Kinetics - Principles of Chemistry II - Lecture Slides, Slides of Chemistry

Download Kinetics - Principles of Chemistry II - Lecture Slides and more Slides Chemistry in PDF only on Docsity! Chemistry 213: Course Outline Chemical Kinetics Acid-Base Equilibria Chemical Equilibrium Nuclear Chemistry Chemistry of the Environment Chemical Thermodynamics Organic/Biological Chemistry Electrochemistry Coordination Compounds 9/7/2013 Chemical Kinetics Rates of Reaction Zeroth-Order First-Order Second-Order Rate Laws (IRL, DRL, t1/2) Temperature KM-Model Arrhenius Catalysis Mechanism Nuclear Chemistry • For the reaction A  B there are two ways of measuring rate: – the speed at which the products appear (i.e. change in moles of B per unit time), or – the speed at which the reactants disappear (i.e. the change in moles of A per unit time). Reaction Rates   t   A of moles A respect to with rate Average   t   B of moles B respect to with rate Average Change of Rate with Time • Most useful units for rates are to look at molarity. Since volume is constant, molarity and moles are directly proportional. • Consider: C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) Reaction Rates TABLE 14.1 itl Kom DYcle elmer Lad ela me meri a GM W IMM Kos Time, t (s) [C4HyCl] (M) Average Rate (M/s) 0.0 0.1000 19 x10 50.0 0.0905 — ty cto 100.0 0.0820 16 X107 150.0 0.0741 14 x10 200.0 0.0671 122 x 10-4 300.0 0.0549 101 x 1074 400.0 0.0448 0.80 x 107 500.0 0.0368 0.560 X 1074 800.0 0.0200 10,000 0 Times [CyHsCl] / M Avg Rate /Ms* 0.0 0.1000 -[(M-Mi)/(t-t)] 50.0 0.0905 1.9E-04: 100.0 0.0820 1.7E-04: 160.0 0.0741 1.6E-04: 200.0 0.0671 1.4£-04: 300.0 0.0549 1.22E-04 400.0 0.0448 1.0E-04 600.0 0.0368 8.0E-05, 300.0 0.0200 5.6E-05, 10,000.0 0.0000 HomeWork - Friday Jan. 14, 2011. EXCEL graph and average rate Red Trend Line obtained without last point. Bonus Point towards Quiz Total [CHa] (My 0.1000 0.0900 o.0800 0.0700 0.0600 0.0500 0.0400 0.0300 0.0200 0.0100 0.9000 0.0 Reaction of Chlorobutane 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 Time (s) [C4HgCl] (M) 0.100 0.090 0.080 0.070 0.060 0.050 0.040 0.030 0.020 0.010 | Instantaneous ~ rate att =0 (initial rate) A [CyHoCl] Instantaneous rate at t = 600s 100 200 300 400 500 600 700 800 900 Time (s) Reaction Rate and Stoichiometry • For the reaction C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) we know • In general for aA + bB  cC + dD Reaction Rates     tt       OHHCClHC Rate 9494         tdtctbta             D1C1B1A1 Rate Exponents in the Rate Law • For a general reaction with rate law we say the reaction is mth order in reactant 1 and nth order in reactant 2. • The overall order of reaction is m + n + …. • A reaction can be zeroth order if m, n, … are zero. • Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry. Concentration and Rate nmk ]2reactant []1reactant [Rate  Using Initial Rates to Determine Rate Laws Given data: 2 NO(g) + 2 H2(g)  N2(g) + 2 H2O(g) Expt. # [NO] / M [H2] / M Rate / M s -1 1 0.10 0.10 1.23x10-3 2 0.10 0.20 2.46x10-3 3 0.20 0.10 4.92x10-3 Determine Rate Law for the reaction. i.e. Rate = k [NO]x [H2] y ; Find x , y , and k . Given data: 2 NO(g) + 2 H2(g)  N2(g) + 2 H2O(g) Expt. # [NO] / M [H2] / M Rate / M s -1 1 0.10 0.10 1.23x10-3 2 0.10 0.20 2.46x10-3 3 0.20 0.10 4.92x10-3         tk ot t t eAA kt kt k t             ][][ A A ln AlnAln ]A[ A][ Rate 0 0 First-Order Reactions The Change of Concentration with Time    0AlnAln  ktt First-Order Reactions • The first-order rate constant for the decomposition of a certain insecticide in water at 12oC is 1.45 yr-1 . A quantity of this insecticide is washed into a lake on June 1, leading to a concentration of 5.0x10-7 g/cm3 of water. Assume that the average temperature of the lake is 12oC. • (A) What is the concentration of the insecticide on June 1 of the following year? • (B) How long would it take for the concentration of the insecticide to drop to 3.0x10-7 g/cm3 ? The Change of Concentration with Time    0AlnAln  ktt Second-Order Reactions • For a second-order reaction with just one reactant • A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0 • For a second-order reaction, a plot of ln[A]t vs. t is not linear. The Change of Concentration with Time    0 2 A 1 A 1 ][ ][      kt Ak t A Rate t Second-Order Reactions The Change of Concentration with Time    0A 1 A 1  kt t Second-Order Reactions The Change of Concentration with Time    0A 1 A 1  kt t The NO2 reaction has a rate constant of 0.543 M -1 s-1 . If the initial concentration of NO2 in a closed vessel is 0.0500 M, what is the remaining concentration after 0.500 hr ? Zeroth-Order Reactions • A zeroth-order reaction has a rate constant of 1.1x10-7 M s-1 . The reaction began with a reactant concentration of 0.0200 M . What is the fraction of reactant concentration remaining after 45.0 hr ? The Change of Concentration with Time 0 0 ][][ ][ ][ AktA