General Chemistry I Concepts - PDF Free Download

Chemical Kinetics

Chemical Kinetics The Rate of a Reaction (14.1) The Rate Law (14.2) Relation Between Reactant Concentration and Time (14.3) Activation Energy and Temperature Dependence of Rate Constants (14.4) Reaction Mechanisms (14.5) Catalysis (14.6)

General Chemistry I Concepts Representations of matter (1.3 and 1.4) Molar concentrations of solutions, particularly units (4.5) Kinetic molecular theory of gases (5.6) Enthalpy and energy diagrams (6.4 and 6.6)

14.1 The Rate of a Reaction What has to happen for a reaction to occur? Consider H 2 (g) + Cl 2 (g) 2HCl(g) What has to happen for the reactants to become products: What bonds need to break/form? Will this take place in one big step or many small steps? (What might these look like? How can we quantify rate?) How can we monitor this over time? How might this impact how long the reaction takes? Kinetics is the study of the arrow and how a reaction happens.

14.1 The Rate of a Reaction Key Definitions: Chemical Kinetics area of chemistry concerned with the speed, or rate, at which a chemical reaction occurs What is rate? How would a rate of a reaction be represented? What would make sense to monitor over time? Reaction rate change in concentration of a reactant or product with time (M/s) How is this represented (generically) and for a: Change in concentration of products Change in concentration of reactants

14.1 The Rate of a Reaction Consider a reaction A reacting to form B What is the stoichiometry of this reaction? What are the rate expression for A and B? Figure 14.2, p. 471

14.1 The Rate of a Reaction What if the stoichiometry of a reaction is not 1:1? What is the stoichiometry of this reaction? What are the rate expression for A and B?

14.1 The Rate of a Reaction Let s consider a reaction of N 2 O 5 decomposing to form NO 2 and O 2 N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) Concentration at 0 s Concentration at 25 s N 2 O 5 2.0 M 1.0 M NO 2 0 M 0 M O 2 concentration What are the missing values What are the rate expressions and the rate? For any reaction (use ar bp), what is rate?

14.1 The Rate of a Reaction What is the best way to determine rate? Is rate constant over time? What is the best time interval to select? Consider our reaction of N 2 O 5 Figure 14.2, p. 471

Decomposition of N 2 O 5 (g) N 2 O 5 / M NO 2 / M O 2 / M 2 0 0 1.95 0.1 0.025 1.9 0.2 0.05 1.85 0.3 0.075 1.8 0.4 0.1 1.75 0.5 0.125 1.7 0.6 0.15 1.65 0.7 0.175 1.6 0.8 0.2 1.55 0.9 0.225 1.5 1 0.25 1.45 1.1 0.275 1.4 1.2 0.3 1.35 1.3 0.325 1.3 1.4 0.35 1.25 1.5 0.375 1.2 1.6 0.4 1.15 1.7 0.425 1.1 1.8 0.45 1.05 1.9 0.475 1 2 0.5

2.5 Reaction of N 2 O 5 Decomposition of N 2 O 5 (g) Concentration / M 2 1.5 1 0.5 N2O5 N 2 O 5 NO2 2 O2 O 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Counts

Decomposition of N 2 O 5 (g) N 2 O 5 / M NO 2 / M O 2 / M Time / s 2 0 0 0 1.95 0.1 0.025 1 1.9 0.2 0.05 2 1.85 0.3 0.075 3 1.8 0.4 0.1 4 1.75 0.5 0.125 5 1.7 0.6 0.15 6 1.65 0.7 0.175 7 1.6 0.8 0.2 8 1.55 0.9 0.225 9 1.5 1 0.25 10 1.45 1.1 0.275 12 1.4 1.2 0.3 13 1.35 1.3 0.325 14 1.3 1.4 0.35 16 1.25 1.5 0.375 17 1.2 1.6 0.4 18 1.15 1.7 0.425 20 1.1 1.8 0.45 22 1.05 1.9 0.475 23 1 2 0.5 25

