Rates of Reactions

RATES OF REACTIONS

Chemistry @ MBCCPre-University Arts & Sciences

Science 1

MODULE 2: KINETICS AND

EQUILIBRIA

TOPIC: RATES OF REACTION

1.1 Explain the concepts associated with reaction rates

Chemical Reactions and Collision TheoryThe following conditions MUST be met for a chemical reaction to occur:o Particles must collideo Particles must collide with the correct orientationo Particles must collide with a certain minimum

amount of energy (activation energy)

When all THREE conditions are met we refer to the collision as an effective collision

The Collision Theory Only collisions with enough

energy react to form products

The energy of the system changes as the reactants approach each other

The minimum amount of energy to make the reaction proceed is called the Activation Energy

The Collision Theory

HomeworkRead up and make notes on: Catalysis Enzymes in industrial and biological

processesBe able to provide examples

What does rate of reaction mean?The speed of different chemical reactions varies

What is the rate of these reactions?

The speed of a reaction is called the rate of the reaction.

rusting baking explosion

slow fast very fast

Rate of a Reaction is the frequency of effective

collisions we have in a given

time

tell us how fast the reaction is

going

is measured in change in

concentration per unit time for

e.g. mol dm-3 s-1 or M s-1

Progress of the Reaction Reactions do not proceed at a steady rate They start off at a certain speed, then get slower and slower until they

stop There is reduced frequency of collisions between particles and so the

reaction slows down As the reaction progresses, the concentration of reactants decreases

percentage completion of reaction

100%0% 25% 50% 75%reactantsproduct

Graphing rates of reaction

Reactant - product mixture

hydr

ogen

pro

duce

d (c

m3 )

time (seconds)10 20 30 40 50

10203040506070

00

x

y

Calculating rate of reaction from graphs

rate of reaction =xy

rate of reaction =20 s

45 cm3 rate of reaction = 2.25 cm3/s

The gradient of the graph is equal to the initial rate of reaction at that time

Measuring the Rates of ReactionsExperimentally, the rate of a reaction is the slope (or gradient) of a concentration vs. time graph

The rate of the reaction may be measured in one of two ways, either:

By measuring the rate at which the product (B) is formed or

By measuring the rate at which the reactant (A) is used up or disappears

Measuring the rate of production

Measuring the rate of disappearance

The slope is negative because the reactants are disappearing with time

CheckpointAre you able to do the following?

1. Explain the collision theory

2. Define activation energy

3. Explain what is meant by an effective collision

4. State what is meant by the rate of a reaction

5. Give the units of measurement for the rate of reaction

Calculating Rates of Rxns

Why do the rates differ, if they are measuring the rates at the same time (between 300s and 400s)?

Calculating Rates of Rxns

MODULE 2: KINETICS AND EQUILIBRIA


1.2 Design and carry out suitable experiments for studying the factors which affect rates of reactions

Measuring Rates ExperimentallyMeasuring the rate of a reaction means measuring the change in the amount of a reactant or the amount of a product.

What can be measured to calculate the rate of reaction between magnesium and hydrochloric acid?

The amount of hydrochloric acid used up (cm3/min)

The amount of magnesium chloride produced (g/min)

The amount of hydrogen product (cm3/min)

+magnesium hydrochloricacid + magnesium

chloride hydrogen

1. Measuring the rate of gas production

gas syringe

rubber bung

rubber connecterglass tube

conicalflask

magnesium

hydrochloricacid

Mg(s) + HCl(aq) MgCl2(aq) + H2(g)

2. The Titration MethodEg. Acid catalysed hydrolysis of an ester (ethyl acetate)

samples are removed from reaction vessel at regular intervals

the reaction is stopped or quenched (snapshot)

Q. How would you quench the reaction?

mixture analysed by titration – concentration of ethanoic acid is determined

by titration

Q. What do you expect to observe as the concentration of acid is measured

over time? Explain your answer

3. Colourimetric MethodThe time taken for the colour of the solution to appear or disappear is measured

samples are removed from reaction vessel at regular intervalsWhat is the colour of aqueous iodine?What do you expect to observe in the reaction vessel as the reaction

proceedsmixture may also be analysed by titration – concentration of remaining

aqueous iodine is determined by titration instead of using a spectrophotometer

MODULE 2: KINETICS AND EQUILIBRIATOPIC: RATES OF REACTION

1.3 Construct rate equations of the form: rate = k [a]n[b]m limited to simple cases involving zero, first and second order reactions

