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Chemical Kinetics Chapter 13 13.1-13.6

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Chemical Kinetics In learning chemical kinetics, you will learn how to: –Predict whether or not a reaction will take place. –Once started, determine how fast a reaction will proceed. –Learn how far a reaction will go before it stops.

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Rate of a Reaction Thermodynamics- Does a reaction take place? Kinetics- How fast does a reaction proceed? Chemical Kinetics- the area of chemistry concerned with the speeds or rates at which a chemical reaction occurs. Reaction Rate- the change in the concentration of a reactant or product with time. (M/s)

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Rate of a Reaction Why do we need to know the rate of a reaction? –Practical knowledge is always useful –Preparation of drugs –Food processing –Home repair

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Rate of a Reaction General equation for a reaction: –A → B –Reactant → Product In order to monitor a reaction’s speed or rate, we can look at one of two things: –Decrease in [ reactant ] –Increase in [ product ] –Can be represented as: rate = - Δ [A] / Δ tor rate = Δ [B] / Δ t

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Rate of a Reaction

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How do we measure this experimentally? –For reactions in solution: Changes in concentration can be measured spectroscopically –For reactions involving gases: Changes in pressure can be measured –For reactions in solution with ions present: Change in concentrations can be measured through electrical conductance

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Rate of a Reaction So if we have an aqueous solution of molecular bromine and formic acid, how do we determine the reaction rate? Br 2 (aq) +HCOOH (aq) → 2Br – (aq) +2H + (aq) +CO 2 (g) time

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Rate of a Reaction Look for color changes Molecular bromine is usually reddish- brown in color. Formic acid is colorless. As the reaction progresses, the color of the solution changes. It fades until it becomes colorless. What does this mean?

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Rate of a Reaction

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Rate Calculations How do we calculate the rate of a reaction? –We first need this information: Time (s) [reactant]

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Rate Calculations Br 2 (aq) + HCOOH (aq) → 2Br – (aq) + 2H + (aq) + CO 2 (g)

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Rate Calculations Instantaneous Rate– rate of a reaction for a specific point in time. Average Rate vs. Instantaneous rate –Examples????

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Rate Calculations Average Rate = -Δ [Br 2 ] / Δt = - [Br 2 ] final – [Br 2 ] initial / [t] final – [t] initial Instantaneous Rate = rate for specific instance in time [Br 2 ] / t

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Rate Calculations Using this information, calculate the average rate of the bromine reaction over the first 50s of the reaction.

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Rate Calculations Average Rate = - [Br 2 ] final – [Br 2 ] initial / [t] final – [t] initial Average Rate = - (0.0101- 0.0120)M / (50s – 0s) Average Rate = -0.002M / 50s Average Rate = 3.80 x 10 -5 M/s

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Average Rate

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Reaction Rates and Stoichiometry For reactions more complex than A → B we cannot use the rate expression initially described. Example: –2A → B –Disappearance of A is twice as fast formation of B –Rate = - ½ Δ[A] /Δt

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Reaction Rates and Stoichiometry In general, for the reaction –aA + bB → cC + dD –Rate = - 1/a Δ[A] /Δt = - 1/b Δ[B] /Δt = 1/c Δ[C] /Δt = 1/d Δ[D] /Δt

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Reaction Stoichiometry Write the rate expression for the following reaction: CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O (g) rate = - [CH 4 ] tt = - [O 2 ] tt 1 2 = [CO 2 ] tt = [H 2 O] tt 1 2

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Rate Constant Look back to molecular bromine chart. What is k? –K- the rate constant. A constant of proportionality between the reaction rate and the concentration of the reactant. –K may change slightly over time. –K is represented as: K = rate/ [reactant] K is not affected by the [reactant] or rate alone, since it is a ratio of these two. At any given point on a graph, k should be similar in value to it’s value at other points in the same graph.