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 Reaction of N 2 O 5 0 50 100 150 200 250 Time / s N2O5 N 2 O 5 NO2 O 2 O2 NO 2 Decomposition of N2O5(g) Concentraion / M

14.1 The Rate of a Reaction What is the best way to determine rate? What is the best time interval to select? Figure 14.5, p. 473

First-order reaction Plotting [N 2 O 5 ] as a function of time (s) N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) [N 2 O 5 ] / M Same time interval (10 seconds), but same rate? Time / s

14.1 The Rate of a Reaction What is the best way to determine rate? What is the best time interval to select? What should we monitor/measure: reactant or product concentration changes? Need a means to measure concentration: Color changes (can use UV-VIS spectroscopy) Gas formation (pressure or volume of a gas generated) Conductivity (changes in ionic species resulting in changes measured with a conductivity probe)

14.2 The Rate Laws Key Definitions: Instantaneous rate slope of the tangent to the curve (or the derivative) or the rate at one time Using the plot of N 2 O 5 decomposition, add two instantaneous rates Why does it make sense to measure the concentration of reactants rather than products? Initial rate change in concentration of reactants at the initial point (without any products present) Where is the initial rate for the decomposition of N 2 O 5?

14.2 The Rate Laws What do changes in rate versus changes in concentration tell us? What if there is a change in rate for a change in concentration? What if there is no change in rate for a change in concentration? How can we determine or generate this? Method 1: plot rate vs. concentration for 1 experiment Method 2: do multiple experiments and determine multiple rates

First-order reaction Plotting [N 2 O 5 ] as a function of time (s) N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) [N 2 O 5 ] / M Time / s

First-order reaction Plotting [N 2 O 5 ] as a function of rate (M / s) N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) [N 2 O 5 ] / M What does this plot and linear fit data show? What does this mean? Rate (M / s)

14.2 The Rate Laws What is the rate law? an expression relating the rate of a reaction to the rate constant and the concentrations of the reactants What is the rate law for the decomposition of N 2 O 5 using Method 1?

14.2 The Rate Laws What is the rate law using the experimental data below (Method 2)? Experiment Initial rate M/ s Initial [N 2 O 5 ] M 1 0.0554 2.0 2 0.0277 1.0 3 0.0139 0.5 4 0.0069 0.25

14.2 The Rate Laws Key Definition: Rate constant, k: a constant of proportionality between the reaction rate and the concentration of the reactants What is the slope of the line for [N 2 O 5 ] vs. rate? What does k tell us: If k is large or small Units on k How will k vary? Is k intensive or extensive?

14.2 The Rate Laws Key Definition: Reaction order: the sum of the powers to which all reactant concentrations appearing in the rate law are raised What is the reaction order for the decomposition of N 2 O 5? What are the units on k for different reaction orders? How are reaction orders and rate constants determined? How can logarithms be useful in solving for reaction order?

14.2 The Rate Laws Practice: What is the rate law? What is k? Experiment Initial rate M/ s [CHCl 3 ] M [Cl 2 ] M 1 0.2846 0.10 2.0 2 0.1423 0.05 2.0 3 1.206 2.0 0.09 4 0.402 2.0 0.01 Must reaction orders be integers? How are reaction orders and rate constants determined?

First-order reactions 14.3 Relation Between Reactant Concentration and Time First-order reactions: Represent the rate by the change in concentration of reactant Represent the rate by the rate law A kt A A kt 0 ln ln ln t 0 A t

14.3 Relation Between Reactant Concentration and Time First-order reactions Back to N 2 O 5 What is the order of this reaction? Plotting what will yield a linear plot? What is the slope of the line?

First-order reaction Plotting ln [N 2 O 5 ] as a function of time (s) N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) ln [N 2 O 5 ] / M Time / s

First-order reaction Plotting [N 2 O 5 ] as a function of time (s) N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) [N 2 O 5 ] / M Time / s

14.3 Relation Between Reactant Concentration and Time First-order reactions Back to N 2 O 5 What is the order of this reaction? Plotting what will yield a linear plot? What happens after 25 seconds? What happens after 50 seconds? What happens after 75 seconds?