Rate Equation (or Rate Law) We can write an expression or an equation to show the relationship between the

concentration of the reactants and the initial rate of reaction For a general reaction A + B product we can write the general rate equation

as:

R=k[A]m[B]n

Where: R = initial rate in mol dm-3 s-1

[A] = concentration of reactant A in mol dm-3 or M

[B] = concentration of reactant B in mol dm-3 or M

k = rate constant

m = order of reaction with respect to reactant A

n = order of reaction with respect to reactant B

m + n = total order of reaction

Order of a reaction w.r.t a reactant shows the relationship between the concentrations of the

reactant species and the rate of a reaction is the exponent to which the concentration of that species

is raised indicates to what extent the rate of a reaction is affected

by the concentration of a particular reactant must be determined experimentally may be zero order, first order and second order

Order of a reaction Zero order

implies that the rate of reaction is not affected by concentration the rate does NOT change even if the concentration increases or decreases

First order implies that the rate of reaction changes proportionally with the change in

concentration if concentration of a reactant doubles, the rate also doubles; if the concentration

triples, the rate also triples etc. Second order

implies that the rate of reaction increases with the square of the change in concentration

if the concentration doubles, the rate quadruples; if the concentration triples, the rate increases nine fold etc.

Overall first order reactions A products Rate = k[A]

Overall second order reactionsA + A products Rate = k[A]2

A+B products Rate = k[A][B]

Overall third order reactionsA+B+C products Rate = k[A][B][C]A+B products Rate = k[A]2[B] or Rate = k[A][B]2 A products Rate = k[A]3


1.4 Deduce the order of reaction from appropriate data

Determining the Order of a ReactionFor a given reaction where the rate law is given as:

R=k[A]m[B]n

m and n must be determined experimentally Perform multiple trials all at the same temperature (k is affected by

temperature) Vary only the concentration of the reactant you are investigating

(conc. of the other reactants are held constant) Any change in the rate of reaction is due to the reactant that was

varied

Can you determine the order with respect to NO?

Rate Constant The rate constant, k, is a proportionality constant for a given

reaction It is dependent on temperature The units for k depend on the order of the reaction What are the units of k for:

A first order reaction? A second order reaction? A third order reaction?

QuestionThe initial rate of reaction between an ester A and aqueous sodium hydroxide was measured in a series of experiments at a constant temperature. The data obtained are shown below.

a) Use the data in the table to deduce the order of reaction with respect to the ester A b) Deduce the order of reaction with respect to NaOHc) Deduce the value of k with the correct unitsd) Hence calculate the initial rate of reaction in Experiment 4

Experiment Initial [NaOH]

(mol dm–3)Initial [A](mol dm–3)

Initial rate(mol dm–3 s–1)

1 0.040 0.030 4.0 × 10–4

2 0.040 0.045 6.0 × 10–4

3 0.060 0.045 9.0 × 10–4

4 0.120 0.060 to be calculated


1.5 Interpret concentration against time and concentration against rate for zero and first order reactions

Concentration-time GraphsWe can deduce order of a reaction from concentration vs. time plots

Rate-concentration GraphsWe can deduce the order of a reaction from rate vs. concentration plots

MODULE 2: KINETICS AND EQUILIBRIA


1.6 Perform calculations from rate data

Past Paper QuestionThe values of initial rates measured for the reaction below are recorded in the table below:

Experiment [S2O82-] [I-] Initial Rate Ms-1

1 0.15 0.25 1.4 x 10-5

2 0.15 0.5 5.6 x 10-5

3 0.075 0.5 2.8 x 10-5

4 0.075 0.25 7.0 x 10-6

a) Use the information from the table to deduce the rate equation and calculate the overall order of the reaction [5 marks]

b) Calculate the: i. Rate constant [2 mark]ii. Initial rate when the concentration of both reagents are 0.12 M [1 mark]

Past Paper Question

Determine the rate law for the reaction between A2 and B2


1.7 Perform simple calculations using half-life data

Half LifeThe time taken for the

concentration of a reactant to reduce to half its value

First order reactions have CONSTANT half lives eg. decay of radioisotopes such as carbon-14

What is the half life for the reaction below?

