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Chemical Kinetics Chapter 13

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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 Drugs- drug interactions, making pharmaceuticals Food Processing- making glazes, combining foods, flavors Home repair- grout, cement, etc.

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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 t or rate = Δ [B] / Δ t Change in concentration (M) over time (t)

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Rate of a Reaction Progression of a to b over time.

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Rate of a Reaction Graph of a and b

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**Rate of a Reaction 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 By definition, we know that in order to measure the rate of a reaction, we have to measure the concentration of the reactants and products….but how do we do this?

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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? Br2(aq)+HCOOH(aq) → 2Br–(aq)+2H+(aq)+CO2 (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? If the color is fading, then the concentration of bromine is decreasing. How can you double check that this is true? Spectrophotometer. Plot wavelength vs. absorption.

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Rate of a Reaction Wavelength vs. absorption graph

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**Rate Calculations How do we calculate the rate of a reaction?**

We first need this information: Time (s) [reactant] Now if you are asked to perform these calculations on a test, then you will have a rate chart provided.

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Rate Calculations Br2 (aq) + HCOOH (aq) → 2Br– (aq) + 2H+ (aq) + CO2 (g) Table rate of reactions

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

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**Rate Calculations Average Rate =**

-Δ [Br2] / Δt = - [Br2]final – [Br2]initial / [t]final – [t]initial Instantaneous Rate = rate for specific instance in time [Br2] / 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 = - [Br2]final – [Br2]initial / [t]final – [t]initial Average Rate = - ( )M / (50s – 0s) Average Rate = M / 50s Average Rate = 3.80 x 10-5 M/s

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Average Rate Different rates can be accounted for by mistakes in experiments. The ratio never changes, but the rate value may slightly change.

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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: CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (g) rate = - D[CH4] Dt = - D[O2] Dt 1 2 = D[CO2] Dt = D[H2O] Dt 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 Small deviations in k are only due to experimental deviations or changes in temperature. Rate vs. reactant concentration graph. K increases with concentration, but the ratio stays the same. “straight line” means direct proportionality.

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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 Rate Law is: rate = k [A]x[B]y X and y are numbers that must be determined experimentally. X and y are not equal to the stoichiometric coefficients a and b.

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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 [F2] [ClO2] 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 F2 (g) + 2ClO2 (g) 2FClO2 (g) rate = k [F2]x[ClO2]y**

Rate expression when x=1 and y=2? rate = k [F2]x[ClO2]y

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Reaction Order If initially [F2] = 1.0M and [ClO2]=1.0M, what will happen to the reaction rate if F2 is doubled? Rate1 = k(1.0M)(1.0M)2 Rate1 = k(1.0M3) [F2 ] = 1.0M Rate2 = k(2.0M)(1.0M)2 Rate2 = k(2.0M3) [F2 ] = 2.0M Rate2 = 2 x Rate1 Rate doubles

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Reaction Order What will happen in the same reaction if the [ClO2] is doubled? Rate1 = k(1.0M)(1.0M)2 Rate1 = k(1.0M3) [ClO2 ] = 1.0M Rate2 = k(1.0M)(2.0M)2 Rate2 = k(4.0M3) [ClO2 ] = 2.0M Rate2 = 4 x Rate1

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**Determination of Rate Law**

F2 (g) + 2ClO2 (g) FClO2 (g) Experiment [F2] [ClO2] Rate (M/s) 1 0.04 0.03 1.0x10-2 2 2.0x10-2 3 0.02 4 0.06

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**Determination of Rate Law**

Experiments 1 & 4 As [F2] doubles, so does the rate Experiments 2 & 3 As [ClO2] doubles, so does the rate 2:2 ratio…..1:1 ratio x = 1 and y = 1 Rate = k [F2] [ClO2]

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**Rate law/Expression Calculations**

Determine the rate law and calculate the rate constant for the following reaction from the following data: S2O82- (aq) + 3I- (aq) SO42- (aq) + I3- (aq) Experiment [S2O82-] [I-] Initial Rate (M/s) 1 0.08 0.034 2.2 x 10-4 2 0.017 1.1 x 10-4 3 0.16 Double [I-], rate doubles (experiment 1 & 2) Double [S2O82-], rate doubles (experiment 2 & 3) rate = k [S2O82-]x[I-]y y = 1 x = 1 rate = k [S2O82-][I-] k = rate [S2O82-][I-] = 2.2 x 10-4 M/s (0.08 M)(0.034 M) = 0.08/M•s

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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. F2 (g) + 2ClO2 (g) FClO2 (g) rate = k [F2][ClO2]

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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[A0] Ln equation has the form of the linear equation y=mx+b. ln At= y. k is the slope of the line. t=0 is start time. T=t is time chosen. Ln A0= y intercept.

