistry XXI Let’s Think o How would you quantify the rate of decomposition of alanine at any given time?

Chemistry XXI o Reaction Rate  [Ala] tt

Chemistry XXI Let’s Think o o What does this data tell you about the kinetic stability of alanine as a function of concentration and temperature? Hint: How does the rate change with C and T? (The higher the rate, the lower the kinetic stability)

Chemistry XXI o In general, the rate of reaction decreases as the concentration of the reactants [R] decreases. o The rate of reaction increases with increasing temperature T. Reaction Rate The slope decreases Kinetic stability is a function of [R] and T.

Chemistry XXI Rate Constant RATE LAW Rate = k [A] a [B] b [C] c Rate Laws The effect of temperature and concentration on reaction rates can be modeled mathematically: x A + y B + z C  w D + y E + z F k depends on the value of T, E a, and other relevant factors for each reaction. k = f (T, E a, surface area….) Reaction order

Chemistry XXI Concentration Effects How can determine reaction orders and rate constants? Rate constant? Reaction order? What are their values? We may assume values for the reaction order a and analyze the implications: If a = 1 (first-order): By integration of this differential equation we get: Rate Law

Chemistry XXI If the reaction is first-order: ln[Ala] t m = -k ln[Ala] o Graphical Analysis y = b + mx t (years)[Ala] (mM) For example, is the decomposition of alanine at 150 o C (423 K) 1 st order?: C 3 H 7 NO 2  C 2 H 7 N + CO 2

Chemistry XXI C 3 H 7 NO 2  C 2 H 7 N + CO 2 t (years)[Ala] (mM)ln[Ala] Reaction Order We have a first-order reaction Rate = k[Ala] a with: a = 1 k = years -1 Rate = [Ala]

Chemistry XXI Let’s Think If [Ala] o = 1.00 mM, predict the time it will take for [Ala] to reach the values 0.50 mM, 0.25 mM and mM. How long does it take to halve the concentration? C 3 H 7 NO 2  C 2 H 7 N + CO 2 Given the Rate Law: Rate = [Ala] [Ala] = [Ala] o e t t 1 = 10 y t 2 = 20 y t 3 = 30 y It takes 10 years to decrease the concentration by half, independent of the concentration.

Chemistry XXI Half Life A half-life is the time it takes for the concentration of a reactant to be reduced in half. t = 0 1 half-life t = 1 half-life 2 half-lives t = 2 half-lives 3 t = 3 half-lives 4 T = 150 o C (423 K)

Chemistry XXI For first order reactions: If [C] = [C] o /2 t 1/2 Half Life Independent of Concentration t 1/2 = 10 years for alanine at 150 o C. Half Life

Chemistry XXI If the reaction is first-order Rate = k[C]: What if Rate = k[C] a with a = 2 (second-order)? By integration we get: 1/[C] t m = k 1/[C] o Concentration Effects

Chemistry XXI Let’s Think Is half-life for second order reactions independent of the initial concentration of reactant? Rate = k[C] 2 If [C] = [C] o /2 t 1/2 Half Life t 1/2 is only independent of [C] o for first order processes.

Chemistry XXI Temperature Effects How can we predict how rate varies with temperature? 6.55 x x x x x x 10 7 t 1/2 (y) The decomposition of alanine at different temperatures illustrates the effect of T on the reaction rate x x x x x x k (y -1 )T (K) Ho do we explain it and make quantitative predictions? Larger T  Larger rate constant  Shorter half lives.

Chemistry XXI Collision Rate Model According to this model: 1.For a reaction to occur, the reactant particles must collide. 2.Colliding particles must be positioned so that the reacting groups interact effectively. 3.Colliding particles must have enough energy to reach a transition state that leads to the formation of the new products. P R EpEp Reaction Coordinate  H rxn Transition State EaEa

Chemistry XXI Arhenius Equation The fraction of molecules with enough energy to react at a given T is proportional to: The rate constant k is then given by: Likelihood of collisions y = mx + b y  ln(k) x  1/T m = -E a /R b = ln(A)

Chemistry XXI Let’s Think Use the data to estimate the activation energy E a for the decomposition of alanine. Estimate t 1/2 at 623 K in seconds x x x x x x k (y -1 )T (K) E a ~177 kJ/mol 7.29 x t 1/2 ~ 30 s

Chemistry XXI Assess what you know Let′s apply!

Chemistry XXI Let′s apply! The strong dependence on T of the decomposition of amino acids makes it difficult to decide whether the “hydrothermal vents” theory of the origin of life is plausible. In fact, the contact of amino acids with hydrothermal solutions during sediment and ocean recycling is likely to be the major geochemical destruction pathway of amino acids on Earth. Analyze Go back and analyze the notes for the decomposition of Alanine. Based on our overall results, analyze the likelihood of amino acids forming in hydrothermal vents on the primitive Earth.

Chemistry XXI Let′s apply! Recent experimental results indicate that there may be other reactions that compete with the decomposition of amino acids at T > 100 o C: New Data The formation of dimers and polymers may have helped amino acids to accumulate on the planet. 2 A  A 2 + B H2OH2O Dimerization Peptide Bond

Chemistry XXI Let′s apply! Analyze Go to: (Dimerization) or use the simulation on the next page. Use the simulation of the dimerization of alanine to:  Determine the order of the reaction;  Compare the half-lives of the process for a 1 M solution of alanine at 100 o C and 200 o C.  Estimate the activation energy E a of the reaction;

Chemistry XXI Let′s apply! Analyze

Chemistry XXI Let′s apply! Graphical analysis indicates this is a second-order reaction. T (K)k (s -1 M -1 )t 1/2 (s) x x x10 -1 T = 373 K T = 473 K

Chemistry XXI Let′s apply! E a /R = E a = 88.7 kJ/mol

Chemistry XXI Identify with a partner two important ideas discussed in this module.

Chemistry XXI Measuring Rates Summary x A  y B Rate Constant RATE LAW Rate = k [A] a The effect of temperature and concentration on a process’ reaction rate is summarized in the RATE LAW: Reaction order Reaction rates allow us to follow the kinetic evolution of a chemical process.

Chemistry XXI Given a rate law, we can derive information about how the concentration of reactants or products changes with time. If a = 1 (first-order): Rate = k [A] a x A  y B If a = 2 (second-order): C and T Effects Temperature effects on reaction rate are determined by Arhenius Equation for the rate constant k:

Chemistry XXI For next class, Investigate how the overall rate of a reaction is related to the reaction mechanism. How can we use the reaction mechanism to derive the rate law or use the rate law to evaluate the reaction mechanism?