Chapter Chemical Kinetics Reaction Rates 0 Reaction Rate: The change in the concentration of a reactant or a product with time (M/s). Reactant Products aa bb Rate = [A] t Rate = [B] t Reaction Rates 0 Reaction Rates 03 Consider the decomposition of N O 5 to give NO and O : N O 5 (g) 4 NO (g) + O (g)
Rate Law & Reaction Order 0 Rate Law & Reaction Order 0 Rate Law: Shows the relationship of the rate of a reaction to the rate constant and the concentration of the reactants raised to some powers. For the general reaction: aa + bb cc + dd rate = k[a] x [B] y x and y are NOT the stoichiometric coefficients. k = the rate constant Reaction Order: The sum of the powers to which all reactant concentrations appearing in the rate law are raised. Reaction order is determined experimentally:. By inspection.. From the slope of a log(rate) vs. log[a] plot. Rate Law & Reaction Order 03 Rate Law & Reaction Order 04 Determination by inspection: aa + bb cc + dd Rate = R = k[a] x [B] y Use initial rates (t = 0) R R R R k[ A] [ B] = k[ A] [ B] x x [ A] y y x [ A] = [ A] x [ B] B [ ] = if [B] = [B] [ A] y Determination by plot of a log(rate) vs. log[a]: aa + bb cc + dd Rate = R = k[a] x [B] y Log(R) = log(k) + x log[a] + y log[b] = const + x log[a] if [B] held constant
Rate Law & Reaction Order 05 Rate Law & Reaction Order 06 The reaction of nitric oxide with hydrogen at 80 C is: NO (g) + H (g) N (g) + H O (g) From the following data determine the rate law and rate constant. Experiment [NO] [H] Initial Rate (M/s) 5.0 x 0 3.0 x0 3.3 x 0 5 0.0 x0 3.0 x 0 3 5.0 x 0 5 3 0.0 x0 3 4.0 x 0 3 0.0 x 0 5 The reaction of peroxydisulfate ion (S O 8 - ) with iodide ion (I - ) is: S O 8 - (aq) + 3 I - (aq) SO 4 - (aq) + I 3 - (aq) From the following data, determine the rate law and rate constant. Experiment [SO8 - ] [I - ] Initi al Rate (M/s) 0.080 0.034. x 0-4 0.080 0.07. x 0-4 3 0.6 0.07. x 0-4 Rate Law & Reaction Order 07 First-Order Reactions 0 Rate Constant: A constant of proportionality between the reaction rate and the concentration of reactants. rate [Br ] rate = k[br ] First Order: Reaction rate depends on the reactant concentration raised to first power. Rate = - A [ ] t Rate = k[a] 3
First-Order Reactions 0 First-Order Reactions 03 Using calculus we obtain the integrated rate equation: Identifying First-Order Reactions: ln [A] t = kt or ln[a] t ln[a] o = kt [A] 0 Plotting ln[a] t against t gives a straight line of slope k. An alternate expression is: [A] t = [A] 0 e kt exponential decay law First-Order Reactions 04 First-Order Reactions 06 Show that the decomposition of N O 5 is first order and calculate the rate constant. Half-Life: Time for reactant concentration to decrease by half its original value. t = ln k 4
Second-Order Reactions 0 Second-Order Reactions 0 Second-Order Reaction: A Products Rate = k[a] These can then be integrated to give: [A] t = kt + [A] 0 A + B Products Rate = k[a][b] Half-Life: Time for reactant concentration to decrease by half its original value. t = k[a] 0 Second-Order Reactions 03 Reaction Mechanisms 0 Iodine atoms combine to form molecular iodine in the gas phase. I (g) + I (g) I (g) This reaction follows second-order kinetics and k = 7.0 x 0 M s at 3 C. (a) If the initial concentration of I was 0.086 M, calculate the concentration after.0 min. (b) Calculate the half-life of the reaction if the initial concentration of I is 0.60 M and if it is 0.4 M. A reaction mechanism is a sequence of molecular events, or reaction steps, that defines the pathway from reactants to products. 5
