Advancedchemistry-lecture Slides-Kinetics Lessons Student Version

8/11/2019 Advancedchemistry-lecture Slides-Kinetics Lessons Student Version

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Chemical Kinetics

The area of chemistry concernedwith the rates, or speeds, of

chemical reactions.

The Rate of a Chemical

Reaction

Reaction rate -

Units of M/s.

1

What is happening to the concentration of A as timegoes by?

A+B C


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What is the sign of the change of

concentration of A: [A]?

Remember, is final initial.

1. Positive

2. Negative

A+ B C

As the reaction proceeds, the concentrationof A decreases

The rate of change can be defined in termsof A decreasing:

What is happening to the concentration of C as timegoes by?

A+B C


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If rate is defined by Cyou have:

A+B C

Which reaction has the faster

rate?1. A + B C

2. D + E F

A+B C

D+E F

Is the rate of the

reaction constant during

the course of the

reaction?

AB


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Therefore, calculations of rate using the change

in concentration formula will give differentresults depending on what time interval youchoose.

Making the interval of time smaller and smallerwe can calculate the rate of the reaction at aspecific instance in time.

Rates can be defined interms of changes of

pressure as well aschanges ofconcentration.


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Comparing Rate of Change

of Reactants and Products

Not all substances in a chemical reaction appearor disappear at the same rate.

Lets look at a simple demonstration tounderstand the relationships.

2

Paper Demo

Two pieces of paper make one booklet.

2A B

The process was recorded for 30 s.

Initial Final

Paper

Booklets

How does the rate of disappearance of

A (the paper) relate to

B (the booklets)?

Paper Demo. 2A B

t

B

t

A

2

1rate

1. B appears at twice the rate that A isdisappearing.

2. A disappears at twice the rate that B isappearing.

3. A disappears at the same rate that B appears.


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t

B

t

A

2

1rate

So, for the reaction:

aA + bB cC + dD

When a question asks you to write therate expression for a reaction in terms ofthe disappearance of the reactants and theappearance of the products, this (above)

is what they want you to do.

For the reaction

BrO3- + 5Br - + 6H+ 3Br2 + 3H2O

the value of [BrO3-]/t = 1.5 10-2 M/s at a particular

time. What is the value of the [Br -]/t at the sameinstant?


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For the reaction

BrO3+ 5Br + 6H+ 3Br2 + 3H2O

Brdisappears at a rate of 7.5 10-2 M/s at a particular

time. What is the value of the appearance of Br2 at the sameinstant?

The Rate Law

Rate Law -

For the reaction:

aA + bB cC + dD

The rate law is:

rate = .

We will learn how to determine

x and y later, for now, lets look at someexamples of reactions and rate laws.

3

A(aq) + B(aq) C(aq) + D(aq)


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k is called the rate constant.

khas units and is obtained by solving theequation for k.

Every time this reaction takes place, at a constanttemperature, the same value for kwill beobtained

Rate = k[A]

For the reaction:

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

The rate law was determined to be:

rate = k[NO]2[H2]

The reaction is said to be

Orders can be zero (whenconcentration does not affect the rate.)

Orders can be fractions

Rate = k[NO]2[H2]

Lets look at what this rate law tells us about

the connection between concentrations and

rate. What happens to the rate if [H2] is

doubled (while [NO] remains constant?)

1. Rate stays the same2. Rate doubles

3. Rate is cut in half

4. Rate quadruples


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Rate = k[NO]2[H2]

Lets look at what this rate law tells us about

the connection between concentrations and

rate. What happens to the rate if [NO] is

doubled (while [H2]remains constant?)

1. Rate stays the same

2. Rate doubles

3. Rate is cut in half

4. Rate quadruples

Determination of a Rate Law

As stated earlier, the orders of the rate law mustbe determined experimentally.

The best way to learn how to take experimentaldata and obtain a rate law is throughdemonstration. Lets work through a couple ofexamples.

