* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chemistry XXI
Electrochemistry wikipedia , lookup
Multi-state modeling of biomolecules wikipedia , lookup
Photoredox catalysis wikipedia , lookup
Hydrogen-bond catalysis wikipedia , lookup
California Green Chemistry Initiative wikipedia , lookup
Marcus theory wikipedia , lookup
Chemical equilibrium wikipedia , lookup
History of chemistry wikipedia , lookup
Supramolecular catalysis wikipedia , lookup
Chemical thermodynamics wikipedia , lookup
Computational chemistry wikipedia , lookup
Basal metabolic rate wikipedia , lookup
Photosynthetic reaction centre wikipedia , lookup
Biochemistry wikipedia , lookup
Inorganic chemistry wikipedia , lookup
Institute of Chemistry Ceylon wikipedia , lookup
Strychnine total synthesis wikipedia , lookup
Nuclear chemistry wikipedia , lookup
Chemical reaction wikipedia , lookup
Stoichiometry wikipedia , lookup
Analytical chemistry wikipedia , lookup
Lewis acid catalysis wikipedia , lookup
Process chemistry wikipedia , lookup
George S. Hammond wikipedia , lookup
Green chemistry wikipedia , lookup
Reaction progress kinetic analysis wikipedia , lookup
Rate equation wikipedia , lookup
Physical organic chemistry wikipedia , lookup
Click chemistry wikipedia , lookup
Unit 5 How do we predict chemical change? 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 M1. Analyzing Structure M2. Comparing Free Energies Comparing the relative stability of different substances Determining the directionality and extent of a chemical reaction. M3. Measuring Rates Analyzing the factors that affect reaction rate. M4. Understanding Mechanism Identifying the steps that determine reaction rates. Unit 5 How do we predict chemical change? Chemistry XXI Module 3: Measuring Rates Central goal: To analyze the effect of concentration and temperature on the rate of chemical reactions. The Challenge Transformation How do I change it? Chemistry XXI 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? Time Issues Determining DGorxn 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. Chemistry XXI Consider these two possible routes for the synthesis of glycine, the simplest amino acid, on the primitive Earth: CH2O(g) + HCN(g) + H2O(l) C2H5NO2(s) DGorxn = -154. kJ 2 CH4(g) + NH3(g) + 5/2 O2(g) C2H5NO2(s) + 3 H2O(l) DGorxn = -965. kJ Activation Energy Ea DG 2 CH4(g) + NH3(g) + 5/2 O2(g) Thermo vs. Kinetics Occurs readily at 25 oC (Low Ea) CH2O(g) + HCN(g) + H2O(l) Chemistry XXI C2H5NO2(s) Themodynamically favored, but does not occur for all practical purposes (High Ea) C2H5NO2(s) + 3 H2O(l) Reaction Coordinate Analyzing Stability 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. 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) DGotr = -2.9 kJ/mol Ea ~ 728 kJ/mol Kinetic Stability Chemistry XXI The analysis of the kinetic stability of biomolecules has been crucial in the analysis of different theories about the origin of life. 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. CH4 and NH3 are abundant in hydrothermal vent regions (60-400 oC). How stable are amino acids under such conditions? Unstable? Many aqueous solutions of amino acids are “thermodinamically unstable.” Let’s consider the case of alanine: 2 2 3 Chemistry XXI Alanine (Ala) 3 + Decarboxylation 2 DGorxn < 0 Ethyl Amine 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. Let’s Think How would you quantify the rate of decomposition of alanine at any given time? o [Ala] (mM) Chemistry XXI T = 200 C (473 K) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 3 6 9 12 15 18 21 24 27 30 33 36 Time (days) Reaction Rate Chemistry XXI [Ala] (mM) T = 200 oC (473 K) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 D[ Ala ] Rate Average Dt Rate Average D[Ala] Dt 0 3 6 [0.5 0.7] mM 0.02 [18 9] year