Reaction Mechanisms 0 Reaction Mechanisms 03 Single steps in a mechanism are called elementary steps (reactions). An elementary step describes the behavior of individual molecules. An overall reaction describes the reaction stoichiometry. NO (g) + CO(g) NO(g) + CO (g) NO (g) + NO (g) NO(g) + NO 3 (g) NO 3 (g) + CO(g) NO (g) + CO (g) Overall Elementary Elementary The chemical equation for an elementary reaction is a description of an individual molecular event that involves the breaking and/or making of chemical bonds. Reaction Mechanisms 04 Reaction Mechanisms 05 Molecularity: is the number of molecules (or atoms) on the reactant side of the chemical equation. Unimolecular: Single reactant molecule. Bimolecular: Two reactant molecules. Termolecular: Three reactant molecules. 6
Reaction Mechanisms 06 Rate Laws and Reaction Mechanisms 0 Determine the overall reaction, the reaction intermediates, and the molecularity of each individual elementary step. Rate law for an overall reaction must be determined experimentally. Rate law for elementary step follows from its molecularity. Rate Laws and Reaction Mechanisms 0 Rate Laws and Reaction Mechanisms 03 The rate law of each elementary step follows its molecularity. The slowest elementary step in a multistep reaction is called the rate-determining step. The overall reaction is a sequence of elementary steps called the reaction mechanism. Therefore, the experimentally observed rate law for an overall reaction must depend on the reaction mechanism. The overall reaction cannot occur faster than the speed of the rate-determining step. The rate of the overall reaction is therefore determined by the rate of the rate-determining step. 7
Rate Laws and Reaction Mechanisms 04 Rate Laws and Reaction Mechanisms 05 The following reaction has a second-order rate law: H (g) + ICl(g) I (g) + HCl(g) Rate = k[h ][ICl] Devise a possible mechanism. The following substitution reaction has a first-order rate law: Co(CN) 5 (H O) (aq) + I Co(CN) 5 I 3 (aq) + H O(l) Rate = k[co(cn) 5 (H O) ] Suggest a mechanism in accord with the rate law. The Arrhenius Equation 0 The Arrhenius Equation 0 Collision Theory: A bimolecular reaction occurs when two correctly oriented molecules collide with sufficient energy. Activation Energy (E a ): The potential energy barrier that must be surmounted before reactants can be converted to products. 8
The Arrhenius Equation 03 The Arrhenius Equation 04 This relationship is summarized by the Arrhenius equation. k = Ae E a RT Taking logs and rearranging, we get: lnk = E a + lna R T The Arrhenius Equation 05 The Arrhenius Equation 07 Temp ( C) 83 356 393 47 508 k (M - s - ) 3.5e-7 3.0e5.9e-4.6e-3 3.95e- The second-order rate constant for the decomposition of nitrous oxide (N O) into nitrogen molecule and oxygen atom has been measured at different temperatures: k(m k - s - ) t( C) t Determine graphically.87x0-3 600 the activation energy 0.03 650 for the reaction. 0.0569 700 0.44 750 9
The Arrhenius Equation 09 Catalysis 0 A simpler way to use this is by comparing the rate constant at just two temperatures: ln k = E a k R T T If the rate of a reaction doubles by increasing the temperature by 0 C from 98. K to 308. K, what is the activation energy of the reaction? A catalyst is a substance that increases the rate of a reaction without being consumed in the reaction. Catalysis 0 Catalysis 03 The relative rates of the reaction A + B AB in vessels a d are :::. Red = A, blue = B, yellow = third substance C. (a) What is the order of reaction in A, B, and C? (b) Write the rate law. (c) Write a mechanism that agrees with the rate law. (d) Why doesn t C appear in the overall reaction? Homogeneous Catalyst: Exists in the same phase as the reactants. Heterogeneous Catalyst: Exists in different phase to the reactants. 0
Catalysis 04 Catalysis 05 Catalytic Hydrogenation: