slide 1 rate law & reaction order02 reaction order: the sum of the powers to which all reactant...

Rate Law & Reaction Order 02Rate Law & Reaction Order 02

Reaction Order: The sum of the powers to which all reactant concentrations appearing in the rate law are raised.

Reaction order is determined experimentally:

1. By inspection.

2. From slope of the line, using the appropriote plot: [A] vs. t, ln[A] vs. t, 1/[A] vs. t

First-Order Reactions 02First-Order Reactions 02

Using calculus we obtain the integrated rate equation:

ln[A]t

[A]0

kt or ln[A]t ln[A]o kt

y = m x + b

ln [A]t = – kt + ln [A]0

Plotting ln[A]t against t will give:

Determining Reaction OrderDetermining Reaction Order

Reaction: H2O2 → H2O + ½ O2

time [H2O2] ln[H2O2]

0 1 0.0000

1 0.705 0.3496

2 0.497 0.6992

3 0.349 1.0527

4 0.246 1.4024

5 0.173 1.7545

P l o t o f [ H 2 O 2 ] v s . T i m e

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

Time (minutes)

Conc

. (M)

Plot [H2O2] vs. time



0 1 0.000

1 0.705 -0.349

2 0.497 -0.699

3 0.349 -1.053

4 0.246 -1.402

5 0.173 -1.754

Plot ln [H2O2] vs. time


P l o t o f l n [ H 2 O 2 ] v s . T i m e

-2.0

-1.5

-1.0

-0.5

0.0

0.0 1.0 2.0 3.0 4.0 5.0

Time (minutes)

Ln (c

onc)

(m

olar

ity)



0 1 0.0000

1 0.705 0.3496

2 0.497 0.6992

3 0.349 1.0527

4 0.246 1.4024

5 0.173 1.7545

P l o t o f l n [ H 2 O 2 ] v s . T i m e

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Time (minutes)

ln [H

2O

2]

(M)

Plot ln [H2O2] vs. time



Show that the decomposition of N2O5 is first order and calculate the rate constant.

Plot: ln[N2O5] vs. t Is it linear?


Half-Life: Time for reactant concentration to decrease by halfits original value.

Second-Order Reactions 01Second-Order Reactions 01

Second-Order Reactions:

A Products A + B Products

Rate = k[A]2 Rate = k[A][B]

These equations can then be integrated to give:

1[A]t

kt 1[A]0

y = m x + bDoes this form look familiar?


Second-Order Reactions:

Rate = k[A]2

1[A]t

kt 1[A]0

y = m x + b

Plot 1/[A] vs. t


Half-Life: Time for reactant concentration to decrease by halfits original value.

0

21

][

1

Akt


Iodine atoms combine, form molecular iodine in gas phase:

I(g) + I(g) I2(g)

The reaction follows second-order kinetics. Rate constant: k = 7.0 x 10–1 M–1s–1 at 23°C.

1. If initial concentration of I is 0.086 M, calculate the concentration after 2.0 min.

2. Calculate the half-life at the start of the reaction if the initial concentration of I is 0.60 M.



I(g) + I(g) I2(g)

2nd Order, k = 7.0 x 10–1 M–1s–1 [I]0 = 0.086 M, Find [I]120

0][

1

][

1

Ikt

I t

Second-Order ReactionsSecond-Order Reactions


I(g) + I(g) I2(g)

2nd Order, k = 7.0 x 10–1 M–1s–1 [I]0 = 0.60 M, Find t1/2

0

21

][

1

Ikt

Review – 1st and 2nd Order ReactionsReview – 1st and 2nd Order Reactions

(integrated form)

Review – Rate ConstantsReview – Rate Constants

Units for “Rate”

will always be M/sec

Molarity units will vary,

depending on reaction order

Review – Equations for Kinetics ProblemsReview – Equations for Kinetics Problems

General Rate Law: rate = k [A]x [B]y

First, determine the order of the reaction (find exponents x and y) by inspection or by graphing.

Then this equation can be used to calculate the rate constant k.

Review – Equations for Kinetics ProblemsReview – Equations for Kinetics Problems

Integrated forms of Rate Laws:

1st Order Reaction:

2nd Order Reaction:

Zero Order Reaction:

rate = k [A]x [B]y

ln[A]t = –kt + ln[A]0

1/[A]t = kt + 1/[A]0

[A]t = -kt + [A]0

slide 1 rate law & reaction order02 reaction order: the sum of the powers to which all reactant...

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