First-order reaction Plotting [N 2 O 5 ] as a function of time (s) N 2 O 5 (g) 2NO 2 (g) + ½O 2 (g) [N 2 O 5 ] / M At 25 s, [N 2 O 5 ] = 1.0 M At 50 s, [N 2 O 5 ] = 0.5 M At 75 s, [N 2 O 5 ] = 0.25 M Time / s

First-order reactions 14.3 Relation Between Reactant Concentration and Time What is the equation for half life (t ½ )? Consider issues of storing 235 U with a half life of 6.37 10 4 years. What mass will be left of a 1.000 g sample after 2000 years? Is this true only for a first order reaction?

Second-order reactions 14.3 Relation Between Reactant Concentration and Time Second order reactions Represent the rate by the change in concentration of reactant Represent the rate by the rate law 1 1 kt A A t 0

Second-order reactions 14.3 Relation Between Reactant Concentration and Time The decomposition of NOCl to NO and Cl 2 has the experimental data shown: Time / hour [NOCl] / M 0.00 4.46 0.25 4.28 0.50 4.11 0.75 3.95 1.00 3.81 1.25 3.67 1.50 3.55 1.75 3.43 2.00 3.32 2.25 3.22

Second-order reactions 14.3 Relation Between Reactant Concentration and Time How do we determine reaction order and the rate law? Compare rates and concentrations Plot [NOCl] versus time with linear plots of: [NOCl] vs time = zero order ln [NOCl] vs time = first order 1 / [NOCl] vs time = second order

Determining Reaction Order Plotting [NClO] as a function of time (hr) NOCl(g) NO(g) + ½Cl 2 (g) [NOCl] 0 = 4.46 mol/l [NOCl] / M Time / hr

Determining Reaction Order Plotting ln [NClO] as a function of time (hr) NOCl(g) NO(g) + ½Cl 2 (g) [NOCl] 0 = 4.46 mol/l ln [NOCl] / M Time / hr

Determining Reaction Order Plotting 1/ [NClO] as a function of time (hr) NOCl(g) NO(g) + ½Cl 2 (g) [NOCl] 0 = 4.46 mol/l 1 / [NOCl] (1/M) Time / hr

Second-order reactions 14.3 Relation Between Reactant Concentration and Time The decomposition of NOCl to NO and Cl 2 is a second order reaction. What is the rate law and k? rate = k [NOCl] 2 k = 0.03844 L mol 1 h 1 What is the half-life? Is it one value? 1 1 1 kt t 1 2 0 0 A A k A t

Second-order reaction Plotting [NClO] as a function of time (hr) NOCl(g) NO(g) + ½Cl 2 (g) [NOCl] 0 = 4.46 mol/l [NOCl] / M At 5.83 h, [NOCl] = ½[NOCl] 0 = 2.23 M t ½ = 5.83 h At 17.5 h, [NOCl] = ¼ [NOCl] 0 = 1.12 M Time / hr t ½ = 11.7 h

Zero-order reactions 14.3 Relation Between Reactant Concentration and Time Zero order reactions: Represent the rate by the change in concentration of reactant Represent the rate by the rate law A kt A t t 0 A 0 1 2 2 k

Order of Reaction Zero-order First-order Second-order Rate law Units on rate constant, k Half-life, t ½ A rate k A 0 k t M time t or mol L time A 0 1 2 2 k A rate t time 1 k A or time A rate t or 2 k A 1 1 1 L 0.693 t 12 k M time t mol time 1 1 2 A 0 k Integrated rate law t 0 A A kt ln ln t 0 A A kt A t 1 1 A A t 0 A 0 A kt e A 0 t 1 A 0 kt kt

14.4 Activation Energy and Temperature Dependence of Rate Constants For a reaction to occur, what must happen? Consider our second order reaction: NOCl g NO g 1 Cl 2 2 g rate k NOCl 2 What must happen for NO and Cl 2 to form?

14.4 Activation Energy What if we just consider collisions? rate collisions s Do the molecules only need to collide? What must also be true for a reaction to occur?