4

Nitric oxide gas, NO, reacts with chlorine gasaccording to the equation: NO + 1/2 Cl2NOCl.

The following initial rates of reaction have beenmeasured for the given reagent concentration.Rate (M/hr) NO (M) Cl2(M)

1.19 0.25 1.5

4.79 0.50 1.59.59 0.50 3.0


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Hydroxide ion is involved in but not consumed by thereaction:

OCl- + I- OI- + Cl-

(a) From the data in the table, determine the order of thereaction with respect to OCl-, I-, and OH-

OH-

[OCl-],M [I-], M [OH-], M Rate, M/s

0.0080 0.0040 2.00 4.8 10-4

0.0040 0.0080 2.00 5.0 10-4

0.0040 0.0040 2.00 2.4 10-4

0.0040 0.0040 1.00 4.6 10-4

0.0040 0.0040 0.50 9.4 10-4

(b) Write therate law, anddetermine avalue of therate constant, k

[OCl-],M [I-], M [OH-] , M Ra te , M/ s

0.0080 0.0040 2.00 4.8 10-4

0.0040 0.0080 2.00 5.0 10-4

0.0040 0.0040 2.00 2.4 10-4

0.0040 0.0040 1.00 4.6 10-4

0.0040 0.0040 0.50 9.4 10-4

Now that we know the order, what

is the rate law and the value of k?

1. Rate = k[OCl-][I-][OH-] k = 60 M/s

2. Rate = k[OCl-][I-]/[OH-] k= 30 1/Ms

3. Rate = k[OCl-][I-][OH-]-1 k= 30 1/s


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The Integrated Rate Law

Rate laws can be used to determine the

concentration of reactants at any time during thecourse of a reaction.

We will look at the most simple cases:

1st order overall

2nd order overall

0th order

5

First-Order Kinetics

For the reaction:

Aproducts

because the coefficient is one

This can give us:

ln = kt[A]

[A]o

The previous equation forms this equation using calculus.


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1st Order Kinetics

2N2O5 4NO2 + O2

Because concentration is proportional topressure in a gas, partial pressures can be usedin place of the concentrations.

ln P = -kt + ln Po


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A(g) B(s) + C(s)

Half-life - (t1/2) -

at t1/2,

For a first order reaction we have:

ln = kt[A][A]o

Gives:

First-Order Kinetics and

the Half-Life6

t1/2 =0.693

k

This is the half-life equation for a first order

reaction.

Notice that it is independent of the [A].


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If a 1st order reaction started with 8 M of

substance A, and the half-life was 1 minute,

what concentration would remain after 3

minutes?1. 5 M

2. 4 M

3. 2 M

4. 1 M

5. 0.5 M

A first-order reaction has a rate constant of 3.0 10-3 s-1.The time required for the reaction to be 75% completeis?


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What if the question were:

A first-order reaction has a rate constant of 3.0 10-3 s-1.The time required for the reaction to be 30% completeis?

Second-Order Reactions

Aproducts

Setting each equation equal to each other and usingcalculus gives:

7

ktoA][

1

A][

1

o

A][

1

A][

1kt


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What will the slope

equal?

y = mx + b

oA][

1

A][

1 kt1. kt

2. k

3. -k

4. 1/[A]o

1[A]

1[A]o

+ kt=

For the half-life equation, [A] = [A]o/2 whent = t1/2.

Substitute this into the above equation gives:

What about zero-order reactions?

Rate = k[A]0 or

A plot of [A] versus t is a straight line.

What would a plot of rate versus time look like?


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Using Plots to Determine Order

Collision Theory

What is the difference between baking a cake at250o versus 350oF?

8

Dependence of Rate Constant

on Temperature


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The Collision Theory of Chemical

Kinetics

What is occurring on the molecular level that

causes rate to increase with concentration andtemperature?

Rate increases with the number of collisions persecond.

What happens to the number ofcollisions as the concentration

increases?

