chapt. 16 – reaction rates 16.1a model for reaction rates 16.2 factors affecting reaction rates...

Chapt. 16 – Reaction Rates

16.1 A Model for Reaction Rates16.2 Factors Affecting Reaction Rates16.3 Reaction Rate Laws16.4 Instantaneous Reaction Rates and

Reaction Mechanisms

Section 16.1 A Model for Reaction Rates

• Calculate average rates of chemical reactions from experimental data, including data in both tabulated and graphical form.

• Use stoichiometry to calculate rates of other reactants or products given the rate for a specific reactant or product.

• Convert a reaction rate expressed in terms of a given unit of time to a rate in a different unit of time.

Collision theory is the key to understanding why some reactions are faster than others.

Section 16.1 A Model for Reaction Rates

• Describe the three key aspects of collision theory and their relationship to reaction rates.

• Explain the meaning of the terms activation energy and activated complex (transition state) and how they are related to collision theory.

• Use an energy versus reaction progress diagram to determine if a reaction is endo- or exothermic and to identify the forward and reverse activation energies and the activated complex (transition state).

• State the relationship between reaction rate and the spontaneity of a reaction.

Key Concepts

• The rate of a chemical reaction is expressed as the rate at which a reactant is consumed or the rate at which a product is formed.

• Reaction rates are generally calculated and expressed in moles per liter per second (mol/(L ● s)).

• In order to react, the particles in a chemical reaction must collide.

• The rate of a chemical reaction is unrelated to the spontaneity of the reaction.

Section 16.1 A Model for Reaction Rates

Expressing Reaction Rates

Very wide range of reaction time scales

Slow - Geologic time (> 104 years)• C(graphite) C(diamond)• Formation of oil underground

Very fast - psec (10-12 s) or faster• Initial electron transfer process in

photosynthesis

Expressing Reaction RatesA + B C

Average rate – change in some quantity related to reactants or products per some specific time interval

Avg Rate = quantity t

Expressing Reaction RatesA + B C

Avg Rate = quantity t

quantity of interest usually molar concentration (M) of reactant (A, B) or product (C)

• Units of rate: mol/(L•s)• Square brackets used for molarity• [A] = concentration of A in mol/L• May be gas phase or in solution

Expressing Reaction Rates

A + B CFor most reaction rate problems, think of reaction equation with some initial concentration of reactants and no products

t = 0 s [A] = 2.0 [B] = 2.0 [C] = 0.0

t = 10 s [A] = 1.8 [B] = 1.8 [C] = 0.2

Expressing Reaction Rates

A B

t= 0 min t= 20 min t= 40 min

Expressing Reaction Rates

Time (min)

Num

ber

of m

oles

A

B

Expressing Reaction Rates

CO(g) + NO2(g) CO2(g) + NO(g)

Avg Rate = quantity t

Have data of [NO] at times t1 and t2

Avg Rate = [NO]2 – [NO]1 = [NO] t2 - t1 t

t1= 0.0 s t2= 2.0 s [NO]1=0 [NO]2= 0.010M

Rate =(0.010M/2.0 s) = 5.0x10-3 mol/(L•s)

Expressing Reaction Rates

CO(g) + NO2(g) CO2(g) + NO(g)

t1= 0.0 s t2= 2.0 s [NO]1=0 [NO]2= 0.010M

Rate =(0.010M/2.0 s) = 5.0x10-3 mol/(L•s)

Above quantity is average rate of production of NO(g)

Could also have expressed rate in terms of consumption of CO(g)

• Get negative number but use + value

Expressing Reaction Rates

2H2(g) + O2(g) 2H2O(l)

Stoichiometry applies to rates• Rate of consumption of H2(g) =

twice rate of consumption of O2(g)

Time unit is not always seconds

4 mol/(L•s) 60 s/min =

240 mol/(L•min)

Expressing Reaction Rates

Example Problem 16.1, page 562

Reaction: butyl chloride (C4H9Cl) & H2O

t1= 0.0 s t2= 4.00 s

[C4H9Cl]1= 0.220M [C4H9Cl]2= 0.100M

Avg Rate = – (0.100 mol/L – 0.220 mol/L) (4.00 s – 0.00 s)(minus sign needed for consumption rate to get positive value for rate)

Avg Rate = 3.00x10-2 mol / (Ls)

Practice

Calculating reaction rate (and converting to different units of time)

Problems 1- 3 page 563

Problem 12 page 567

Problems 47 – 49 page 586

Problems 1 page 987

Collision Theory

A2 + B2 2AB

At molecular level, A2 and B2 must collide with each other for reaction to occur

Large numbers of collisions occur per unit time, but only small fraction of collisions result in reaction

