CHAPTER 12 Chemical Kinetics. Overview of Kinetics Macroscopic Study— Rates of reaction,...

CHAPTER 12

Chemical Kinetics

Overview of Kinetics

Macroscopic Study— Rates of reaction, described by rate laws Meaning of reaction rate—change of concentration of

reactants per unit of time. How to determine rate from experimental data How does temperature and concentration reaction affect

rateCollision Theory—

Recall kinetic theory--particles that are in motion Chemical reactions occur when particles collide with

sufficient energy and the correct orientation to cause a chemical reaction

Reaction mechanism—the detailed pathway taken by atoms and molecules in the reaction process

12.1

What is kinetics?

A study of reaction rates or speeds.Reaction Rates—a measure of how quickly a

reaction occurs. Is it spontaneous? If not how much energy does it take?

How is it useful?Make sure the reaction proceeds at a fast

enough rate to be useful. (Is it practical? Show me the money!)

Solving Kinetic Problems

You will either be given experimental data and need to use mathematical relationships to solve for an unknown .

ORYou will be given a graph, and need to

understand how to read the data to solve for the unknown. So you need to understand the types of graphs involved and the data they provide.

Graphing

How are Reaction Rates Measured?

Reaction Rates are Measured in Terms of Concentration

Rate = final concentration – intial concentration

tfinal-tintial

Rate = Δ [A] Δ t --Where A is the reactant or product

being considered.

Consider the following reaction:

2 N2O5(g) 4NO2(g) + O2 (g)

In terms of the reactant, the rate of reaction can be written:

Rate = - [N2O5]final – [N2O5]intial = - Δ [N2O5]

tfinal – tintial ΔtAs the rate proceeds, N2O5 decomposes, so Δ

[N2O5] is negative or is decreasing.Since rate must be positive, a negative sign

must be included for reaction rates of reactants.

Example Continued

In terms of the products, the rate of reaction can be written as:

Rate = Δ [NO2] or Rate = Δ [O2] Δt ΔtWhere there is no negative sign since products

are made so both would be positive slopes already.

What is an instantaneous reaction rate?

We can obtain the reaction rate at any given instant.

The instantaneous reaction rate is the slope of a line tangent to the curve of an instant in time

Instantaneous rate = - slope of tangent (for a reactant)

Example of instantaneous rate, at t = 2.0 minutes, concentration = .056M Rate = -0.056 M = -.028M/min 2.o min

Reaction Rates and Stoichiometry

Because the coefficients are different for each reactant and product, these three rates will have different values.

Dividing by their Stoichiometric coefficients, we can relate the three rates:

Rate = Δ [N2O5] = Δ [NO2] = Δ [O2] 2Δt 4 Δt Δt Now we can choose any of the reactants or

products to determine the rate.

Example of Instantaneous Rate Reaction

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12a–13

Figure 12.5: A plot of [N2O5] versus time for the decomposition reaction of N2O5.

Figure 12.1: Starting with a flask of nitrogen dioxide at 300°C, the concentrations of nitrogen dioxide, nitric oxide, and oxygen are plotted versus time.

12.2

Rate Law and Rate Constant

Experimental data, of the rate of reaction versus [N2O5]: Using the general formula for

a line is y = mx + b Where m = slope, b = y-

intercept

The straight line through the origin indicates that the rate is directly proportional to [N2O5]: rate = k [N2O5] In this case, k = the slope of

the line!

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

[N2O5]

Rate

(M

/min

)

What are Rate Laws?

The reaction rate depends on the concentrations of only the reactants. (see note below)

Rate = k[A]n

“k” the rate constantn = the order of the reactantValue of n, must be found experimentally,

cannot be found through stoichiometry!Note:• Chemical reactions are reversible• When there are a lot of products and

little reactants the reaction can reverse, so we usually measure rates soon after mixing.

What affects reaction rates?

Reactions occur as a result of collisions between reactant molecules.1. Concentration2. Temperature3. Nature of Reactants4. Catalysts

What is a Reaction Order?

The rate laws for most reactions have the general form:

Rate = k [reactant 1]m [reactant 2]n…The exponents m and n are called reaction

orders, and the sum of all the reaction orders (m + n) is the overall reaction order.

