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IUnit 5

How do we predict chemical change?

M3. Measuring Rates Analyzing the factors that affect reaction rate.

M2. Comparing Free EnergiesDetermining the directionality and

extent of a chemical reaction.

M1. Analyzing Structure Comparing the relative stability of different substances

M4. Understanding Mechanism Identifying the steps that determine reaction rates.

The central goal of this unit is to help you identify and apply the different factors that help predict the

likelihood of chemical reactions.

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IUnit 5

How do we predict chemical change?

Module 3: Measuring Rates

Central goal:

To analyze the effect of concentration and

temperature on the rate of chemical reactions.

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The Challenge

Imagine that you were interested in comparing the

rates at which different substances appeared or were decomposed on the

primitive Earth.

How could we evaluate the kinetic stability of a substance?

How could we determine the effect of concentration and temperature on reaction rates?

TransformationHow do I change it?

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Determining Gorxn or K for a chemical reaction

allows us to predict the directionality and extent of the process, but tell us nothing about how long

it will take to happen.

Time Issues

Consider these two possible routes for the synthesis of glycine, the simplest

amino acid, on the primitive Earth:

CH2O(g) + HCN(g) + H2O(l) C2H5NO2(s) Gorxn = -154. kJ

2 CH4(g) + NH3(g) + 5/2 O2(g) C2H5NO2(s) + 3 H2O(l)Go

rxn = -965. kJ

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Thermo vs. KineticsG

2 CH4(g) + NH3(g) + 5/2 O2(g)

C2H5NO2(s) + 3 H2O(l)

Reaction Coordinate

CH2O(g) + HCN(g) + H2O(l)

C2H5NO2(s)

Themodynamically favored,

but does not occur for all practical purposes

(High Ea)

Occurs readily at 25 oC (Low Ea)

Activation Energy Ea

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Analyzing chemical systems from both the thermodynamic and kinetic point of view is crucial

in making decisions about the actual “stability” of substances.

Analyzing Stability

For example, the decomposition or

transformation of a substance may be

favored thermodynamically, but can take millions

of years to occur. How stable is it then?

C(diamond) C(graphite)

Gotr = -2.9 kJ/mol

Ea ~ 728 kJ/mol

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IKinetic Stability

The analysis of the kinetic stability of biomolecules has been crucial in the analysis of

different theories about the origin of life.

How stable are amino acids under such conditions?

For example, it has been proposed that amino acid

synthesis could have occurred deep in the Earth's crust and that these amino acids were subsequently

shot up along with hydrothermal fluids into

cooler waters.

CH4 and NH3 are abundant in hydrothermal vent regions (60-400 oC).

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IUnstable?

Many aqueous solutions of amino acids are “thermodinamically unstable.”

Let’s consider the case of alanine:

Decarboxylation

Gorxn < 0

The kinetics of this reaction has been thoroughly explored by measuring the concentration of

alanine [Ala] as a function of time (t) in aqueous solutions at various temperatures.

Alanine (Ala) Ethyl Amine

2

3

2 2+

3

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Let’s Think

o

How would you quantify the rate of decomposition of alanine at any given time?

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o

Reaction Rate

t

AlaRateAverage

][

dt

AladRateInst

][

[Ala]

t

year

mMRateAverage 02.0

]918[

]7.05.0[

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Let’s Thinko

o

What does this data tell you about the kinetic stability of

alanine as a function of concentration and

temperature?

Hint: How does the rate change with

C and T?

(The higher the rate, the lower the kinetic

stability)

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In general, the rate of reaction decreases

as the concentration of the reactants [R]

decreases.o

The rate of reaction increases with

increasing temperature T.

Reaction Rate

The slope decreases

Kinetic stability is a function of [R] and T.

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I Rate Constant

RATE LAW Rate = k [A]a [B]b [C]c

Rate LawsThe effect of temperature and concentration on reaction rates can be modeled mathematically:

x A + y B + z C w D + y E + z F

k depends on the value of T, Ea, and other relevant factors for each reaction.

k = f (T, Ea, surface area….)

Reaction order

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Concentration EffectsHow can determine reaction orders and rate constants?

aAlakRate ][Rate constant?

Reaction order?

What are their values?

We may assume values for the reaction order a and analyze the implications:

][][

Alakdt

AladRate

If a = 1 (first-order):

ktAlaAla o ]ln[]ln[

By integration of this differential equation we get:

ktoeAlaAla ][][

Rate Law

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If the reaction is first-order:

ktAlaAla o ]ln[]ln[

ln[Ala]

t

m = -k

ln[Ala]o

Graphical Analysis

y = b + mxt (years) [Ala] (mM)

0 1.000

2 0.8705

4 0.7578

6 0.6597

8 0.5743

10 0.5000

12 0.4352

14 0.3789

16 0.3298

For example, is the decomposition of alanine

at 150 oC (423 K) 1st order?:

C3H7NO2 C2H7N + CO2

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C3H7NO2 C2H7N + CO2

t (years) [Ala] (mM) ln[Ala]

0 1.000 0

2 0.8705 -0.1387

4 0.7578 -0.2773

6 0.6597 -0.4160

8 0.5743 -0.5546

10 0.5000 -0.6931

12 0.4352 -0.7914

14 0.3789 -0.9704

16 0.3298 -1.1092

Reaction Order

We have a first-order reaction Rate = k[Ala]a

with:

a = 1 k = 0.0693 years-1

Rate = 0.0693[Ala]

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ILet’s Think

If [Ala]o = 1.00 mM, predict the time it will take for [Ala] to reach the values

0.50 mM, 0.25 mM and 0.125 mM. How long does it take to halve the concentration?