Collision Theory

A2 + B2 2AB

A2 B2 AB AB

Thanks to Sam Mantel

Collision Theory - Orientation

Molecules must have proper orientation relative to each other so that new bond can form

Collisions with correct orientation yield short-lived activated complex (AC), also known as transition state

AC may form products or break apart and re-form reactants

Collision Theory - Orientation

Collision Theory - Orientation

Short-Lived Activated Complex

(Transition State)

+

Nature of the transition state in the reaction between CH3Br and OH-

Activation Energy

Ea = Activation energy = minimum amount of energy needed by reacting particles to form activated complex

High Ea – few collisions have required energy to produce products

• Low rate of reaction relative to collision rate

Low Ea – most collisions have energy required to produce products

Activation Energy

Collision Theory – Activation Energy

Activation Energy – Exothermic Reaction

Activation Energy – Endothermic Reaction

Collision Theory Summary

For reactants to produce products:1. Reacting particles must collide

2. Collision must have proper orientation

3. Collision energy must be activation energy (Ea)

Activation Energies

Energy level diagram allows you to determine Ea for both forward and reverse reactions

A + B C + D forward

C + D A + B reverse

Ea (forward)Ea (reverse)

Ene

rgy

Spontaneity & Rate

Reaction rate not related to spontaneity GHighly spontaneous reactions (large and negative G) may be very slow

Slightly spontaneous reactions may be very fast

Practice

Concepts related to modeling reaction rates

Problems 4 – 11 page 567

Problem 40 – 46 page 586

Chapt. 16 – Reaction Rates

16.1 A Model for Reaction Rates16.2 Factors Affecting Reaction Rates16.3 Reaction Rate Laws16.4 Instantaneous Reaction Rates and

Reaction Mechanisms

Section 16.2 Factors Affecting Reaction Rates

• Identify the factors that affect the rates of chemical reactions and the direction in which they act (speed up or slow down).

• Give specific examples of substances which are highly reactive and which are relatively inert.

• Explain the role of a catalyst.• Explain the role of an inhibitor.

Factors such as reactivity, concentration, temperature, surface area, and catalysts affect the rate of a chemical reaction.

Section 16.2 Factors Affecting Reaction Rates

• Explain the difference between homogeneous and heterogeneous catalysts and provide specific examples of each.

• Use a rule-of-thumb to estimate the effect of a given temperature change on the rate of reaction.

• Explain the effect of a temperature change on reaction rate in terms of the change in the distribution of reactant energies with temperature and also on its effect on collision frequencies.

Key Concepts

• Key factors that influence the rate of chemical reactions include reactivity, concentration, surface area, temperature, and catalysts.

• Raising the temperature of a reaction generally increases the rate of the reaction by increasing the collision frequency and the number of collisions that form an activated complex.

• Catalysts increase the rates of chemical reactions by lowering activation energies.

Section 16.2 Factors Affecting Reaction Rates

Rates and Nature of Reactants

Similar types of reactions occur at different ratesReactions of metal with water:Fast

2 Na(s) + 2H2O(l) H2(g) + 2 NaOH(aq)Slower

Ca(s) + 2H2O(l) H2(g) + Ca(OH)2(aq)Slow

Fe(s) + 2H2O(l) H2(g) + Fe(OH)2(aq)

Rates and Nature of Reactants

What are some highly reactive materials?

?

Highly combustible or explosive• TNT, nitroglycerin, gasoline,methane

Unreactive materials?

?

Teflon, water, titanium, nitrogen, helium

Surface Area and Rate

Increasing area provides more opportunity for collisions – rates increase

• Steel wool burns, nails don’t• Pulverizing (powdering) a solid makes it

dissolve faster in liquid than it would if left as big chunk

Temperature and Rate

Generally, increasing T will increase rate (see next slide)

Rule-of-thumb: increasing T by 10 degrees (C or K) will double reaction rate

Temperature and Rate

Temperature (K)

Rel

ativ

e R

ate

Increasing T by 10 K can

~ double rate

Temperature and Rate

Increasing T will increase rate

Effect due to:• Increased collision frequency• Increased collision energies

Greater number of collisions have energy activation energy Ea

Particle Energy and Temperature

T2 >T1Fraction of particles having energy > Ea larger at T2 than at T1

higher rate of reaction at T2

Activation Energy

Ea

Catalyst and Rate

Catalyst – substance that increases rate of chemical reaction without itself being consumed in reaction

Catalysts do not change amount of product produced, just rate at which it is produced