RateInst d [ Ala ] dt 9 12 15 18 21 24 27 30 33 36 Time (days) Let’s Think Hint: How does the rate change with C and T? (The higher the rate, the lower the kinetic stability) [Ala] (mM) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 Time (Years) T = 200 oC (473 K) [Ala] (mM) Chemistry XXI What does this data tell you about the kinetic stability of alanine as a function of concentration and temperature? T = 150 o C (423 K) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 3 6 9 12 15 18 21 24 27 30 33 36 Time (days) Chemistry XXI The rate of reaction increases with increasing temperature T. Kinetic stability is a function of [R] and T. [Ala] (mM) In general, the rate of reaction decreases as the concentration of the reactants [R] decreases. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 The slope decreases 0 2 4 6 8 10 12 14 16 18 20 Time (Years) T = 200 oC (473 K) [Ala] (mM) Reaction Rate T = 150 o C (423 K) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 3 6 9 12 15 18 21 24 27 30 33 36 Time (days) Rate Laws The effect of temperature and concentration on reaction rates can be modeled mathematically: xA+yB+zC wD+yE+zF RATE LAW Rate = k [A]a [B]b [C]c Reaction order Chemistry XXI Rate Constant k depends on the value of T, Ea, and other relevant factors for each reaction. k = f (T, Ea, surface area….) Concentration Effects How can determine reaction orders and rate constants? Rate Law Rate k[ Ala ] a Reaction order? Rate constant? What are their values? Chemistry XXI We may assume values for the reaction order a and analyze the implications: If a = 1 (first-order): d [ Ala ] Rate k[ Ala ] dt By integration of this differential equation we get: [ Ala ] [ Ala ]o e kt ln[ Ala] ln[ Ala]o kt Graphical Analysis If the reaction is first-order: ln[ Ala] ln[ Ala]o kt y = b For example, is the decomposition of alanine at 150 oC (423 K) 1st order?: C3H7NO2 C2H7N + CO2 + mx t (years) [Ala] (mM) ln[Ala] Chemistry XXI ln[Ala]o m = -k t 0 1.000 2 0.8705 4 0.7578 6 0.6597 8 0.5743 10 0.5000 12 0.4352 14 0.3789 16 0.3298 Reaction Order t (Years) C3H7NO2 C2H7N + CO2 0 2 4 6 8 10 12 14 16 18 0 -0.2 ln[Ala] 0 1.000 0 2 0.8705 -0.1387 -0.4 -0.6 ln([Ala]) t (years) [Ala] (mM) -0.8 -1 -1.2 4 0.7578 -0.2773 ln([Ala]) = -0.0693t -1.4 Chemistry XXI -1.6 6 0.6597 -0.4160 8 0.5743 -0.5546 10 0.5000 -0.6931 12 0.4352 -0.7914 14 0.3789 -0.9704 16 0.3298 -1.1092 -1.8 We have a first-order reaction Rate = k[Ala]a with: a=1 k = 0.0693 years-1 Rate = 0.0693[Ala] 20 Let’s Think Given the Rate Law: Rate = 0.0693[Ala] C3H7NO2 C2H7N + CO2 Chemistry XXI [Ala] = [Ala]oe-0.0693t 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 0.125 mM. How long does it take to halve the concentration? t1 = 10 y t2 = 20 y t3 = 30 y It takes 10 years to decrease the concentration by half, independent of the concentration. Half Life 1 A half-life is the time it takes for the concentration of a reactant to be reduced in half. 0.75 [Ala] (mM) Chemistry XXI t=0 t = 1 half-life T = 150 oC (423 K) 0.875 0.625 1 half-life 0.5 0.375 2 half-lives 0.25 3 4 0.125 0 0 t = 2 half-lives t = 3 half-lives 5 10 15 20 25 30 t (Years) 35 40 Half Life For first order reactions: Chemistry XXI If [C] = [C]o/2 t1/ 2 [C ] ln kt [C ]o 1 ln o kt1/ 2 2 ln( 1 / 2) k t1/2 Half Life Independent of Concentration t1/2 = 10 years for alanine at 150 oC. Concentration Effects If the reaction is first-order Rate = k[C]: ln[ C ] ln[ C ]o kt What if Rate = k[C]a Chemistry XXI d [C ] Rate k[C ]2 dt with a = 2 (second-order)? 