Let s think about this reaction and try to understand what goes into a reaction happening

14.4 Activation Energy and Temperature Dependence of Rate Constants In order to have this reaction happen requires: Collision Sufficient energy Correct orientation Formation of an activated complex What does this look like in an energy diagram?

Or more general

14.4 Activation Energy What is activation energy? If the activation energy is large, what does this mean in terms of: The kinetic energy required for this reaction to occur The rate of the reaction and the value of k If the activation energy is small, what does this mean in terms of: The kinetic energy required for this reaction to occur The rate of the reaction and the value of k

14.4 Activation Energy (5.6) Review: Describe the Maxwell- Boltzmann distribution.

14.4 Activation Energy Consider a gas at 300 K:

14.4 Activation Energy Now consider one reaction at two temperatures (100 K and 300 K):

14.4 Activation Energy Will E a change with temperature? Will the rate change with temperature? How is this modeled in an equation: E a E RT k Ae ln k a ln A RT Consider a reaction between CO and NO 2 to form CO 2 and NO

Second-order reaction Plotting ln k as a function of 1 / Temperature NO 2 (g) + CO(g) NO(g) + CO 2 (g) ln k 1 / T

14.4 Activation Energy How many points are needed? ln k2 E 1 1 a E a T2 T 1 k1 R T1 T2 R TT 1 2 Frequency factor = A Orientation factor = p k pae E a RT

14.4 Activation Energy Practice: For an activation energy of 45.5 kj/mol for a particular reaction, if the rate constant at 300 K is k 1, at what temperature will the rate constant double?

14.5 Reaction Mechanisms Assuming that there is sufficient energy and orientation, what reactions are possible: A Products A A Products A B Products A 2B Products A B C Products

14.5 Reaction Mechanisms Why does the rate law not necessarily relate to the stoichiometric coefficients? 2CH l 25O g 16CO g 18HO l 8 18 2 2 2 Does this happen? Does this happen in this elementary step? What is a reasonable first elementary step Do the stoichiometric coefficients of the balanced equation give information about the elementary step? Why or why not?

14.5 Reaction Mechanisms Key Definition: Reaction mechanism: the sequence of elementary steps that leads to product formation What does this mean? Overall reaction: A B C Elementary step 1: A E Elementary step 2: E B C For the reaction to the above, are the elementary steps reasonable (possible)? Do the elementary steps add up to the overall reaction? Is this reaction mechanism reasonable?

14.5 Reaction Mechanisms Consider: NO g CO g NO g CO g 2 2 Without a catalyst, this occurs in two steps: NO g NO g NO g NO g k 1 2 2 3 NO g CO g NO g CO g k 2 3 2 2 k 1 << k 2

14.5 Reaction Mechanisms Key Definitions: Rate determining step (RDS): The slowest step in the sequence of steps leading to product formation What is the rate determining step for the reaction of NO 2 and CO? Intermediate: Appears in the mechanism of the reaction (that is, the elementary steps) but not in the overall balanced equation What is the intermediate in the reaction of NO 2 and CO?

14.5 Reaction Mechanisms How does an experimental rate law help in determining: A rate determining step A reaction mechanism What does an energy diagram for a twostep process look like?

14.5 Reaction Mechanisms Practice: If the data is given for the reaction of NO 2 and CO, is this consistent with the theoretical rate law? Experiment [NO 2 ] / M [CO] / M Rate (M / min) 1 0.20 0.20 0.0900 2 0.10 0.20 0.0225 3 0.20 0.10 0.0900 4 0.20 0.05 0.0900

14.6 Catalysis Key Definition: Catalyst: A catalyst is a substance that increases the rate of a reaction by lowering the activation energy How can E a change? With temperature? With a change in reaction? What does a catalyst really do? Think about this in terms of an energy diagram

14.6 Catalysis Figure 14.20, p. 494

14.6 Catalysis How can these be identified in a reaction or a reaction mechanism? What are some examples of catalysis? Heterogeneous catalysis Homogeneous catalysis Enzyme catalysis