Catalysts function by lowering activation energy

Catalyst and Rate

Reaction Progress

Ene

rgy

Reactants

Products

Ea no catalyst

Ea with catalyst

Catalyzed reaction pathway

Uncatalyzed reaction pathway

Metal-catalyzed hydrogenation of ethyleneH2C=CH2(g) + H2(g) H3C-CH3

H2 & C2H4 approach & absorb to metal surface

Rate-limiting step: H—H bond breakage

Metal-catalyzed hydrogenation of ethyleneH2C=CH2(g) + H2(g) H3C-CH3

One H atom bonds to adsorbed C2H4

Another C—H bond forms and C2H6 leaves surface

Catalytic Converter in Engines

Catalysts and Oil Refining

Fluid Catalytic Cracking Unit (FCCU) is the heart of a petroleum refinery

Role is to upgrade gas oil to high octane (profitable) gasoline

http://www.unb.ca/che/che5134/fcc.html

FCCU – Simplified Schematic

Hot petroleum stream injected into catalyst

stream

Reaction generates vapor – velocities ~ 20 m/s; residence

time ~ 5 sec

Separation of solids and vapor

Fluid Catalytic Cracking UnitCatalyst: fine zeolite – has pore size that allows reactant molecules to fit in

http://www.unb.ca/che/che5134/fcc.html

Zeolite catalyst structurehttp://www.unb.ca/che/che5134/fcc.html

EnzymesCatalysts of biochemical worldAlmost all are proteinsEnzymes identified by –ase ending in name; root part of name indicates function of that enzyme

• Oxidase/Reductase – catalyze oxidation or reduction of something

• Transferase - catalyze transfer of chemical groups

• Hydrolase – catalyze hydrolysis

Enzymes

Activities determined by their 3-dimensional structure

Most much larger than substrates they act on; only small portion of enzyme (~ 3–4 amino acids) directly involved in catalysis

Active site: region that contains these catalytic residues, binds substrate, and then carries out reaction

Enzymes

Usually very specific as to which reactions they catalyze and substrates involved in these reactions

Complementary shape, charge and hydrophilic/hydrophobic characteristics of enzymes and substrates are responsible for this specificity

Enzyme Catalysis: Lock & Key Model

Substrate

Enzyme Enzyme-Substrate Complex

Enzyme

Products

Shapes of enzyme & substrate have “lock and key” relationship; this particular enzyme’s function is to split substrate apart

Enzyme Catalysis: Induced Fit ModelActive site continually reshaped by interactions with substrateSubstrate does not simply bind to rigid active site; amino acid side chains which make up active site are molded into precise positions that enable enzyme to perform its catalytic function

Inhibitors and Rate

Inhibitor: substance that slows down, or inhibits reaction rates

In food industry, inhibitors called preservatives

Inhibited No inhibitor

Types of Catalysts

Heterogeneous catalyst – exists in physical state different than that of reaction it catalyzes

• Metal (solid) catalytic convertor catalyzes reactions of gases in exhaust

Homogeneous catalyst – exists in same physical state as reaction it catalyzes

• Enzymes (aqueous solution)

Practice

Concepts related to factors affecting reaction rates

Problems 13 – 18 page 573

Problems 50 – 59 page 586

Chapt. 16 – Reaction Rates16.1 A Model for Reaction Rates16.2 Factors Affecting Reaction Rates16.3 Reaction Rate Laws16.4 Instantaneous Reaction Rates and

Reaction Mechanisms

Section 16.3 Reaction Rate Laws

• Express the relationship between reaction rate and concentration.

• Determine the proper units for the rate constant for a given rate law.

• Describe several experimental methods that can be used to collect concentration versus time data.

• Determine reaction orders and rate constants using the method of initial rates.

The reaction rate law is an experimentally determined mathematical relationship that relates the speed of a reaction to the concentrations of the reactants.

Key Concepts

• The mathematical relationship between the rate of a chemical reaction at a given temperature and the concentrations of reactants is called the rate law.

rate = k[A]rate = k[A]m[B]n

• The rate law for a chemical reaction is determined experimentally using the method of initial rates.