Concentration and Number of

Collisions

We must have a collision in order to have areaction.

If every collision resulted in a reaction, all reactionswould occur virtually instantaneously.

So, why do some reactions take minutes, hours,

even days to happen?

Activation Energy -


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Potential Energy Diagrams

Based on what we have learned, why does the

reaction rate increase with temperature?

The Arrhenius Equation

k= Ae-Ea/RT

What unit would

temperature be in?

9


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k= Ae-Ea/RT

If we take the natural log of both sides we get:

RTAlnln Eak A plot of lnk

vs 1/T gives a

straight line

with slope = ?

As Ea goes ,

As T goes ,

ln k vs. 1/T

Take the Arrhenius equation:

and derive a two point equation for two differenttemperatures (T1 and T2) and two different rateconstants (k1 and k2)

AlnT

1

R

Eln a

k


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The activation energy for the following first-order reactionis 102 kJ/mol.

N2O5(g) 2NO2(g) + 1/2O2(g)

The value of the rate constant (k) is 1.35 10-4

s-1

at 35o

C.What is the value of kat 0oC?

The quantity A is thefrequency factor.

This takes into accounttwo factors:

1.

2.

Reaction Mechanisms

A chemical equation does not give us a goodpicture of how the atoms rearrange themselves toform products. It is a sum of several

Elementary steps -

Reaction mechanism -

10


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Lets consider the reaction:

2NO + O2 2NO2

Fact: While monitoring the reaction, it was found thatN2O2 existed for a brief time.

What does this mean?

Instead this is what is proposed:

NO + NO N2O2

N2O2 + O2 2NO2

Elementary step

Elementary step

N2O2 is an intermediate -

They are canceled as you add theelementary steps

unimolecular reaction - an elementary step inwhich only one reacting molecule participates

bimolecular reaction -

termolecular reaction - an elementary stepinvolving three molecules


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In thes mechanism for the formation

of NO 2, what type or types of

elementary step does it have?

1. Unimolecular

2. Bimolecular

3. termolecular

NO + NO N2O2

N2O2 + O2 2NO2

2NO + O2 2NO2

Rate Laws and Elementary Steps

The rate law of an elementary step canbedetermined by using the coefficients as the order.

Aproducts

A + B products

A + A products

NOTE: this is not true for the overall equation!only for the elementary step!

Remember: How do you determine theorders of an overall reaction?

Rate-determining step -

.

The rate of this step gives the rate of the overallreaction.

Lets look at a specific example:


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The rate law for the reaction:

H2O2 + 2H+ + 2I- I2 + 2H2O

is rate = k[H2O2][I-]. The following mechanism has

been suggested.H2O2 + I

- HOI + OH-

OH- + H+ H2O

HOI + H+ + I- I2 + H2O

Which step would be the rate-determining step?

slow

fast

fast

What is(are) the intermediate(s)

in the mechanism?

1. HOI

2. OH-

3. H+

4. HOI and OH-

5. I- and H2O H2O2 + I- HOI + OH-

OH- + H+ H2O

HOI + H+ + I- I2 + H2O

slow

fast

fast

Catalysis

Catalyst -

The substance reacts within an elementary step ofthe mechanism but is regenerated in a subsequentstep.

11


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Uncatalyzed vs. Catalyzed

There are three general types of catalysts.

Heterogeneous Catalyst

Homogeneous Catalyst

Enzyme Catalyst

Heterogeneous and

Homogeneous Catalysts

These are simply defined by the state of the catalyst.

Often a solid catalyst that a gas is passed through

Catalytic converter on a car is an example

All aqueous or all gases, for example.


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Enzymes

Often made up of very large and complexmolecules with molar masses in the thousands.

All aspects of a catalyst apply to enzymes.

Enzyme

UbiquitinActivatedEnzyme

End of Kinetics Unit

Advancedchemistry-lecture Slides-Kinetics Lessons Student Version

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