Chapter 14 - Chemical Kinetics

The area of chemistry concerned with the speeds, or rates, of reaction is called CHEMICAL KINETICS.

Section 14.1 Factors that Affect Reaction Rates ** The book combines nature of reactants and particle size.

** We used chapter 12 notes from the grade 12 academic program for this section

{Grade 12 notes below}

REACTION RATE - is the number of particles that react in a given time to form products. (IE

the change in the reactants or products over time)

The COLLISION THEORY provides an explanation for why reactions proceed at different rates.

It depends on:

1. Collisions (# and angle)

2. Energy

In most reactions, the reactants come together and form products. In order to do this the

reactants must collide with each other. The more often the collisions, the faster the reaction

(usually).

Not only do the reactants need to collide, but also they need to break bonds and create new ones

to form the products. These processes require energy. Without sufficient energy, even when

particles do collide, they won’t form products. The minimum energy colliding particles must

have in order to react is the ACTIVATION ENERGY.

For a brief moment (10-13

seconds) the particles are between the reactant and product stages.

Here they are called the ACTIVATED COMPLEX. This is a very unstable state and the

complex may just as easily transform back into reactants as they would from products. The top

of the potential energy diagram represents the TRANSITION STATE or change over point of the

reaction.

A POTENTIAL ENERGY DIAGRAM is a diagram that charts the potential energy of a reaction

against the progress of a reaction.

[Be sure to do both potential energy diagrams here]

Five Factors that Affect Reaction Rates

1. Temperature:

inc temp inc KE inc collisions inc rate of reaction

more particles are able to reach the activation energy

inc rate of reaction

2. Concentration:

inc concentration of reactants (ie more particles) inc collision inc rate of

reaction

3. Surface area:

dec particle size inc surface area inc collisions inc rate of reaction

4. Catalyst:

(A CATALYST is a substance that increases the rate of a reaction without being used up)

a catalyst lowers the activation energy needed for reactants to become products by

providing an alternative mechanism (route) for the reaction inc rate of reaction

5. Nature of Reactants: - the reactivity of the reactants

a. ionic compounds react faster than molecular compounds

b. reactions involving breaking weaker bonds are faster than those involving

breaking stronger bonds

c. reactions that involve breaking fewer bonds are generally faster than reactions

involving breaking a greater number of bonds.

Section 14.2 Reaction Rates The speed of a chemical reaction, its REACTION RATE, is the change in the concentration of reactants or products per unit of time. Units are usually molarity per second, M/s. Rates of reaction often decrease as the reaction proceeds because the concentration of reactants decreases. When calculating the AVERAGE RATE OF REACTION, you can either: A ⇄ B

(i) describe the rate as the appearance of your product (B)

average rate = △ [B] △ t

(ii) describe the rate as the disappearance of your reactant (A) average rate = - △ [A] (** the negative is necessary so that the rate △ t is positive)

(iii) describe the rate of the overall reaction (section 14.3)

{do sample problem 14.1 p.576}

INSTANTANEOUS RATE • the rate at a particular moment in the reaction

• graphs can allow us to evaluate the instantaneous rate.

- It is determined from the slope of the tangent of the curve (from a point of

interest)

- calculate the slope by rise over run

- slope of a product is positive; slope of a reactant is negative

- so, the instantaneous rate of a product is the slope of the line, but the rate of a

reactant is the slope of the tangent multiplied by negative 1 because of the

negative slope (we don’t want rate to be negative)

• ‘rate’ means instantaneous rate unless otherwise stated.