Determining Half Lives for 1st Order Reactions

For first order reactions:

REACTION MECHANISMS

Reaction Mechanisms Some reactions are too complicated to happen in one simple stage Instead, the reaction may involve a series of small changes one after the

other e.g. Overall reaction:

A2 + B2 C may consist of several steps:

A2 A + A (step 1)

B2 B+ B (step 2)

2A + 2B C (step 3)

Reaction Mechanisms A reaction mechanism is the step by step sequence of elementary reactions

by which an overall chemical change occurs

An elementary reaction is the simplest step of the reaction mechanism and may be classified by its molecularity:

The number of reactant particles involved in an elementary step is called the molecularity1. Unimolecular – involves only one reactant

2. Bimolecular – involves collision of two reactant molecules

3. Termolecular – involves collision of three reactant molecules (rare)

Elementary ReactionsUnimolecular

BimolecularTermolecular

http://chemwiki.ucdavis.edu/Core/Physical_Chemistry/Kinetics/Rate_Laws/Reaction_Mechanisms/Elementary_Reactions



Reaction Mechanisms One of the steps in the reaction sequence is the slowest step, known

as the rate determining step (rds) The molecularity of a process tells how many molecules are

involved in the process The rate law for an elementary step is written directly from that step

Multistep Mechanisms 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. The rate of the overall reaction depends upon the rate of the slow

step

The rate law for this reaction above is found experimentally to be

Rate = k [NO2]2

CO is necessary for this reaction to occur, but notice that the rate of the reaction does not depend on [CO] (i.e. [CO] does not appear in the rate law

This suggests the reaction occurs in two steps

Rate Determining StepA proposed mechanism for this reaction is

The NO3 intermediate is consumed in the second step

Since CO is not involved in the slow, rate-determining step, it does not appear in the rate law

Rate Determining Step (RDS) The rate of the RDS (or slow step) determines the overall

rate of the reaction

The rate law (or rate equation) is written from the RDS

The order for the RDS is the order of the overall reaction

ExampleConsider the following reaction

2 NO2 + F2 2 NO2FIf the reaction follows the mechanism:

NO2 + F2 = NO2F + F (slow)NO2 + F = NO2F (fast)

i. Which step is the RDS?ii. Write an expression for the rate lawiii. What is the molecularity of the RDS?iv. What is the overall order of the reaction?

http://www.science.uwaterloo.ca/~cchieh/cact/c123/elmntary.html




1.8 Explain the effect of temperature and catalysts on the rate of the reaction using boltzmann distribution of energies (and of collision frequency)

FACTORS AFFECTING REACTION RATES

Concentration and PressureTemperatureSurface AreaCatalysts

Concentration of ReactantsConcentration is the number

of particles in a given volume

As the concentration of reactants increases, so does the probability that reactant molecules will collide

More effective collisions means increased rate of reaction

Increasing the concentration, increases the rate of reaction

PressureIncreasing the pressure of a gas has the same effect as increasing its concentration

Increasing the pressure on a reaction involving gases increases the rate of reaction

Changing the pressure on a reaction which involves only solids or liquids has no effect on the rateIncreasing the pressure, increases the rate of reaction

Surface AreaSurface area is the exposed

matter of a solid substance

By increasing surface area, there are more collisions per unit of time

Therefore, as the surface area increases, so does the rate of reaction

Mg(s) + 2 HCl(aq) → MgCl2(aq) + H2(g)

Maxwell–Boltzmann Distributions (Effect of Temperature on Rate)

Temperature is defined as a measure of the average kinetic energy of the molecules in a sample

At any temperature there is a wide distribution of kinetic energies

At higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy

Maxwell–Boltzmann Distributions (Effect of Temperature on Rate)

As the temperature increases, the curve flattens and broadens

Thus at higher temperatures, a larger population of molecules has higher energy

If the dotted line represents the activation energy, as the temperature increases, the fraction of molecules that can overcome the activation energy barrier also increases (area under the curve)

Increasing the temperature, increases the

rate of reaction

Maxwell–Boltzmann Distributions (Effect of Catalyst on Rate)

.

Energy-Profile Diagram(Effect of Catalyst on Rate)

A catalyst speeds up a reaction by finding an alternate reaction pathway or mechanism which has a lower activation energy

Using a catalyst increases the rate of reaction

Rates of Reactions

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