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CONCEPT: RATES OF CHEMICAL REACTIONS is the study of reaction rates, and tells us the change in concentrations of reactants or products over a period of time. Although a chemical equation can help us calculate the theoretical yield from reactants, it can t tell us how fast it goes. Looking at a chemical reaction in the simplest way can be seen as breaking down to form. Reaction : A B 0 Seconds 30 Seconds 60 Seconds 90 Seconds Page 2
CONCEPT: FACTORS INFLUENCING REACTION RATES VS. 1. Concentration: Molecules must to react. Increasing the number of molecules in a container, increases their and thereby causes the rate to increase. Reaction : A + B A B 2. Surface Area: The frequency of collisions increases with surface area. H 2 C CH 2 CH3CH2CH2CH3 VS. H 2 C CH 2 3. Temperature: Increasing the temperature increases the reaction rate by increasing the and of collisions. 4. Catalyst: A catalyst increases the rate of a reaction by the energy of activation. Page 3
CONCEPT: GENERAL RATE The General Rate of a chemical reaction is the change in some variable over a period of time. Rate = Δ [A] Δ time A = or. The use of brackets. [ ], means. EXAMPLE 1: The following equation shows the production of NO and H2O by oxidation of ammonia. 4 NH3 (g) + 5 O2 (g) 4 NO (g) + 6 H2O (l) a. What is the average rate of each compound in the balanced equation? b. What is the rate of NH3 in the reaction between 2 and 6 minutes at 40 o C? c. Determine the instantaneous rate of the following reaction. Page 4
PRACTICE: STOICHIOMETRIC RATES EXAMPLE: The decomposition of dinitrogen pentoxide is described by the chemical equation 2 N2O5 (g) 4 NO2 (g) + O2 (g) If the rate of disappearance or decomposition of O2 is equal to 2.20 M/min at a particular moment, what is the rate of appearance or formation of N2O5 at that moment? PRACTICE: The formation of alumina, Al2O3, can be illustrated by the reaction below: 4 Al (s) + 3 O2 (g) 2 Al2O3 (s) At 750 K it takes 267 seconds for the initial concentration of Al2O3 to increase from 6.18 x 10-5 M to 5.11 x 10-4 M. What is the rate of Al? Page 5
CONCEPT: TEMPERATURE AND RATE Temperature can have a huge effect on the reaction rate. It affects the rate by affecting the rate constant, k. Increasing the temperature or amount of catalyst will the rate constant, k. The Equation relates both the temperature and the rate constant. k = Ae E a RT A = E a = R = T = For a reaction to be successful the molecules must collide with sufficient and the correct. Conversion of the equation into its logarithmic form can help us find Ea when two rate constants or temperatures are given. ln k 2 = Ea k 1 R " 1 1 % $ ' # T 2 T 1 & A plot-wise approach can also be used to convert the equation in order to find Ea. ln A " ln k = E a $ # R % & ' " 1 % $ # T '+ ln A & ln k slope = Δy Δx = E a R 1 T Page 6
PRACTICE: TEMPERATURE AND RATE (CALCULATIONS) EXAMPLE: The reaction 2 HCl (g) H2 (g) + Cl2 (g) has Ea of 1.77 x 10 4 kj/mol and a rate constant of 1.32 x 10-1 at 700 K. What is the rate constant at 685 K? PRACTICE 1: If a first order reaction has a frequency factor of 3.98 x 10 13 s -1 and Ea of 160 kj, then calculate the rate constant at 25 o C. PRACTICE 2: Generally, the slower the rate of the reaction then the the energy of activation (Ea) and the higher the temperature, the the value of rate constant, k. a) larger, larger b) smaller, smaller c) smaller, larger d) larger, smaller Page 7