• do sample 14.2 orally

Reaction Rates and Stoichiometry p. 578 In an equation with a 1:1 ratio, such as A ⇄ B , then the rate would be: rate = - △ [A] = △ [B] △ t △ t But, if the stoichiometric ratio is 2:1 such as 2A ⇄ B + C rate = - 1△ [A] = △ [B] = △ [C] 2△ t △ t △ t So in general, for any reaction: aA + bB ⇄ cC + dD rate = - 1△ [A] = - 1 △ [B] = 1 △ [C] = 1 △ [D] a△ t b △ t c △ t d △ t {Sample problem 14.3 p. 579}

Section 14.3 The Rate Law: The Effect of Concentration on Rate

RATE LAW - the third way of studying rates - states that rate is directly proportional to the concentration of the

reactants Rate = k[reactant1]m[reactant2]n

- rate = the rate of the disappearance of reactant over time - k = rate constant (it changes with temperature). k units vary. - (NOTE: the above equation is not given on the AP exam)

Reaction Orders: The Exponents in Rate Law For, Rate = k[reactant1]m[reactant2]n The exponents ‘m’ and ‘n’ in the rate law are called REACTION ORDERS.

The exponents in a rate law have to be determined experimentally; it can not be predicted

by merely looking a the chemical equation. ie the coefficients do NOT become the

exponents as in Keq problems

In most reaction the reaction orders are 0, 1, or 2.

The OVERALL REACTION ORDER is the sum of the orders with respect to each

reactant in the rate law. So, overall reaction order = m + n

NOTE:

• If a reaction order for a reactant is a first order, then doubling the

concentration of the reactant will double the rate. [2]1 = 2

• If a reaction order for a reactant is a second order, then doubling the

concentration of the reactant will quadruple the rate. [2]2 = 4. Or, if you

triple the concentration the rate will increase by ninefold. [3]2 = 9

• If the reaction order is 0, then that reactant has no effect on the rate. [x]0 =

1

the units for k will vary depending on overall order. (NOTE: you will be required to

determine the overall order of reaction from the units of k)

Sample Exercise 14.4 p. 582 do orally along with Practice Problem Sample Exercise 14.5 p. 583 do orally along with Practice Problem

Using Initial Rates to Determine Rate Laws

The rate law must be determined experimentally. It can not be predicted by looking at the equation. So we look at experiential data to observe the effect of changing the initial concentration of the reactants on the initial rate of the reaction.

- a zero order means that changing the concentration will have no effect on the rate.

- the rate of a reaction depends on concentration, BUT the rate constant does not. The

rate constant is affected by temperature and the presence of a catalyst.

Sample Exercise 14.6 and Practice (The concentration of the species you are NOT testing for MUST stay the same)

Section 14.4 The Change of Concentration with Time

Read paragraph on p. 586

First Order Reactions A first order reaction is one whose rate depends on the concentration of a single reactant raised to the first power.

For, A B

Rate = - ∆[A] = k[A] Differential rate law

∆ t ln[A]t – ln[A]0 = -kt or ln [A]t = -kt Integrated Rate law [A]0

ln[A]t = -kt + ln[A]0

Sample Exercise 14.7 Using the integrated First-Law Order Rate Law

To verify whether a reaction is first order, plot the equation as: y = mx + b. If the graph is a straight line then the reaction is first order. (If is it is not a straight line then it is not a first order reaction). The x-axis is time and the y-axis is ln[A]t.

Second Order Reactions

A second order reaction is one whose rate depends on the reactant concentration raised to the second power OR on the concentration of two different reactants each raised to the first power.

1 = kt + 1 Integrated Rate Law [A]t [A]0

If the reaction is second order, a plot of 1/[A]t vs t will yield a straight line.

1 = kt + 1 [A]t [A]0 To distinguish between a first and second order reaction you can graph ln[A]t vs t AND 1/[A]t vs t to determine which gives you a straight line.

Sample Exercise 14.8

Half-Life The HALF-LIFE of a reaction, t1/2, is the time required for the concentration of a reactant to reach one-half of its initial value, [A]t1/2 or ½[A]0. Half-life is a convenient way to describe how fast a reaction occurs. A fast reaction will have a short half-life.

First Order Reactions

in a first order reaction, the concentration of the reactant decreases by half in each of a

series of regularly spaced time intervals, namely, t1/2.

Does not depend on the starting concentration of the reactants

Radioactive decay is a first-order process

(A) At 3200C, the rate constant of a first order reaction is 2.2 x 10-5 s-1. What is the half-life at this temperature? (B) At 600 K, the half-life for a first order reaction is 2.3 x 105 s. What is the rate constant at this temperature? (C) At what time will the concentration of the reactant of a first order reaction decline to one tenth of its original value, if the rate constant is 4.5 x 10-2 s-1?