kAk t A Rate t      •A zeroth-order reaction has a rate constant of 1.1x10-7 M s-1 . The reaction began with a reactant concentration of 0.0200 M . What is the fraction of reactant concentration remaining after 45.0 hr ? Solution Key Half-Life • Half-life is the time taken for the concentration of a reactant to drop to half its original value. • For a first-order process, half life, t½ is the time taken for [A]0 to reach ½[A]0. • Mathematically, The Change of Concentration with Time   kk t 693.0ln 2 1 2 1  Summary of Rate Laws First-Order Second-Order Zeroth-Order DRL (-Δ[A]/Δt) k[A] k[A]2 k IRL [A]t = [A]oe -kt ln[A]t = -kt + ln[A]o 1/[A]t = kt + 1/[A]o [A]t = -kt + [A]o Linear Equation ln[A]t vs. t 1/[A]t vs. t [A]t vs. t Linear Plot Half-Life ln(2)/k 1/k[A]o [A]o/2k Units on k time-1 M-1 time-1 M time-1 m = -k b = ln[A]o m = k b = 1/[A]o m = -k b = [A]o Temperature and Rate The Collision Model • As temperature increases, the rate increases. The Collision Model • The collision model: in order for molecules to react they must collide. • The greater the number of collisions the faster the rate. • The more molecules present, the greater the probability of collision and the faster the rate. • The higher the temperature, the more energy available to the molecules and the faster the rate. • Complications: not all collisions lead to products. In fact, only a small fraction of collisions lead to product. Temperature and Rate a Reaction pathway HC: - (Activated i N H;C—C=N ioe Fraction of molecules Activation Energy | Lower temperature | Higher temperature ~~ Minimum energy | i needed for reaction, E, | | Kinetic energy The Arrhenius Equation • Arrhenius discovered most reaction-rate data obeyed the Arrhenius equation: – k is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in K. – A is called the frequency factor. – A is a measure of the probability of a favorable collision. – Both A and Ea are specific to a given reaction. Temperature and Rate RT Ea eAk   —10 —11 0.0019 0.0020 1/T 0.0021 0.0022 Determining the Activation Energy • If we do not have a lot of data, then we recognize Temperature and Rate                      122 1 21 21 2 2 1 1 11 ln lnlnlnln lnln and lnln TTR E k k A RT E A RT E kk A RT E kA RT E k a aa aa Ea ~ 160 kJ/mol (previous slide of ln(k) versus 1/T plot) • The balanced chemical equation provides information about the beginning and end of reaction. • The reaction mechanism gives the path of the reaction. • Mechanisms provide a very detailed picture of which bonds are broken and formed during the course of a reaction. Elementary Steps • Elementary step: any process that occurs in a single step. Reaction Mechanisms Energy ——~ 2H,0, + 2Br- + 2H+ Uncatalyzed reaction H,O, + 2H,O + Br 5 2H,O+O, + 2Br- + 2H* Reaction pathway Enzymes Substrate o a. Products \ 7 Enzyme Enzyme-substrate Enzyme complex Nuclear Equations • Nucleons: particles in the nucleus: – p+: proton – n0: neutron. • Mass number: the number of p+ + n0. • Atomic number: the number of p+. • Isotopes: have the same number of p+ and different numbers of n0. • In nuclear equations, number of nucleons is conserved: 238 92U  234 90Th + 4 2He Radioactivity TABLE 21.2 Common Particles in Radioactive Decay and Nuclear Transformations Particle Symbol Neutron jn Proton iH or ip Electron %e Alpha particle — 3He or 5a Beta particle Ye or 9B Positron 1e€ Neutron-to-Proton Ratio • The heavier the nucleus, the more neutrons are required for stability. • The belt of stability deviates from a 1:1 neutron to proton ratio for high atomic mass. Radioactive Series For 238U, the first decay is to 234Th (-decay). The 234Th undergoes -emission to 234Pa and 234U. 234U undergoes -decay (several times) to 230Th, 226Ra, 222Rn, 218Po, and 214Pb. 214Pb undergoes -emission (twice) via 214Bi to 214Po which undergoes -decay to 210Pb. The 210Pb undergoes - emission to 210Bi and 210Po which decays () to the stable 206Pb. Patterns of Nuclear Stability • Half-lives can range from fractions of a second to millions of years. • Naturally occurring radioisotopes can be used to determine how old a sample is. • This process is radioactive dating. Rates of Radioactive Decay Dating • Carbon-14 is used to determine the ages of organic compounds because half-lives are constant. • We assume the ratio of 12C to 14C has been constant over time. • For us to detect 14C the object must be less than 50,000 years old. • The half-life of 14C is 5,730 years. • It undergoes decay to 14N via -emission: 14 6C 14 7N + 0 -1e Rates of Radioactive Decay Calculations Based on Half Life • Radioactive decay is a first order process: • In radioactive decay the constant, k, is the decay constant. • The rate of decay is called activity (disintegrations per unit time). • If N0 is the initial number of nuclei and Nt is the number of nuclei at time t, then Rates of Radioactive Decay kNRate kt N Nt  0 ln