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**Relation between Reactant Concentration and Time**

Decrease in reactant concentration with time. (b) will allow you to determine –k….slope and ln[A0]…..y-intercept.

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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 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ? [A]0 = 0.88 M ln[A] = ln[A]0 - kt [A] = 0.14 M kt = ln[A]0 – ln[A] ln 0.88 M 0.14 M 2.8 x 10-2 s-1 = ln [A]0 [A] k = ln[A]0 – ln[A] k = 66 s t =

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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**

The fact that the points lie on a straight line proves that the rate is first order. How do we calculate k? Y2-y1/ x2-x1= slope Slope= -k

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Gas Phase Reactions First order gas phase reactions have a linear relationship between partial pressure of gas and time. lnPt = -kt + lnP0

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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, t1/2 – 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: t1/2 = ln2/k or t1/2 = 0.693/k What can you tell about the half-life of a reaction from this equation? The half-life of a first order reaction is independent of the concentration of the reactant. Measuring the half-life of a reaction is one way to determine the rate constant of a first order reaction.

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Reaction Half-life College student’s four years of undergraduate work. Independent of how many students are present.

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Reaction Half-life What is the half-life of N2O5 if it decomposes with a rate constant of 5.7 x 10-4 s-1? t½ ln2 k = 0.693 5.7 x 10-4 s-1 = t½ t½ = 1200 s t½ = 20 minutes

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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] = [A]0 + kt INTEGRATED RATE LAW has the form of a linear equation. Plot of 1/[A]t vs. t gives a staright line with a slope of k and a y-intercept of 1/[A]0.

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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? t½ = 1 k[A]0 This equation relies on the concentration of the reactants. The half-life is inversely proportional to the initial reaction concentration. Makes sense because in the first part of the reaction, the half-life should be shorter in the early stages. This is when more reactant molecules are present to collide with one another. If you didn’t know if you had a first or second order reaction, how could you tell mathematically? Measure the half-life at different initial concentrations. Look for variations.

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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? t½ = [A]0 2k It is a zero order reaction. [A] ^0 = 0

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Summary

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**Activation Energy and Temperature Dependence of Rate Constants**

Reactions usually take place at a raster rate when temperature is increased. Ex: cooking spaghetti in water at 80 degrees vs. 100 degrees. Why do people put food in freezers? To preserve food and stop bacterial decay.

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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 Billions of collisions every second in the gas phase of a reaction. Not every collision causes a reaction. If that happened, most reactions would be instantaneous. Molecules need to have enough kinetic energy upon collision to break apart to cause vibration and break apart compounds. If not enough kinetic energy, molecules remain intact and no change results from the collisions.

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**The Collision Theory of Chemical Kinetics**

Activation Energy (Ea)- 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. Exothermic. Products are more stable than reactants and after product formation, there is release of heat. endothermic.

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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. Collision frequency, temperature, activation energy.

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**The Arrhenius Equation**

Relation between activation energy and temperature. lnk = (Ea/R) x (1/T) + lnA Shows dependence or rate on temperature. Plot of lnk vs. 1/t gives a straight line. Can use to determine activation energy of a reaction.

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**Rate Constants and Temperature**

lnK1 = Ea x (T1 – T2) lnK R (T1T2) Can be used to calculate Ea or rate constant at another temperature if the Ea is known.

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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 Ea. 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 Rate of a reaction doubles for every 10 degrees reaised.

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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. The first criterion provides the basis for defining a catalyst as something that increases the rate of a reaction. The second reflects the fact that anything consumed in the reaction is a reactant, not a catalyst. The third criterion is a consequence of the second; because catalysts are not consumed in the reaction, they can catalyze the reaction over and over again. The fourth criterion results from the fact that catalysts speed up the rates of the forward and reverse reactions equally, so the equilibrium constant for the reaction remains the same.

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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 Catalysts lower the Ea, so that more molecules can reach the ke and proceed to product. More collisions occur and reaction rate increases.

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**Enzyme Catalysts Biological catalyst. Lock and key method.**

Normally substrate converts to products slowly. With enzyme, reaction speeds up drastically.

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Enzyme Catalysts

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The End!!!!!!!

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This continues our discussion of kinetics (Chapter 13) from the previous lecture. We will also start Chapter 14 in this lecture.

This continues our discussion of kinetics (Chapter 13) from the previous lecture. We will also start Chapter 14 in this lecture.

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