Second Order Reactions The half-life for a second order and other reactions depends on reactant concentrations and therefore changes as the reaction progresses. The half-life depends on the initial concentration of the reactant

Section 14.5 Temperature and Rate

The rates of most chemical reactions increase as the temperature rises. The faster rate at higher temperatures is due to an increase in the rate constant with increasing temperature.

(Background from grade 12 An increase in temperature affects the rate in 2 ways: 1. it increase the number of effective collisions 2. it allows more particles to reach the activation energy faster

The KE of the molecules (during a collision) can be used to stretch, bend, or ultimately break bonds. So the KE is used to change the PE of the molecule.)

The rate depends on the magnitude of the Ea. Generally, the lower the Ea the faster the rate of reaction.

The fraction of molecules that has an energy equal to or greater than the Ea is given by: f = e-Ea/RT

The Arrhenius Equation - for most reactions the increase in rate with the increase in temperature is non-linear - most reaction rate data obeys an equation based on 1. Fraction of molecules that has an energy of Ea or greater 2. Number of collisions per second 3. Fraction of collisions with proper orientation

These 3 factors make up the Arrhenius Equation:

k = Ae-Ea/RT k = rate constant Ea = activation energy R = gas constant (8.314 J/mol-K) T = absolute temperature A = frequency factor (a constant related to the frequency and proper orientation of the collisions)

So, as Ea increase, the rate decreases because k decreases. Do Sample Exercise 14.10 orally

Determining the Activation Energy

So, graphing ln k vs 1/T will give a straight line. The slope = -Ea/R. Since Ea is part of the slope equation you can use the slope to determine the Ea. We can calculate another k by manipulating the equation.

Sample Exercise 14.11 Determining the Energy of Activation

Section 14.6 Reaction Mechanisms A REACTION MECHANISM is a series of steps that make up an overall reaction.

Each step is called an ELEMENTARY REACTION which involves a single molecular event (eg a collision, change in energy, or change in geometry)

Particles (molecules, atoms or ions) that are formed in an elementary reaction and consumed in a following elementary reaction are called REACTION INTERMEDIATES. (IE the product of one step becomes the reactant of the next step).

Elementary reactions in reaction mechanisms all occur at different rate. Usually one elementary reaction is slower than the rest and is called the RATE DETERMINING STEP. (Hence it determines the overall rate)

You may have a different number of reactants in each elementary reaction. The term MOLECULARITY refers to the number of reactant particles you have.

- If you have one particle reaction it is called a UNIMOLECULAR elementary reaction. - If you have two particles reacting it is called a BIMOLECULAR elementary reaction. - If you have three particles reacting it is called a TERMOLECULAR elementary

reaction (very rare) {Teach samples grade 12 way} Do Sample Exercise 14.12 - Orally Rate laws for Elementary Reactions If a reaction is an elementary, then its rate law is based directly on its molecularity. So, unimolecular reactions are first order: rate = k[A] while bimolecular elementary reactions are second order. (refer to Table 4.3)

Do sample exercise 14.13 orally

The Rate-Determining Step for a Multistep Mechanism Rate-Determining Step = the slow step in a reaction mechanism Mechanisms with a Slow Initial Step The rate law for a reaction with a slow initial step is equal the rate law of that slow step only. Do sample Exercise 14.14

Mechanisms with a Fast initial Step

situation: a multi-step mechanism where the first step is fast and is therefore NOT the

rate-determining step.

Whenever a fast step precedes a slow one we can solve for the concentration of an

intermediate by assuming that an equilibrium is established in the fast step

(the intermediate is unstable and does not accumulate to a significant extent)

Sample Exercise 14.15

Section 14.7 Catalysis A catalyst is a substance that changes the speed of a chemical reaction without being used up. HOMOGENEOUS CATALYSIS - a catalyst that is present in the same phase as the reacting molecules HETEROGENOUS CATALYSIS - a catalyst that is present in a different phase form the reactant molecule.