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Review:Review: There are two methods for There are two methods for determining rate law variablesdetermining rate law variables

1. Initial rate method◦ Look at how fast reactant

disappears at the beginning of the reaction (initial rate)

◦ Technique= vary [R], look at initial rate

Double [R], if rate Stays the same = Zero order Doubles = First order Quadruples = Second order

Review:Review: There are two methods for There are two methods for determining rate law variablesdetermining rate law variables

2. Graphical method [R] vs. time ln[R] vs. time 1/[R] vs. time

◦ Linear plot determines order◦ Caveat: This method is only useful

when only one reactant changes◦ BUT: We can play with reactant

concentrations to get around this

Both the graphical and initial rate Both the graphical and initial rate methods were used in the dye methods were used in the dye kinetics labkinetics labPseudo-order kinetics

What is the order of this What is the order of this reaction?reaction?

1 2 3

66%

5%

29%

1. First2. Second3. Third

What is the rate constant (k) What is the rate constant (k) for this reaction?for this reaction?

1. 2. 3.

11%3%

86%1. 0.01162. 0.50463. 73.942

The integrated rate law yields a The integrated rate law yields a relationship between [R]relationship between [R]00, [R], [R]tt, k, , k, and tand tZero order reaction:

[R]0 - [R]t = kt

First order reaction:[R]t = [R]0e-kt and ln([R]t/[R]0)= -kt

Second order reaction:1/[R]t – 1/ [R]0 = kt

Summary of rate laws and Summary of rate laws and graphical methodgraphical method

Reaction Order

Integrated Rate Law

Characteristic Kinetic

Plot

Slope of Kinetic

Plot

Units of Rate Constant

Zero [R]0 - [R]t = kt [R] vs. t -kmole L-1 sec-

1

First[R]t = [R]0e-kt

ln([R]t/[R]0)= -ktln[R] vs. t -k sec-1

Second1/[R]t – 1/ [R]0 =

kt1/[R] vs. t k

L mole -1 sec-

1

Half life is the time it takes for one Half life is the time it takes for one half of something to “go away” half of something to “go away” (react, decay, etc.)(react, decay, etc.)Half life = t1/2

For a reaction= time for [R] to drop to half its original value

We can use the integrated rate law We can use the integrated rate law to derive a relationship between tto derive a relationship between t1/21/2 and kand kFor a first order reaction

ktR

R t 0][

][ln

ktand

tk

693.0693.02/1

2/1

Radioactive decay is a 1Radioactive decay is a 1stst order order processprocessAlways 1st orderIndependent of changes in T, P,

and [R]◦N0= # radioactive atoms

◦Nt= # radioactive atoms after time t

Measure in counts per minute (cpm)

cpm N kttt o

o

Nln = -kt N = N e

N

Radioactive Decay: Example 1Radioactive Decay: Example 1Radioactive gold-198 is used in the diagnosis of liver

problems. The half-life of this isotope is 2.7 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 1.0 day?

kttt o

o

Nln = -kt N = N e

N

Carbon-14 dating can be used to Carbon-14 dating can be used to date objects that are up to 60,000 date objects that are up to 60,000 years oldyears old

Radioactive Decay: Example 2Radioactive Decay: Example 2The Carbon-14 activity of an artifact in a burial site is found

to be 8.6 counts per minute per gram. Living material has an activity of 12.3 counts per minute per gram. How long ago did the artifact die? t1/2 = 5730 years

kttt o

o

Nln = -kt N = N e

N

EXAMPLE: Carbon-14 dating of an EXAMPLE: Carbon-14 dating of an artifactartifactThe Carbon-14 activity of an artifact in a burial site is found to be 8.6 counts per minute per gram. Living material has an activity of 12.3 counts per minute per gram. How long ago did the artifact die? t1/2 = 5730 years

Other things besides concentration Other things besides concentration can affect reaction ratescan affect reaction ratesCollision theory: Reactions occur

when◦Molecules collide…◦In the correct orientation…◦With enough energy