CONCEPT: RATE LAW Although, chemical reactions can be reversible we will only look at the reaction for chemical reactions. By ignoring reactions then the rate depends only on concentrations and. 4 NO (g) + O2 (g) 2 N2O3 (g) Rate Law = k [NO] x [O2] y k = x & y = Unless the reaction is classified as a step, a rate-determining step, then x & y must be calculated experimentally. EXAMPLE: For the following reaction, use the given rate law to determine the best answer for the reaction with respect to each reactant and the overall order. H2O2 (aq) + 3 I (aq) + 2 H + (aq) I3 + 2 H2O (l) Rate = k [H2O2] 2 [I ] a) H2O2 is 1 st order, I is 1 st order, 2 nd order overall. b) H2O2 is 2 nd order, I is 1 st order, 3 nd order overall. c) H2O2 is 0 th order, I is 1 st order, H + is 1 st order, 3 rd order overall. d) H2O2 is 2 nd order, I is 1 st order, H + is 0 th order, 3 rd order overall. Page 8
PRACTICE: REACTION ORDERS Answer each of the following question based on the following chemical reaction: 3 A (g) + B (g) + 2 C (g) D (g) Experiment Initial [A] Initial [B] Initial [C] Initial Rate 1 0.0500 M 0.0500 M 0.0100 M 6.25 x 10-3 2 0.1000 M 0.0500 M 0.0100 M 1.25 x 10-2 3 0.1000 M 0.1000 M 0.0100 M 5.00 x 10-2 4 0.0500 M 0.0500 M 0.0200 M 6.25 x 10-3 EXAMPLE 1: Calculate the reaction order for reactant A. PRACTICE: Calculate the reaction orders for reactants B and C. EXAMPLE 2: Calculate the rate constant and the new rate for the given reaction if the the initial concentrations of [A] = 0.300 M, [B] = 0.150 M and [C] = 0.150 M. Page 9
PRACTICE: RATE CONSTANT & RATE EXAMPLE 1: A certain chemical reaction has the given rate law: Rate = k [A] 3 [B] 2 [C] -1 What are the units of the rate constant for the given reaction? a) M -2 s -1 b) M 2 s -1 c) M -4 s -1 d) M -3 s -1 e) M 3 s -1 EXAMPLE 2: The reaction of 3 A + B 2 C + D, was found to be: Rate = k [A] 2 [B] 3. How much would the rate increase by if A were tripled while B were increased by half? a) 0.50 b) 30.38 c) 0.75 d) 20.25 e) 1.125 PRACTICE: If the rate law for the following reaction is found to be the following: Rate = [Cl 2 ] [HCCl 3 ]. What are the units for the rate constant, K? Cl2 (g) + HCCl3 (g) HCl (g) + CCl4 (g) a) M 3/2 s b) M s c) 1 M s d) 1 M 3/2 s e) M s Page 10
CONCEPT: REACTION PATHWAYS A reaction is a sequence of single reaction steps that add up to the overall chemical reaction. For example a possible chemical setup for the overall reaction: A + 2 B E might involve these steps: 1) A + B C 2) B + C D 3) D E EXAMPLE 1: The elementary reaction, 2 NOBr (g) 2 NO + Br2, is an example of a reaction. a) Unimolecular b) Dimolecular c) Bimolecular d) Tetramolecular EXAMPLE 2: Answer the following questions to the following reaction: Br + O2 + O BrO + O2 [FAST] Br + BrO + O Br2O + O [SLOW] a. Identify the intermediate(s). b. Identify the catalyst(s). c. What is the overall reaction? Page 11
CONCEPT: 1 ST, 2 ND or 0 TH : WHAT S YOUR ORDER? If you were super observant you might have noticed that although we were talking about rate, the rate law didn t include as a variable. Reaction : A B The good thing is that the Rate Laws help to answer an important question in kinetics: How long will it take x moles per liters of A to be consumed? Rate Laws Rate Equations Zero-Order First-Order Second-Order [A] t = kt +[A] 0 ln[a] t = kt + ln[a] 0 1 [A] t = kt + 1 [A] 0 [A] 0 ln[a] 0 [A] Slope = - k ln[a] Slope = - k 1/[A] Slope = k 1/[A] 0 Half-Life t 12 = [A] 0 2k t 12 = ln 2 k 1 t 12 = k[a] 0 Page 12