Infer the number of steps for the reaction!

Using Initial Rates to Determine Rate Laws

Reaction order involving a single reactantFor this type of reaction: A Products the rate law has the form: rate = k [A]m

where m = order of reaction If m = 0, the reaction is “zero-order” If m = 1, the reaction is “first-order”, etc.

The order of the reaction cannot be obtained from the chemical equation, it must be determined from experimental data.

Graphs represent concentration versus time!

To determine the order…

You need the rates and concentrations for two different instances:

rate 1 = k [A]1m rate 2 = k [A]2

m

We can solve for m by dividing the second rate by the first:

rate 2 = [A]2m = [A]2 m

rate 1 = [A]1m [A]1

Example Problem

Given the following data, determine the reaction order, m, the decomposition of N2O5:

2 N2O5 (g) 4 NO2 (g) + O2 (g)

[N2O5] Rate (M/s)

0.90 M 5.4 x 10-4

0.45 M 2.7 x 10-4

Reaction Order with More than One Reactant

Most reactions are of the form: A + B products

And the general form of the rate law is: Rate = k [A]m [B]n

And the overall reaction order: order = m + n

For example, if the rate law for a reaction is: Rate = k [NO]2 [O2], the reaction is second-order in

NO, first-order in O2, and third-order overall.

Given the following data,

Experiment [O2] [NO] Rate (M/s)

1 0.0110M 0.0130 M 3.21 x 10-3

2 0.0220 M 0.0130 M 6.40 x 10-3

3 0.0110 M 0.0260 M 12.8 x 10-3

Determine m and n, and thus, the reaction order and the rate law for the reaction: O2 (g) + 2NO (g) 2 NO2 (g)

a. First, use data from two experiments where the [NO] remains constant (e.g. Experiments #1 and # 2) to get m.

b. Next use data from two experiments were the [O2] remains constant (e.g. Experiments #1 and #3) to get n.

c. Finally write the rate law for the reaction.

Integrated Rate Equations

Using calculus, we can develop integrated rate equations to relate reactant concentration to time.

Zero-order reaction of this type A products, we get: rate = -k

Thus, the rate for a zero-order reaction is constant and independent of the concentration of the reactants. It does not matter how much you have!!!

Plotting [A] versus time should give us a straight line.

[A]

Figure 12.7: A plot of [A] versus t for a zero-order reaction.

First-Order Reactions

For a first-order reaction of this type: A Products, we get: rate = - Δ [A]t = k [A]t where [A]t is the [A] at time t

ΔtRearranging the equation above and integrating gives us

the relationship between concentration and time:

ln [A]t = -kt or ln [A]t - ln [A]o = -kt

[A]o

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12a–28

Figure 12.4: A plot of ln[N2O5] versus time.

Only for first-order reactions does one get a straight line when plotting ln [A] versus time!

Half-life (t1/2)

The time required for one half of a sample to decompose.

For first-order reactions, half-life is a fixed value, independent of concentration.

We can solve for the half-life:ln [A]t = ln ½[A]o = ln 1 = -0.693 = -kt1/2

[A]o [A]o 2

So t1/2 = 0.693

k

Second-Order Reactions

For a second-order reaction of this type: A productsWe get:

rate = - Δ[A]t = k [A]2

ΔtRearranging the equation above and integrating gives us

the relationship between concentration and time: 1 - 1 = kt or 1 = kt + 1 [A]t [A]o [A]t [A]o

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12a–31

Figure 12.6: (a) A plot of ln[C4H6] versus t. (b) A plot of 1y[C4H6] versus t.

Only for second-order reactions does one get a straight line when plotting 1/[A]t versus time!

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12b–32

To determine the order of reaction given experimental data, plot the data and determine which set of data gives a linear plot

The Collision Model

Main Idea: Molecules must collide to reactThree Factors:1. Kinetic Energy—for a reaction to occur, molecules

have to be moving quickly enough that they can break and reform bonds when they collide, if moving too slowly they will merely bounce off each other.

Activation Energy (Ea): the minimum amount of energy required to initiate a chemical reaction

2. Concentration—The higher the concentration, the more molecules present, higher probability of collisions, thus a higher reaction rate!

