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Chapt. 13KineticsSec. 1

Define ‘Rate’

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R P

D[R]

Dt

D[R]Dt

slope

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Reaction Rate: Good[ ]R

rate of reactiont

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Average vs Instantaneous Rates

D[R]

Dt

dtd[R]

Average

Instantaneous

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Reaction Rate: Better

Use the instantaneous rate

[ ]Rrate of reaction

dt

d

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Reaction Rate: Even Better

● Use the instantaneous rate

Make product or reactant measurements interchangeable

[ ] [ ]P Rrate of reaction

d d

dt dt

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Reaction Rate: Best

● Use the instantaneous rate

● Make product or reactant measurements interchangeable

Correct for stoichiometry

1 [ ] 1 [ ]

P R

P Rrate of reaction

d d

dt dt

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Example: Stoichiometry and Rates

In an electrolysis cell, electric current forces water to decompose into its elements, producing hydrogen at the rate of 0.12 mol/L-s.

2 H2O 2 H2 + O2

a) What is the rate of formation of oxygen?

b) What is the rate of disappearance of water?

c) What is the reaction rate?

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Chapt. 13Kinetics

Sec. 2Define ‘Rate Law’

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Rate and Concentration vs Time

rate at 0 s

rate at 20 s

rate at 40 s

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Rate Law

Most Common Form

● reactants only

● x, y small integersor simple fractions(0,1/2, 1, 3/2, 2, ...)

● x a; y b (Not Keq)

rate = k [A]x [B]y

Definitions

● k = rate constant

● x = order in Ay = order in B

● x+y = overall order

aA + bB products

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Chapt. 13Kinetics

Sec. 2Data k

Method of Initial Rates

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[A] vs t Data Rate Law

Method of Initial Rates (Sec. 13.2)

Trial and Error with Common Laws (Sec. 13.3)

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Define Initial Rate

initial rateinitial

conc. Assume rate and concentration are constant over initial time period

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Example: Method of Initial Rates

Initial rates are given below for the reaction

F2 + 2ClO2 2FClO2

Determine the rate law.Trial [F2]

(mol/L) [ClO2]

(mol/L) Initial Rate

(mol/L-s)

1 0.10 0.010 1.2x10-3

2 0.10 0.040 4.8x10-3

3 0.20 0.010 4.8x10-3

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(1) Use Ratios

Trial [F2](mol/L)

Rel.conc.

[ClO2](mol/L)

Rel.conc.

InitialRate

Rel.rate

1 0.10 1 0.010 1 1.2x10-3 1

2 0.10 1 0.040 4 4.8x10-3 4

3 0.20 2 0.010 1 4.8x10-3 4

Initial rates are given below for the reaction

F2 + 2ClO2 2FClO2

Determine the rate law.

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(2) [F2] const y

Trial [F2](mol/L)

Rel.conc.

[ClO2](mol/L)

Rel.conc.

InitialRate

Rel.rate

1 0.10 11 0.010 1 1.2x10-3 1

2 0.10 11 0.040 4 4.8x10-3 4

3 0.20 2 0.010 1 4.8x10-3 4

Initial rates are given below for the reaction

F2 + 2ClO2 2FClO2

Determine the rate law.

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(3) [ClO2] const x

Trial [F2](mol/L)

Rel.conc.

[ClO2](mol/L)

Rel.conc.

InitialRate

Rel.rate

1 0.10 1 0.010 11 1.2x10-3 1

2 0.10 1 0.040 4 4.8x10-3 4

3 0.20 2 0.010 11 4.8x10-3 4

Initial rates are given below for the reaction

F2 + 2ClO2 2FClO2

Determine the rate law.

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(4) Find k

Trial [F2](mol/L)

Rel.conc.

[ClO2](mol/L)

Rel.conc.

InitialRate

Rel.rate

1 0.10 1 0.010 11 1.2x10-3 1

2 0.10 1 0.040 4 4.8x10-3 4

3 0.20 2 0.010 11 4.8x10-3 4

Choose any set

Initial rates are given below for the reaction

F2 + 2ClO2 2FClO2

Determine the rate law.

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Trial [NO]M

[H2]M

Initial RateM/s

1 0.057 0.130 4.50x10-3

2 0.057 0.260 9.00x10-3

3 0.11 0.130 1.80x10-2

Student Problem

Write the rate law for the reaction given the following data

2NO + 2H2 N2 + 2H2O

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Chapt. 13Kinetics

Sec. 3Common Rate Laws

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Common Rate Laws

A products

a) First-orderRate = k [A]

b) Second-orderRate = k [A]2

c) Zero-orderRate = k [A]0 = k

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Common Rate Laws

A products

a) First-orderRate = k [A]

b) Second-orderRate = k [A]2

c) Zero-orderRate = k [A]0 = k

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1st-Order Rate Law

Differential Form

Rate = k [A](t)

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1st-Order Rate Law

Differential Form

Rate = k [A](t)

Integral Forms

[A](t) = [A]0 e-kt

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[A] = [A]0 exp(-k t)

Time0 2 4 6 8 10

[A]

0

1

2

3

4

5

6Time [A]

0.00 5.001.00 3.352.00 2.253.00 1.514.00 1.015.00 0.686.00 0.457.00 0.308.00 0.209.00 0.14

10.00 0.09

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Concentration at a Later Time

C12H22O11 + H2O ® C6H12O6 + C6H12O6 sucrose glucose fructose

This reaction is 1st order with a rate constant of 6.2 x10-5 s-1. If the initial sucrose concentration is 0.40 M, what is the concentration after 2 hrs (7200 s)?

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Time to Reach a Concentration

C12H22O11 + H2O ® C6H12O6 + C6H12O6 sucrose glucose fructose

This reaction is 1st order with a rate constant of 6.2 x10-5 s-1. If the initial sucrose concentration is 0.40 M, at what time does the concentration fall to 0.30 M?