PRACTICE: INTEGRATED RATE LAWS (CALCULATIONS) EXAMPLE 1: The oxidation of ethane follows a first order mechanism, with a very high rate constant of 32 s -1, to form H2O and CO2 as products. If the initial [C2H6] is 4.12 M, what is the concentration after 1.12 x 10-3 minutes? EXAMPLE 2: Iodine-123 is used to study thyroid gland function. This radioactive isotope breaks down in a first order process with a half-life of 8.50 hours at 800 K. How long will it take for the concentration of iodine-123 to be 74.1% complete? PRACTICE 1: At 25 o C, 2 NOBr (g) 2 NO (g) + Br2 (g). The rate of the reaction is found to be: rate = k [NOBr] 2. The constant at 25 o C is 7.80 x 10-4 M -1 s -1. If 0.550 moles of HBr (g) is placed in a 5.0 L container, how long will take for the concentration to reach 0.063 moles of HBr (g)? PRACTICE 2: In a typical chemical reaction, nitrogen trioxide, NO3, reacts to produce nitrogen dioxide, NO2, and oxygen gas, O. 2 NO3 (g) 2 NO2 (g) + 2 O (g) A plot of [NO3] vs. time is linear and the slope is equal to 0.183. If the initial concentration of NO3 is 0.930 M, how long will it take for the final concentration to reach 0.400 M? Page 13
PRACTICE: INTEGRATED RATE LAWS (CALCULATIONS 2) EXAMPLE: Given the following graph for a second order reaction: a) Calculate the frequency factor. b) Calculate the energy of activation in (J/mol): 0.005 0.0045 0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0 ln K 0, 0.569 0.0047, 0 0 0.2 0.4 0.6 1/T (K) PRACTICE: The three plots were done based on a chemical reaction. a. What is the rate constant of the reaction if it takes 21.2 minutes for the reaction to be 38.0% complete? Page 14
CONCEPT: HALF LIFE Half-life is defined as the time it takes for half of the amount of a substance to decay in a certain amount of time. However, this is mainly true for a order reaction. Zero-Order First-Order Second-Order t 12 = [A] 0 2k t 12 = ln 2 k 1 t 12 = k[a] 0 Page 15
CONCEPT: INTEGRATED RATE LAWS Zeroth Order The concentration of reactants decreases in a uniform manner over time. The rate of the reaction remains constant. Concentration [Reactants] Rate [Products] Rate First Order The concentration of reactants decreases in a logarithmic manner. More recognizable by a constant half-life. The rate of the reaction decreases uniformly. Concentration [Reactants] Rate [Products] Rate Second-Order The largest drop in concentration occurs initially followed by a decreasing loss of reactant. More recognizable by an increasing half-life The rate of the reaction decreases substantially before leveling off. Concentration [Reactants] Rate [Products] Rate Page 16
CONCEPT: COLLISION THEORY Under Collision Theory, a chemical reaction is successful when it involves the union of two sufficiently energetic reactants. A B + A B In the Arrhenius equation the frequency factor A represents the number of approaches to the activation barrier per unit of time. k = A e Ea/RT A = E a = R = T = Frequency Factor Energy of Activation Gas Constant 8.314 J/mol * K Temperature In the collision theory model, the frequency factor can be split into two new variables: k = A e Ea/RT = p z e Ea/RT p = z = The larger a reacting molecule then the the orientation factor. H (g) + Cl (g) HCl (g) H 2 O (l) + CO 2 (g) H 2 CO 3 (aq) Rate of Reaction = Number of Fraction of Sufficiently Collisions Energetic Collisions Fraction of Collisions w/ proper orientation } } } (Frequency) (Energy) (Probability) Page 17