Section 16.3 Reaction Rate Laws

Varying Reaction Rates

Avg Rate = concentration t

If pick constant t (e.g., 10 min) and monitor reaction for an hour, generally will find that average rate decreases with time

See following slide for reaction

A B

Expressing Reaction Rates

Time (min)

Num

ber

of m

oles

A

B

Varying Reaction Rates

Reaction rates generally decrease because as reactants are depleted to form products:• reactant concentration drops • collision frequency between reactants

drop

Use rate law to quantify how instantaneous rate depends on instantaneous concentration of reactants

Reaction Rate Laws

A B

Rate law for this reaction: Rate = k [A]

k = specific rate constant

Units for k depend on form of law• Rates always have units of mol /(L•s)• For rate law above, k has units of s-1

k unique for each reaction• k depends on T, P, other conditions

Units for Rate Constant

2NO(g) + 2H2(g) N2(g) + 2H2O(g)

Rate law

Rate = k[NO]2[H2]

What units does k have in this rate law?

mol = ? mol2 mol(L•s) L2 L

? = mol•L3 = L2 _

mol3•L•s mol2•s

Reaction Rate LawsA B Rate = k [A]

Double [A], rate doubles• k large, fast rate• k small, slow rate• for the particular rate law shown, k is

analogous to 1/(RC) in an R-C circuit

Rate constants determined by fitting experimental data to an assumed rate law

Measuring Reaction Rates

There exist a variety of experimental methods to determine rates

Most appropriate method depends on specific nature of reaction (gas phase, solution phase, etc.) as well as on the speed of the reaction

Spectrophotometric MonitoringReactions Producing Change in

Light-Absorbing Species

Spectrophotometric Monitoring Student Version

Conductometric MonitoringMonitor Conductivity – Reactions That

Produce/Remove Ions

Manometric MonitoringMonitor Pressure for Reactions Involving Gases

Reaction Order

A B Rate = k [A]

Reaction order for reactant defines how rate affected by concentration of that reactant

Rate law above = k [A]1

Reaction order: power that concentration raised to in rate law

Above rate law first order in [A]

Reaction Order

A B Rate = k [A]

Reaction is first order in reactant A• Double [A], double rate

Nuclear decay follows first order rate process

• All first order processes have an associated ½ half – time necessary to decrease reactant concentration by 1/2

Determining Reaction Order

Like k, reaction orders for reactants must be experimentally determined

Examine how changing concentration of a particular reactant changes rate

Reaction Order

aA +bB products

General rate law Rate = k[A]m[B]n

Reaction said to be:• mth order in A• nth order in B

m and n:• Do not have to be integers• Can be zero

Reaction Order

aA +bB products

General rate law Rate = k [A]m [B]n

Overall reaction order: sum of orders for individual reactants in rate law

For above, overall order = m + n

Under special circumstances (reaction occurs in single step & with single activated complex), then: m = a, n = b

Reaction Order

2NO(g) + 2H2(g) N2(g) + 2H2O(g)

Experimentally determined rate law

Rate = k[NO]2[H2]

Reaction second order in NO• [NO] 2 [NO], rate 4 x rate

Reaction first order in H2

• [H2] 2 [H2], rate 2 x rate

Overall reaction: third order (2+1)

Determining Reaction Order

One approach: method of initial rates

Compare initial rates of reactions carried out with varying reactant concentrations

Method of Initial RatesRate of decomposition of H2O2 (produces O2(g))

Measure initial rate vs concentration – get data shown in graph

Rate = k[H2O2]

First order reaction: initial rate proportional to initial concentration of H2O2.

Method of Initial Rates: Find Rate LawaA +bB Products (see table 16.2)

Trial Initial [A] Initial [B] Initial Rate (mol/(L•s)

1 0.100 0.100 2.00 10-3

2 0.200 0.100 4.00 10-3

3 0.200 0.200 16.00 10-3

Trial 1 vs 2 m = 1Overall

reaction order = 2+1 = 3

x2 x2

x4x2

Trial 2 vs 3 n = 2

Rate = k[A]m[B]n

Method of Initial Rates: Find Rate Law

Trial Initial [A] Initial [B] Initial Rate (mol/(L•s)

1 0.100 0.100 2.00 10-3

2 0.200 0.100 4.00 10-3

3 0.200 0.200 16.00 10-3

Rate Law: Rate = k[A][B]2 Value of k?Using trial 1: Rate = 2.00 10-3 mol/(L•s) = k(0.100 mol/L)(0.100 mol/L)2 = k 1.00x10-3 mol3/L3 k = 2.00 L2/(mol2•s)

Practice

Rate laws and using the initial rates method to determine reaction order

Problems 18 – 19, p 577 (rate laws)

Problems 21 - 22, p 577 (initial rates)

Problems 64 - 68 p 587

Problems 2 - 4 page 987

Chapt. 16 – Reaction Rates

16.1 A Model for Reaction Rates16.2 Factors Affecting Reaction Rates16.3 Reaction Rate Laws16.4 Instantaneous Reaction Rates and

Reaction Mechanisms

Section 16.4 Instantaneous Reaction Rates and Reaction Mechanisms

• Identify the difference between average and instantaneous rates of chemical reactions.

• Calculate instantaneous rates of chemical reactions from a rate law and both average and instantaneous rates from graphical data.