C3H7NO2 C2H7N + CO2

Given the Rate Law:

Rate = 0.0693[Ala]

[Ala] = [Ala]oe-0.0693t

t1 = 10 y

t2 = 20 y

t3 = 30 y

It takes 10 years to decrease the concentration by half,

independent of the concentration.

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Half LifeA half-life is the time

it takes for the concentration of a

reactant to be reduced in half.

t = 0

1 half-life

t = 1 half-life2 half-lives

t = 2 half-lives

3

t = 3 half-lives

4

T = 150 oC (423 K)

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ktC

C

o

][

][lnFor first order reactions:

If [C] = [C]o/2 2/12

1ln kto

t1/2

Half Life

kt

)2/1ln(2/1 Independent of

Concentration

t1/2 = 10 years for alanine at 150 oC.

Half Life

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If the reaction is first-order Rate = k[C]:

ktCC o ]ln[]ln[

2][][

Ckdt

CdRate

What if Rate = k[C]a with a = 2 (second-order)?

By integration we get:

ktCC o

][

1

][

1

1/[C]

t

m = k1/[C]o

Concentration Effects

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ILet’s Think

Is half-life for second order reactions independent of the initial concentration of reactant?

ktCC o

][

1

][

1Rate = k[C]2

If [C] = [C]o/2 ][

12/1 Ck

t t1/2

Half Life

t1/2 is only independent of [C]o for first order processes.

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Temperature EffectsHow can we predict how rate varies with temperature?

6.55 x 10-4

4.87 x 10-2

1.87 x 10-5

1.00 x 101

8.56 x 103

5.90 x 107

t1/2 (y)

The decomposition of alanine at different temperatures illustrates the effect of

T on the reaction rate.

1.06 x 103523

1.42 x 101473

3.71 x 104573

6.93 x 10-2423

8.10 x 10-5373

1.17 x 10-8323

k (y-1)T (K)

Ho do we explain it and make quantitative predictions?

Larger T Larger rate constant

Shorter half lives.

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Collision Rate Model

According to this model:

1. For a reaction to occur, the reactant particles must collide.

2. Colliding particles must be positioned so that the reacting groups interact effectively.

3. Colliding particles must have enough energy to reach a transition state that leads to the formation of the new products.

P

R

Ep

Reaction Coordinate

Hrxn

Transition State

Ea

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Arhenius EquationThe fraction of molecules

with enough energy to react at a given T is

proportional to:

RT

Ea

e

The rate constant k is then given by:

RT

Ea

Aek

Likelihood of collisions

)ln()ln( ART

Ek a

y = mx + b

y ln(k) x 1/T

m = -Ea/R b = ln(A)

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Let’s ThinkUse the data to estimate the activation energy Ea

for the decomposition of alanine. Estimate t1/2 at 623 K in seconds.

1.06 x 103523

1.42 x 101473

3.71 x 104573

6.93 x 10-2423

8.10 x 10-5373

1.17 x 10-8323

k (y-1)T (K) 2

3

2 2+3

21310R

Ea

Ea ~177 kJ/mol7.29 x 105623 t1/2 ~ 30 s

kt

)2/1ln(2/1

)ln()ln( ART

Ek a

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I Assess what you know

Let′s apply!

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Let′s apply!

The strong dependence on T of the decomposition of amino acids makes it difficult

to decide whether the “hydrothermal vents” theory of the origin of life is plausible.

In fact, the contact of amino acids with hydrothermal solutions during sediment and ocean recycling is

likely to be the major geochemical destruction pathway of amino acids on Earth.

Analyze

Go back and analyze the notes for the decomposition of Alanine. Based on our overall results, analyze the likelihood of amino acids forming in hydrothermal

vents on the primitive Earth.

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Let′s apply!

Recent experimental results indicate that there may be other reactions that compete with the decomposition of amino acids at T > 100 oC:

New Data

The formation of dimers and polymers may have helped

amino acids to accumulate on the planet.

2 A A2 + B

2

3

+2

3 3

2

H2O

Dimerization

Peptide Bond

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Let′s apply! Analyze

Go to: http://www.chem.arizona.edu/chemt/C21/sim

(Dimerization)or use the simulation on the next page.

Use the simulation of the dimerization of alanine to:

Determine the order of the reaction;

Compare the half-lives of the process for a 1 M solution of alanine at 100 oC and 200 oC.

Estimate the activation energy Ea of the reaction;

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Let′s apply! Analyze

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ILet′s apply!

Graphical analysis indicates this is a

second-order reaction.

T (K) k (s-1M-1) t1/2(s)

373 0.0085 1.17x102

423 0.247 4.05x100

473 3.606 2.77x10-1

ktAlaAla o

][

1

][

1

kAlat

o][

12/1

T = 373 K

T = 473 K

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ILet′s apply!

Ea/R = 10672

Ea = 88.7 kJ/mol

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Identify with a partner two important ideas discussed

in this module.

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Measuring Rates

Summary

x A y B

Rate Constant

RATE LAW Rate = k [A]a

The effect of temperature and concentration on a process’ reaction rate is summarized in the RATE LAW:

Reaction order

dt

AdRateInst

][

Reaction rates allow us to follow the kinetic evolution of

a chemical process.

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Given a rate law, we can derive information about how the concentration of reactants or

products changes with time.

If a = 1 (first-order):

Rate = k [A]ax A y B

ktAA o ]ln[]ln[

ktAA o

][

1

][

1If a = 2 (second-order):

C and T Effects

Temperature effects on reaction rate are determined by Arhenius Equation for the rate constant k:

RT

Ea

Aek

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For next class,

Investigate how the overall rate of a reaction is related to the reaction mechanism.

How can we use the reaction mechanism to derive the rate law or use the rate law to

evaluate the reaction mechanism?