3. Orientation of molecules (or steric factor)—molecules have to be in the correct orientation for a reaction to occur (see figure 12.13)

Importance of the steric factor

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12b–35

Figure 12.13: Several possible orientations for a collision between two BrNO

molecules. Orientations (a) and (b) can lead to a reaction, but orientation (c) cannot.

Kinetic Molecular Theory

Recall with the kinetic molecular theory of gases, the higher the temperature, the higher the kinetic energy of molecules.

By increasing temperature, more molecules have the required activation energy for a reaction.

Activation Energy

Figure 12.12: Plot showing the number of collisions with a particular

energy at T1 and T2, where T2 > T1.This figure shows the energy of molecules at two temperatures.

At higher temperature T2 more molecules have higher energy

The shaded region indicates molecules with the activation energy (Ea)

At the higher temperature, more molecules have Ea.

Transition-State Model: Energy Profiles

We can show a reaction in terms of an Energy Profile.

The transition state (also called the activated complex) is the arrangement of atoms at the peak of the energy profile.

The activation energy, Ea, is the difference in energy between the reactants and the transition state.

The difference in energy between reactants and products is ΔHrxn. Note the next slide for a diagram.

Figure 12.11: (a) The change in potential energy as a function of reaction progress for the reaction 2BrNO

2NO + Br2. The activation energy Ea represents the energy needed to disrupt the BrNO molecules so that they can form

products. The quantity DE represents the net change in energy in going from reactant to products. (b) A molecular

representation of the reaction.

The Arrhenius Equation

Svante Arrhenius noted that for most reactions, the temperature dependence for the rate constant is given by:

k = A e-Ea/RT

Where A = frequency factor which accounts for the frequency of collision and the probability that the molecules are in the correct orientation.

Ea = activation energyR = 8.314 J/mol *KT = Temperature in Kelvins

The Arrhenius Equation continued…

If we take the natural log of both sides and rearranging the equation we get:

ln k = - Ea + ln A RTFrom this equation plotting ln k versus 1/T

should give a straight line;

Thus, we can determine the activation energy for a given reaction if we have experimental data on its rate constant at different temperatures.

Figure 12.14: Plot of ln(k) versus 1/T for the reaction 2N2O5(g) 4NO2(g) + O2(g). The value of the activation energy for this reaction can be obtained from the slope of the line, which equals -Ea/R.

“Two-Point” Equation Relating k and T

We can also determine the activation energy for a given reaction if we have experimental data for the reaction at two different temperatures:

ln k2 = Ea 1 - 1

k1 R T1 T2

This equation will also allow us to determine the rate constant at a different temperature if we have the activation energy.

Example

The rate constant for a first-order reaction is 0.346 s-1 at 298K. What is the rate constant at 355 K if the activation energy for the reaction is 50.2 kJ/mol?

Reaction Mechanisms

A reaction mechanism is a sequence of steps by which a reaction occurs at the molecular level.

Elementary Steps: The individual steps that make up a reaction mechanism

The molecularity of a reaction describes the number of molecules reacting in an elementary step. Unimolecular: only one reactant Bimolecular: two reactants Termolecular: three reactants (less common as very low

probability of 3 molecules colliding in the correct orientation for a reaction )

The types of elementary steps and their corresponding rates are given below:

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Catalysts

Substances that accelerate a chemical reaction but are not themselves transformed into a product of the reaction. If the catalyst is the same state as the reactant(s) it is a homogeneous catalysts and if it is not it is a heterogeneous catalysts (usually a solid).

How to tell if it is a intermediate or a catalyst

If it is a catalyst, it will appear first on the reactant side.

If it is an intermediate, it will first appear on the product side.

Important Equations

Arrhenius Equation

k = A e-Ea/RT

ln k = - Ea + ln A RT A = frequency factor which

accounts for the frequency of collision and the probability that the molecules are in the correct orientation.

Ea = activation energyR = 8.314 J/mol *KT = Temp in Kelvins

Note: From this equation plotting ln k versus 1/T should give a straight line;

Thus, we can determine the activation energy for a given reaction if we have experimental data on its rate constant at different temperatures.

Two different temperature problems:ln k2 = Ea 1 - 1ln k1 R T1 T2