1/[C] By integration we get: 1 1 kt [C ] [C ] o 1/[C]o m=k t Let’s Think Is half-life for second order reactions independent of the initial concentration of reactant? Rate = k[C]2 Chemistry XXI If [C] = [C]o/2 t1/ 2 1 1 kt [C ] [C ] o 1 k[C ] t1/2 Half Life t1/2 is only independent of [C]o for first order processes. Temperature Effects How can we predict how rate varies with temperature? Chemistry XXI The decomposition of alanine at different temperatures illustrates the effect of T on the reaction rate. T (K) 323 373 423 473 523 573 k (y-1) t1/2 (y) 1.17 x 10-8 5.90 x 107 8.10 x 10-5 8.56 x 103 6.93 x 10-2 1.00 x 101 1.42 x 101 4.87 x 10-2 1.06 x 103 6.55 x 10-4 3.71 x 104 1.87 x 10-5 Larger T Larger rate constant Shorter half lives. Ho do we explain it and make quantitative predictions? Collision Rate Model According to this model: 1. For a reaction to occur, the reactant particles must collide. Chemistry XXI 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. Ep Transition State Ea R DHrxn P Reaction Coordinate Arhenius Equation The fraction of molecules with enough energy to react at a given T is proportional to: Chemistry XXI e Ea RT The rate constant k is then given by: k Ae Ea RT Likelihood of collisions Ea ln( k ) ln( A) RT y = y ln(k) mx + b x 1/T m = -Ea/R b = ln(A) Let’s Think ln( k ) Ea ln( A) RT T (K) 323 373 423 473 523 573 623 k (y-1) 1.17 x 10-8 8.10 x 10-5 6.93 x 10-2 1.42 x 101 1.06 x 103 3 t1/ 2 ln( 1 / 2) k + 15 10 ln (k) = -21310(1/T) + 47.709 5 0 0.0016 -5 0.002 0.0024 0.0028 -10 t1/2 ~ 30 s 2 3 Ea 21310 R 3.71 x 104 7.29 x 105 2 2 ln (k) Chemistry XXI Use the data to estimate the activation energy Ea for the decomposition of alanine. Estimate t1/2 at 623 K in seconds. -15 Ea ~177 kJ/mol -20 1/T (1/K) 0.0032 Chemistry XXI Let′s apply! Assess what you know Let′s apply! Analyze Chemistry XXI 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. 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. New Data Let′s apply! Recent experimental results indicate that there may be other reactions that compete with the decomposition of amino acids at T > 100 oC: Dimerization 2 2 2 3 Chemistry XXI + H2O 3 The formation of dimers and polymers may have helped amino acids to accumulate on the planet. 3 Peptide Bond 2 A A2 + B Let′s apply! Analyze Go to: http://www.chem.arizona.edu/chemt/C21/sim (Dimerization) or use the simulation on the next page. Use the simulation of the dimerization of alanine to: Chemistry XXI Determine the order of the reaction; Compare the half-lives of the process for a 1 M solution of alanine at 100 oC and 200 oC. Estimate the activation energy Ea of the reaction; Chemistry XXI Let′s apply! Analyze 10.16 Let′s apply! T = 373 K Graphical analysis indicates this is a second-order reaction. 1/[Ala] (1/mM) 10.14 10.12 10.1 10.08 1 1 kt [ Ala ] [ Ala ]o 10.06 18 T (K) k (s-1M-1) 20 22 24 26 28 30 32 t(s) 1 [ Ala ]o k t1/2(s) 373 0.0085 1.17x102 423 0.247 4.05x100 473 3.606 2.77x10-1 1/[Ala] (1/mM) Chemistry XXI t1/ 2 1/[Ala] = 0.0085t + 9.8997 50 45 40 35 30 25 20 15 10 5 0 T = 473 K 1/[Ala] = 3.6056t - 62.715 15 20 25 t(s) 30 35 Let′s apply! 2 1 ln(k) 0 0.0016 -1 0.002 0.0024 0.0028 -2 -3 -4 Chemistry XXI -5 ln(k) = -10672/T + 23.841 -6 1/T (1/K) Ea/R = 10672 Ea = 88.7 kJ/mol 0.0032 Chemistry XXI Identify with a partner two important ideas discussed in this module. Measuring Rates Summary Reaction rates allow us to follow the kinetic evolution of a chemical process. xAyB Rate Inst d [ A] dt Chemistry XXI The effect of temperature and concentration on a process’ reaction rate is summarized in the RATE LAW: RATE LAW Rate = k [A]a Reaction order Rate Constant C and T Effects Given a rate law, we can derive information about how the concentration of reactants or products changes with time. xAyB If a = 1 (first-order): Chemistry XXI If a = 2 (second-order): Rate = k [A]a ln[ A] ln[ A]o kt 1 1 kt [ A] [ A] o Temperature effects on reaction rate are determined by Arhenius Equation for the rate constant k: k Ae Ea RT 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?