Rates of ReactionLearning Goal: I will understand units of measure of reaction rates, and know the factors that increase reaction rate.

Chemical Reaction Rates

Chemical kinetics is the study of the rate at which chemical reactions occur.

The term reaction rate, or rate of reaction refers to:• the speed that a chemical reaction occurs at, or• the change in amount of reactants consumed or products

formed over a specific time interval

Determining Reaction Rates

The reaction rate is often given in terms of the change in concentration of a reactant or product per unit of time.

The change in concentration of reactant A was monitored over time.

Average and Instantaneous Reaction Rates

Average rate of reaction:• change in [reactant] or [product] over a given time period (slope

between two points)

Instantaneous rate of reaction:• the rate of a reaction at a particular point in time (slope of the

tangent line)

Average rate of reaction and instantaneous rate of reaction can be determined from a graph of concentration vs. time.

A B

13.1

rate = -D[A]

Dt

rate = D[B]

Dt

time

Determining Reaction Rates Example # 1a)Using the data below, determine the instantaneous reaction rate that occurs between 40.0 and 50.0 seconds.

b) Determine the reaction rate between time 0 and t=60.0s.

The change in concentration of reactant A was monitored over time.

Example #2

For the reaction 2A + B 3C, it was found that the rate of disappearance of B was 0.300molL-1s-1. What is the rate of disappearance of A and appearance of C?

Learning CheckAt a certain temperature, the rate of decomposition of N2O5 is 2.5 x 10-6molL-1s-1. How fast is

each product being formed?

N2O5 NO2 + O2

Learning Check #2If NaOH and HCl react to form 25 g of water in 3 seconds, express the reaction rate in g/s,

then mol/s

Learning Check #3If two moles of nitrogen monoxide reacts with oxygen gas to form nitrogen dioxide,

a) Write a balanced chemical equation for this reaction

b) If 0.58 mol of oxygen reacts in 30s, calculate the:

i) grams of oxygen consumed per second

ii) moles of nitrogen monoxide consumed per second

iii) moles of nitrogen dioxide formed per second

Factors Affecting Reaction Rate

1. Nature of reactants• reactions of ions tend to be faster than those of molecules

2. Concentration• a greater number of effective collisions are more likely

with a higher concentration of reactant particles

3. Temperature• with an increase in temperature, there are more particles

with sufficient energy needed for a reaction

4. Pressure• for gaseous reactants, the number of collisions in a certain

time interval increases with increased pressure

5. Surface area• a greater exposed surface area of solid reactant means a

greater chance of effective collisions

6. Presence of a catalyst• a catalyst is a substance that increases a reaction rate

without being consumed by the reaction

Apply Your Knowledge

1. What a campfire burn faster with kindling or large logs? Why…which factor does this relate to?

2. Why do we use a refrigerator to keep our food fresh longer? Which factor does this relate to?

3. How can a magnifying glass be used to start a fire? Which factor does this relate to?

4. If you spill concentrated HCl on your skin, will it have a stronger/weaker effect? Why? What factor does this relate to?

Homework

•Pg 361 Q 1, 2, 5•Pg 365 Q1

Collision Theory and Factors Affecting Rates of Reaction

According to collision theory, a chemical reaction occurs when the reacting particles collide with one another.

Only a fraction of collisions between particles result in a chemical reaction because certain criteria must be met.

Effective Collision Criteria 1:The Correct Orientation of Reactants

For a chemical reaction to occur, reactant molecules must collide with the correct orientation relative to each other (collision geometry).

Five of many possible ways that NO(g) can collide with NO3(g) are shown. Only one has the correct collision geometry for reaction to occur.

Effective Collision Criteria 2:Sufficient Activation Energy

The shaded part of the Maxwell-Boltzmann distribution curve represents the fraction of particles that have enough collision energy for a reaction (ie the energy is ≥ Ea).

For a chemical reaction, reactant molecules must also collide with sufficient energy.

Activation energy, Ea, is the minimum amount of kinetic energy the reactants must possess in order to have an effective collision (energy required for products to form)

Collision energy depends on the kinetic energy of the colliding particles.

In other words, there is a minimum amount of energy required for reaction: the activation energy, Ea.

Just as a ball cannot get over a hill if it does not roll up the hill with enough energy, a reaction cannot occur unless the molecules possess sufficient energy to get over the activation energy barrier.

