Chapter 15: Chemical Kinetics Rates of Reactions

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Chapter 15 Chemical KineticsRates of Reactions

• How does a reaction take place?
• Consider NO O3 ? NO2 O2

product molecules separate
Molecules collide
Bonds are formed and break
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So, what controls the rate of a reaction?

• Number of collisions
• How often they collide in a shape that allows new
  bonds to form
• The energy of the colliding reactant molecules

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Collision Theory

• For a reaction to take place
• Molecules must collide
• They must do so in the correct orientation
• They must collide with an energy greater than the
  activation energy

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Concentration Dependence

• It makes sense that as concentration increases,
  the number of collisions per second will increase
• Therefore, in general, as concentration
  increases, rate increases
• But, it depends on which collisions control the
  rate
• So, you cant predict concentration dependence-
  it must be measured experimentally

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But, what do we mean by rate?

• In real life, rate distance/time
• This is change in position over time
• In chemistry, generally change in concentration
  over time

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Types of measured rates

• Rate over time
• Instantaneous rate
• Initial rate

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Example of rate measurement
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Rate Laws (also called Rate Equations)

• For the reaction 2 N2O5 ? 4 NO O2
• Rate kN2O5
• For the reaction NO2 ? NO ½ O2
• Rate kNO22
• For the reaction CO NO2 ? CO2 NO
• Rate kCONO2

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Rate Laws (also called Rate Equations)

• For the reaction 2 N2O5 ? 4 NO O2
• Rate kN2O5 first order reaction
• For the reaction NO2 ? NO ½ O2
• Rate kNO22 second order reaction
• For the reaction CO NO2 ? CO2 NO
• Rate kCONO2 first order in CO and in
• NO2 second order overall

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Determining a Rate Law

• Remember it must be done by experiment the
  reaction equation does not tell you the rate law
• Two methods Initial Rates Graphical Method

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Determining a Rate Law Initial Rate Method

• Measure the rate of the reaction right at the
  start.
• Vary the starting concentrations
• Compare initial rates to initial concentrations

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Determining a Rate Law Initial Rate Method

• Useful rules Vary only one concentration at a
  time
• If concentration doubles and
• Rate does not change, then zero order
• Rate doubles, then first order
• Rate quadruples, then second order
• General Rule

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Initial Rate Method Example 1
When concentration is doubled, rate increases by
Therefore reaction is second order Rate
kNH4NCO2
Now, use one of the experiments to find the rate
constant, k
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Initial Rate Method Example 2
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Initial Rate Method Example 2
NOTICE When O2 is doubled without changing
NO, the rate doubles. Therefore the reaction
is first order in O2.
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Initial Rate Method Example 2
NOTICE When NO is doubled without changing
O2, the rate quadruples. Therefore the
reaction is second order in NO.
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Initial Rate Method Example 2
The reaction is first order in O2 and second
order in NO. Rate kO2NO2 Now we find
the value of k.
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Concentration-Time Relationships
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Concentration-Time Relationships
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Graphical Method for Determining Rate Laws
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Graphical Method for Determining Rate Laws
A plot of 1/R vs. Time will be linear.
A plot of concentration vs. Time will be linear.
A plot of lnR vs. Time will be linear.
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Graphical Method for Determining Rate Laws
How it works 1. Collect R over an interval of
times. 2. Make plots of R vs. time lnR
vs. time 1/R vs. time Only one will be linear.
That tells you the reaction order. The slope of
the linear plot is the rate constant.
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Graphical Method for Determining Rate Laws

• Example 2 H2O2 ? 2 H2O O2
• Time(min) H2O2(mol/L)
• 0 0.0200
• 200 0.0160
• 400 0.0131
• 600 0.0106
• 800 0.0086
• 1000 0.0069

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Graphical Method for Determining Rate Laws

• Example 2 H2O2 ? 2 H2O O2
• Time(min) H2O2(mol/L)
• 0 0.0200
• 200 0.0160
• 400 0.0131
• 600 0.0106
• 800 0.0086
• 1000 0.0069

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Graphical Method for Determining Rate Laws
time concentration
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Graphical Method for Determining Rate Laws
ln(conc)
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Graphical Method for Determining Rate Laws
Rate kH2O2 k 0.0011 min-1
ln(conc)
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Graphical Method for Determining Rate Laws
1/concentration
Check the second order plot to be sure it doesnt
also look linear.
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Half-Life

• Half-Life the time it takes for half the
  reactant concentration to drop to half of its
  original value

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First Order Reaction2 H2O2 ? 2 H2O O2Rate
kH2O2 k 1.05 x 10-3/min
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First Order Reaction2 H2O2 ? 2 H2O O2Rate
kH2O2 k 1.05 x 10-3/min
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First Order Reaction2 H2O2 ? 2 H2O O2Rate
kH2O2 k 1.05 x 10-3/min
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First Order Reaction2 H2O2 ? 2 H2O O2Rate
kH2O2 k 1.05 x 10-3/min
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First Order Reaction2 H2O2 ? 2 H2O O2Rate
kH2O2 k 1.05 x 10-3/min
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Calculations involving Half-Life

• For a first order reaction

At the half-life, one half is gone, so Rt ½
Ro and
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Radioactive Decay

• Radioisotopes decay via first order reactions.
  Instead of concentrations, amounts are used.

Measured as radioactive activity, in counts per
minute (cpm) using a detector.
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Radioactive Decay Example 1

• Radioactive 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?

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Radioactive Decay Carbon Dating
C-14 In living thing
Sunlight Nitrogen
Atmospheric C-14
C-14 Dead thing
Sunlight Nitrogen
Atmospheric C-14
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Radioactive Decay Example 2

• The 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