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Rate Constant

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The Rate Law Rate Law- expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some power. Using the general reaction: aA + bB → cC + dD aA + bB → cC + dD Rate Law is: Rate Law is: rate = k [A] x [B] y rate = k [A] x [B] y

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The Rate Law aA + bB cC + dD Rate = k [A] x [B] y reaction is xth order in A reaction is yth order in B reaction is (x + y)th order overall

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Reaction Order Reaction Order- the sum of the powers to which all reactant concentrations appearing in the rate law are raised. Reaction order is always defined in terms of reactant concentration. Overall reaction order- x + y Example: Rate = k [F 2 ] [ClO 2 ] Reaction order = first Overall reaction order = second

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Reaction Order What is the rate expression for aA + bB → cC + dD where x=1 and y=2? –Rate = k[A][B] 2 What is the reaction order? –First in A, second in B Overall reaction order? –2 +1 = 3

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Reaction Order F 2 (g) + 2ClO 2 (g) 2FClO 2 (g) rate = k [F 2 ] x [ClO 2 ] y

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Reaction Order If initially [F 2 ] = 1.0M and [ClO 2 ]=1.0M, what will happen to the reaction rate if F 2 is doubled? If initially [F 2 ] = 1.0M and [ClO 2 ]=1.0M, what will happen to the reaction rate if F 2 is doubled? Rate 1 = k(1.0M)(1.0M) 2 Rate 1 = k(1.0M 3 )[F 2 ] = 1.0M Rate 2 = k(2.0M)(1.0M) 2 Rate 2 = k(2.0M 3 )[F 2 ] = 2.0M Rate 2 = 2 x Rate 1

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Reaction Order What will happen in the same reaction if the [ClO 2 ] is doubled? What will happen in the same reaction if the [ClO 2 ] is doubled? Rate 1 = k(1.0M)(1.0M) 2 Rate 1 = k(1.0M)(1.0M) 2 Rate 1 = k(1.0M 3 )[ClO 2 ] = 1.0M Rate 2 = k(1.0M)(2.0M) 2 Rate 2 = k(4.0M 3 )[ClO 2 ] = 2.0M Rate 2 = 4 x Rate 1 Rate 2 = 4 x Rate 1

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Determination of Rate Law Experiment [F 2 ] [ClO 2 ] Rate (M/s) 10.040.03 1.0x10 -2 20.040.04 2.0x10 -2 30.020.04 1.0x10 -2 40.040.06 2.0x10 -2 F 2 (g) + 2ClO 2 (g) 2FClO 2 (g)

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Determination of Rate Law Experiments 1 & 4 As [F 2 ] doubles, so does the rate Experiments 2 & 3 As [ClO 2 ] doubles, so does the rate 2:2 ratio…..1:1 ratio x = 1 and y = 1 Rate = k [F 2 ] [ClO 2 ]

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Rate law/Expression Calculations Experimen t [S 2 O 8 2- ] [I - ] Initial Rate (M/s) 10.080.034 2.2 x 10 - 4 20.080.017 1.1 x 10 - 4 30.160.017 2.2 x 10 - 4 rate = k [S 2 O 8 2- ] x [I - ] y Double [I - ], rate doubles (experiment 1 & 2) y = 1 Double [S 2 O 8 2- ], rate doubles (experiment 2 & 3) x = 1 k = rate [S 2 O 8 2- ][I - ] = 2.2 x 10 -4 M/s (0.08 M)(0.034 M) = 0.08/Ms rate = k [S 2 O 8 2- ][I - ] Determine the rate law and calculate the rate constant for the following reaction from the following data: S 2 O 8 2- (aq) + 3I - (aq) 2SO 4 2- (aq) + I 3 - (aq)

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Rate Law/Reaction Order Rate laws are always determined experimentally Reaction order is always defined in terms of reactant Reactant order is not related to the stoichiomteric coefficient in the overall reaction. F 2 (g) + 2ClO 2 (g) 2FClO 2 (g) rate = k [F 2 ][ClO 2 ]

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Relation between Reactant Concentration and Time First Order Reaction- a reaction whose rate depends on the reactant concentration raised to the first power. Reaction Type: A → B Rate of: -Δ [A]/Δt or k[A] Combining and simplifying these equations brings us to the following rate equation: ln[A] t = -kt + ln[A 0 ]

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Relation between Reactant Concentration and Time