Potential Energy Curves

From left to right on a potential energy curve for a reaction:

• potential energy increases as reactants become closer• when collision energy is ≥ maximum potential energy, reactants will transform

to a transition state• products then form (or reactants re-form if ineffective)

Exothermic Endothermic

Activation Energy and EnthalpyThe Ea for a reaction cannot be predicted from ∆H.

• ∆H is determined only by the difference in potential energy between reactants and products.

• Ea is determined by analyzing rates of reaction at differing temperatures.

• Reactions with low Ea occur quickly. Reactions with high Ea occur slowly.

Potential energy diagram for the combustion of octane.

Analyzing Reactions Using Potential Energy Diagrams

The BrCH3 molecule and OH- collide with the correct orientation and sufficient energy and an activated complex forms. When chemical bonds reform, potential energy decreases and kinetic energy increases as the particles move apart.

Activation Energy for Reversible ReactionsPotential energy diagrams can represent both forward and reverse reactions.• follow left to right for the forward reaction• follow right to left for the reverse reaction

Draw a potential energy curve for a reversible exothermic reaction. Label the reactants, products, transition state (activated complex), activation energy (for both the forward and reverse reaction (Ea(fwd) & Ea(rev)) and the change in enthalpy.

LEARNING CHECK

Reaction MechanismsReaction Mechanisms are individual steps that led to the overall chemical change

Ex. HBr + O2 H2O + Br2… is not likely to occur in 1 single step

Instead:

HBr + O2 H2O Fast

HOOBr + HBrHOBrSlow

HOBr HBr H2O + Br2 Slow

Transition-State Theory

• This explains the reaction in terms of the collision of two high energy species – activated complexes

▫An activated complex (transition state) is an unstable grouping of atoms that can break up to form products

▫A simple analogy would be the collision of three billiard balls on a billiard table Suppose two balls are coated with a slightly stick adhesive

We’ll take a third ball covered with an extremely sticky adhesive and collide it with our joined pair

Reaction Mechanisms

• Steps in the overall reaction that detail how reactants change into products

▫ Reaction Mechanism – set of elementary reactions that leads to overall chemical equation

▫ Reaction Intermediate – species produced during a chemical reaction that do not appear in chemical equation

▫ Elementary Reactions – single molecular event resulting in a reaction▫ Molecularity – number of molecules on the reactant side of elementary

reaction

▫ Rate Determining Step (RDS) – slowest step in the reaction mechanism

This is the reaction used to construct the rate law; it is not necessarily

the overall reaction

26

•In a multistep process, one of the steps will be slower than all others.

•The overall reaction cannot occur faster than this slowest, rate-determining step.

Rate Determining Step

Which would be the rate determining step for the following potential energy curve?

A Catalyst Influences the Reaction Rate

A catalyst lowers the Ea of a reaction.

• this increases the percentage of reactants that have enough kinetic energy to overcome the activation energy barrier

• a catalyzed reaction has the same reactants, products, and enthalpy change as the uncatalyzed reaction

A catalyst decreases both Ea(fwd) and Ea(rev).

Catalysts in IndustryA metal catalyst is used for industrial-scale production of ammonia from nitrogen and hydrogen.

Hydrogen and nitrogen molecules break apart when in contact with the catalyst. These highly reactive species then recombine to form ammonia.

Many industries use biological catalysts, called enzymes, which are most often proteins.

For example: the use of enzymes decreases the amount of bleach (an environmental hazard) needed to whiten fibres used in paper production.

Homework

•Pg 372 Q1, 4, 5ab, 6

Rate LawLearning Goals:

I will be able to express an average or instantaneous reaction rate for a given reaction, as well as understand the rate law and its components and be able to determine the reaction order, and solve for the rate (k)

“How fast does the reaction occur?”

•Kinetics is the study of the rate of chemical reactions▫rate is a time dependent process

Rate units are concentration over time

•Consider the reaction A B▫Reactant concentrations [A] decrease while

product concentrations [B] increase

• The rate of reaction for the formation of the products is the same as for the reactants, but opposite, that is the concentrations are increasing

The rate of change of Ethane (C2H4) and Ozone (O3)

is the same, but exactly opposite for Acetaldehyde (C2H4O) and Oxygen (O2)

Product concentration increases at the same rate that the reactant concentrations decrease