• Identify intermediates and catalysts in complex reaction mechanisms.

The slowest step in a sequence of steps determines the rate of the overall chemical reaction.

Section 16.4 Instantaneous Reaction Rates and Reaction Mechanisms

• Identify intermediates and activated complexes (transition states) for a complex reaction on an energy versus reaction progress diagram.

• Identify the rate determining step of a complex reaction.

Key Concepts

• The reaction mechanism of a chemical reaction must be determined experimentally.

• For a complex reaction, the rate-determining step limits the instantaneous rate of the overall reaction.

Section 16.4 Instantaneous Reaction Rates and Reaction Mechanisms

Instantaneous Rate of Reaction

Avg Rate = concentration t

Average rate applies to relatively long time interval (one long enough so that measurable change in concentration has occurred)

Really want to know rate at specific instant of time = instantaneous rate

Instantaneous Reaction Rate

Average reaction rate depends on size of time intervalAs Dt approaches zero, average reaction rate approaches value equal to slope of line drawn tangent to curve at time tValue called instantaneous rate of reaction

Instantane-ous Rate

Given by slope

of tangent to curve at time

of interest

Instantaneous = [H2O2] Rate Dt

[H

2O2]

Relative Time

Dt

D[H

2O2]

C4H9Cl(aq) + H2O(l) →

C4H9OH(aq) + HCl(aq)

Instantaneous Rate of Reaction

=

Average Rate

H2 + 2ICl I2 + 2HCl

0

0.20.40.60.81.01.2

0 1 2 3 4 5 6 7 8 9

Time (s)

Mol

es/L

H2

s

mol/L

0.10.8

65.020.0

t

H

2rate Avg = = 6.4x10-2 mol/(Ls)

Average rate over this interval?

=

Instantaneous Rate

H2 + 2ICl I2 + 2HCl

0

0.20.40.60.81.01.2

0 1 2 3 4 5 6 7 8 9

Time (s)

Mol

es/L

H2

s

mol/L

1.18.3

30.060.0

= 0.11 mol/(Ls)

Instantaneous rate at 2.0 sec?

Rate = slope of tangent line =

Instantaneous Rate of Reaction

Besides determining from graph of concentration vs time, can get instantaneous rate directly from rate law for known concentration

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

Rate = k[N2O5] k = 1.0x10-5 s-1

For [N2O5] = 0.350 MRate = 1.0x10-5 s-1 0.350 M = 3.5x10-6 mol/(Ls)

Practice

Instantaneous rate of reaction

Problems 31- 33 page 579

Problem 39 page 582

Problems 73 - 74 page 587

Problem 5(a-b) page 988

Reaction Mechanisms

Most reactions are multi-step (complex) – consist of sequence of two or more simpler reactions, called elementary steps

• Generally involve one, two, or three (rare) molecules as reactants

• Statistically unlikely to have more than 3 molecules simultaneously collide – even 3 is relatively uncommon

Reaction MechanismsKnowing reaction’s mechanism means knowing complete sequence of elementary steps

Elementary steps contain intermediates – substances produced in one elementary step and consumed in another

Catalysts may be involved – speed rate without being consumed in reaction

Mechanism – Ozone Decomposition

2O3(g) 3O2(g) Complex overall reaction

ES = Elementary step

ES1 Cl + O3 O2 + ClO

ES2 O3 O2 + O

ES3 ClO + O Cl + O2

ES1 + ES2 + ES3 = overall reaction

Catalyst (Cl) regenerated

Cl catalyst

Intermediates produced and consumed

ClO intermediate

O intermediate

Rate Determining Step

Complex (multi-step) reactions can proceed no faster than their slowest elementary step – rate-determining step

Rate Determining Step

2NO(g) + 2H2(g) N2(g) + 2H2O(g)

ES1 2NO N2O2 (fast)

ES2 N2O2 + H2 N2O + H2O (slow)

ES3 N2O + H2 N2 + H2O (fast)

ES2 is rate-determining step – limits overall reaction rate

Intermediates in this reaction?N2O2 N2O

Reaction with Two Intermediates

Reaction Progress

Activated Complex #1

Products

Activated Complex #3

Activated Complex #2

Intermediates #1

Intermediates #2

Reactants

Ene

rgy

Reaction with Two Intermediates

Reaction Progress

Products

Intermediates #1

Intermediates #2

Reactants

Ene

rgy

Highest Ea for forward reaction

– rate determining step

Ea

Practice

Reaction mechanism, rate determining step

Problems 36 – 38 page 582

Problems 69 – 72 page 587

Problem 79, page 588

End of Chapter