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Reaction Time The reaction 2A B is first order in A with a rate constant of 2.8 x 10 -2 s -1 at 80 0 C. How long will it take for A to decrease from 0.88 M to 0.14 M ? ln[A] = ln[A] 0 - kt kt = ln[A] 0 – ln[A] t = ln[A] 0 – ln[A] k = 66 s [A] 0 = 0.88 M [A] = 0.14 M ln [A] 0 [A] k = ln 0.88 M 0.14 M 2.8 x 10 -2 s -1 =

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Decomposition of Nitrogen Pentoxide Data on page 560 Plot of ln[N2O5] (M) vs. t (s) will allow us to see and calculate more information about the reaction taking place

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Decomposition of Nitrogen Pentoxide

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Gas Phase Reactions First order gas phase reactions have a linear relationship between partial pressure of gas and time. lnP t = -kt + lnP 0 lnP t = -kt + lnP 0

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Gas Phase Reactions

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Reaction Half-life As a reaction proceeds, the concentrations of the reactants decreases. Another way to measure [reactant] over time is to use the half-life. Half-life, t 1/2 – the time required for the concentration of a reactant to decrease to half of its initial concentration.

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Reaction Half-life Expression for half-life of a first order reaction is: t 1/2 = ln2/k t 1/2 = ln2/k or or t 1/2 = 0.693/k t 1/2 = 0.693/k

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Reaction Half-life

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What is the half-life of N 2 O 5 if it decomposes with a rate constant of 5.7 x 10 -4 s -1 ? t½t½ ln2 k = 0.693 5.7 x 10 -4 s -1 = = 1200 s = 20 minutes t½t½ t½t½ t½t½

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Second-Order Reactions Second-order reaction- a reaction whose rate depends on the concentration of one reactant raised to the second power OR on the concentrations of two different reactants, each raised to the first power. Simple Type: A → B – rate = k[A] 2 Complex Type: A + B → C –rate = k[A][B]

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Second-order Reactions For A → B, the following expression is used: 1 [A] = 1 [A] 0 + kt

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Half-life of a Second-order Reaction Equation for half-life What is the difference between this equation and the equation for half- life of first-order reactions? t ½ = 1 k[A] 0

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Zero-order Reactions Very rare reactions Usually occur on metallic surfaces Half-life Equation: Reaction rate is described by: –Rate = k –Why? t ½ = [A] 0 2k2k

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Summary

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Activation Energy and Temperature Dependence of Rate Constants

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The Collision Theory of Chemical Kinetics Gas molecules frequently collide with one another Expect that the rate of a reaction is equivalent to the number of collisions Reaction rate is dependent on concentration

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The Collision Theory of Chemical Kinetics Activation Energy (E a )- the minimum amount of energy required to initiate a chemical reaction. Activated Complex (Transition State)- a temporary species formed by the reactant molecules as a result of the collision before they form the product.

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The Collision Theory of Chemical Kinetics What does this have to do with temperature? –High energy molecules –High temperatures –Increased product formation

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The Collision Theory of Chemical Kinetics Factors that affect rate –1. –2. –3.

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The Arrhenius Equation Relation between activation energy and temperature. lnk = (E a /R) x (1/T) + lnA lnk = (E a /R) x (1/T) + lnA

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Rate Constants and Temperature lnK 1 = E a x (T 1 – T 2 ) lnK 1 = E a x (T 1 – T 2 ) lnK 2 R (T 1 T 2 )

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Activation Energy, Reaction Rates and Temperature As stated earlier, for a reaction to take place, molecules must posses enough kinetic energy. Kinetic energy must be higher than E a. Each reaction takes place at a specific temperature……but what happens if we adjust this temp.?

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Activation Energy, Reaction Rates and Temperature Increasing Temperature leads to: –Molecules reach high ke faster –Number of molecules with high enough ke increases –Reaction rate increases

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Catalysts A catalyst is defined by the ability of a substance to do each of the following: –Catalysts increase the rate of reaction. –Catalysts are not consumed by the reaction. –A small quantity of catalyst should be able to affect the rate of reaction for a large amount of reactant. –Catalysts do not change the equilibrium constant for the reaction.

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Catalysts Heterogeneous catalyst- the reactants and the catalyst are in different phases. catalyst = solid reactants = liquid/gas Homogeneous catalyst- catalyst and reactants are in the same phase, usually liquid.

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Catalysts

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Enzyme Catalysts

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The End!!!!!!!

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