The curves have the same shape, but are inverted

C2H4 + O3 → C2H4O + O2

Rate = -∆[C2H4] = -∆[O3] = +∆[C2H4O] = +∆[O2] ∆t ∆t ∆t ∆t

• The Rate expression must be consistent with stoichiometry

• When the stoichiometric molar ratios are not 1:1, the reactants still disappear and the products still appear, but at different rates

H2(g) + I2(g) → 2HI (g)

For every molecule of H2 that disappears, one molecule of I2 disappears and 2 molecules of HI appear

The rate of H2 decrease is the same as the rate of I2 decrease, but both are only half the rate of HI increase

Rate = -∆[H2] = - ∆[I2] = 1 ∆[HI]∆t ∆t 2 ∆t

•Summary equation for any reaction:

aA + bB → cC + dD

Rate = -1 ∆[A] = -1 ∆[B] = +1 ∆[C] = +1 ∆[D] a ∆t b ∆t c ∆t d ∆t

Rate Law• The dependence of reaction rate on

concentrations is expressed mathematically by the rate law

• The rate law expresses the rate as a function of reactant concentrations, product concentrations, and temperature

Only the Reactants Appear in the Rate Law

• For a general reaction at a fixed temperature:aA + bB + … cC + dD + …

the rate law has the form:

Rate = k[A]m[B]n …

aA + bB + … cC + dD + …

• Note: The Stoichiometric Coefficients – a, b, c – are not used in the rate law equation; they are not related to the reaction order terms – m, n, p, etc

▫ The rate law “k” changes with temperature; thus it determines how temperature affects the rate of the reaction

▫ The exponents (m, n, p, etc.) are called reaction orders, which must be determined experimentally

▫ Reaction orders define how the rate is affected by the reactant concentration

If the rate doubles when [A] doubles, the rate depends on [A] raised to the first power, i.e.,

m =1 (a 1st order reaction)

If the rate quadruples when [B] doubles, the rate depends on [B] raised to the second power, i.e.,

n = 2 (a 2nd order reaction)

If the rate does not change even though [A] doubles, the rate does not depend on the concentration of A and p = 0 (zero order reaction)

Reaction Order Tells How Changing Reactant Concentration Affects Rate

• Oth Order; rate =k[A]0; double [A], rate same• 1st Order; rate = k[A]1; double [A], double rate• 2nd Order; rate =k[A]2; double [A]; quadruple rate• 3rd Order; rate =k[A]3; double [A]; rate 8X

ExampleGiven: NO(g) + O3(g) NO2(g) +

O2(g)

Given: Rate = k[NO]1[O3]1

What is the reaction order with respect to

a) NO

b) O3

c) Overall?

Overall reaction order: Sum of Exponents in Rate Equation

Order of Rxn Possible Expression of Rate Law1 k[A]2 k[A]2

2 k[A][B]3 k[A]2[B] 3 k[A][B][C]

ExampleExperiments are performed for the reaction:

A B + C and the rate law has the been determined to be

of the form Rate = k [A]x

Determine the value of the exponent “x” for each to determine the rate law of each of the following:

a) [A] is tripled and you observe no rate change

b) [A] is doubled and the rate doubles

c) [A] is double and the rate quadruples

F2 (g) + 2ClO2 (g) 2FClO2 (g)

rate = k [F2]x[ClO2]y

Double [F2] with [ClO2] constant

Rate doubles

x = 1

Quadruple [ClO2] with [F2] constant

Rate quadruples

y = 1

rate = k [F2][ClO2]

13.2

Initial Reactant Concentration (mol/L)

Experiment

O2 NOInitial Rate

Mol/Ls

1 1.10x10-2 1.30x10-2 3.21x10-3

2 2.20x10-2 1.30x10-2 6.40x10-3

3 3.30x10-2 1.30x10-2 9.60x10-3

4 1.10x10-2 2.60x10-2 12.8x10-3

5 1.10x10-2 3.90x10-2 28.8x10-3

As [O2] doubles, the reaction rate _________, therefore m=___As [NO] doubles, the reaction rate _________, therefore n= ___

Example• A certain reaction that follows the equation

A + B C +D gave the following data:

Calculate the reaction order a) reactant A b) reactant B c) the overall reaction order d) the rate law e) the rate law constant

Initial Reactant Concentration (mol/L)

Experiment [A] [B]

Initial Rate

Mol/Ls

1 0.4 0.3 1.0x10-4

2 0.8 0.3 4.0x10-4

3 0.8 0.6 1.6x10-3

Homework

•pg 382 Q1, 2, 4abc