Figure 12'27: Layers of ions surrounding charged colloidal particles'

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Average84.2 Standard Deviation13.4
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Average161.6 Standard Deviation24.9
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Reaction Rates

• Chemical kinetics is the study of reaction rates,
  how reaction rates change under varying
  conditions, and what molecular events occur
  during the overall reaction.

• What variables affect reaction rate?

Surface area of a solid reactant or catalyst.
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Dependence of Rate on Concentration

• Reaction Order

• Consider the reaction of nitric oxide with
  hydrogen according to the following equation.

• Thus, the reaction is second order in NO, first
  order in H2, and third order overall.

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Dependence of Rate on Concentration

• Reaction Order

• Zero and negative orders are also possible.
• The concentration of a reactant with a zero-order
  dependence has no effect on the rate of the
  reaction.

• Although reaction orders frequently have whole
  number values (particularly 1 and 2), they can be
  fractional.

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Dependence of Rate on Concentration

• Determining the Rate Law.

• One method for determining the order of a
  reaction with respect to each reactant is the
  method of initial rates.

• It involves running the experiment multiple
  times, each time varying the concentration of
  only one reactant and measuring its initial rate.
• The resulting change in rate indicates the order
  with respect to that reactant.

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Dependence of Rate on Concentration

• Determining the Rate Law.

• If doubling the concentration of a reactant has a
  doubling effect on the rate, then one would
  deduce it was a first-order dependence.

• If doubling the concentration had a quadrupling
  effect on the rate, one would deduce it was a
  second-order dependence.
• A doubling of concentration that results in an
  eight-fold increase in the rate would be a
  third-order dependence.

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A Problem to Consider

• Iodide ion is oxidized in acidic solution to
  triiodide ion, I3- , by hydrogen peroxide.

• A series of four experiments was run at different
  concentrations, and the initial rates of I3-
  formation were determined.
• From the following data, obtain the reaction
  orders with respect to H2O2, I-, and H.
• Calculate the numerical value of the rate
  constant.

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A Problem to Consider

• Comparing Experiment 1 and Experiment 2, you see
  that when the H2O2 concentration doubles (with
  other concentrations constant), the rate doubles.
• This implies a first-order dependence with
  respect to H2O2.

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A Problem to Consider

• Comparing Experiment 1 and Experiment 3, you see
  that when the I- concentration doubles (with
  other concentrations constant), the rate doubles.
• This implies a first-order dependence with
  respect to I-.

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A Problem to Consider

• Comparing Experiment 1 and Experiment 4, you see
  that when the H concentration doubles (with
  other concentrations constant), the rate is
  unchanged.
• This implies a zero-order dependence with respect
  to H.

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A Problem to Consider

• The reaction orders with respect to H2O2, I-, and
  H, are 1, 1, and 0, respectively.

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A Problem to Consider

• You can now calculate the rate constant by
  substituting values from any of the experiments.
  Using Experiment 1 you obtain

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A Problem to Consider

• You can now calculate the rate constant by
  substituting values from any of the experiments.
  Using Experiment 1 you obtain

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Change of Concentration with Time

• A rate law simply tells you how the rate of
  reaction changes as reactant concentrations
  change.

• A more useful mathematical relationship would
  show how a reactant concentration changes over a
  period of time.

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Change of Concentration with Time

• A rate law simply tells you how the rate of
  reaction changes as reactant concentrations
  change.

• Using calculus we can transform a rate law into a
  mathematical relationship between concentration
  and time.

• This provides a graphical method for determining
  rate laws.

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Concentration-Time Equations

• First-Order Rate Law

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Concentration-Time Equations

• First-Order Rate Law

• Using calculus, you get the following equation.

• Here At is the concentration of reactant A at
  time t, and Ao is the initial concentration.
• The ratio At/Ao is the fraction of A
  remaining at time t.

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A Problem to Consider

• The decomposition of N2O5 to NO2 and O2 is first
  order with a rate constant of 4.8 x 10-4 s-1. If
  the initial concentration of N2O5 is 1.65 x 10-2
  mol/L, what is the concentration of N2O5 after
  825 seconds?

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A Problem to Consider

• The decomposition of N2O5 to NO2 and O2 is first
  order with a rate constant of 4.8 x 10-4 s-1. If
  the initial concentration of N2O5 is 1.65 x 10-2
  mol/L, what is the concentration of N2O5 after
  825 seconds?

• Substituting the given information we obtain

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A Problem to Consider

• The decomposition of N2O5 to NO2 and O2 is first
  order with a rate constant of 4.8 x 10-4 s-1. If
  the initial concentration of N2O5 is 1.65 x 10-2
  mol/L, what is the concentration of N2O5 after
  825 seconds?

• Substituting the given information we obtain

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A Problem to Consider

• The decomposition of N2O5 to NO2 and O2 is first
  order with a rate constant of 4.8 x 10-4s-1. If
  the initial concentration of N2O5 is 1.65 x 10-2
  mol/L, what is the concentration of N2O5 after
  825 seconds?

• Taking the inverse natural log of both sides we
  obtain

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A Problem to Consider

• The decomposition of N2O5 to NO2 and O2 is first
  order with a rate constant of 4.8 x 10-4 s-1. If
  the initial concentration of N2O5 is 1.65 x 10-2
  mol/L, what is the concentration of N2O5 after
  825 seconds?

• Solving for N2O5 at 825 s we obtain

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Concentration-Time Equations

• Second-Order Rate Law

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Concentration-Time Equations

• Second-Order Rate Law

• Using calculus, you get the following equation.

• Here At is the concentration of reactant A at
  time t, and Ao is the initial concentration.

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Graphing Kinetic Data

• In addition to the method of initial rates, rate
  laws can be deduced by graphical methods.

• If we rewrite the first-order concentration-time
  equation in a slightly different form, it can be
  identified as the equation of a straight line.

• This means if you plot lnA versus time, you
  will get a straight line for a first-order
  reaction. (see Figure 14.9)

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Figure 14.9 A plot of log R versus time.
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Graphing Kinetic Data

• In addition to the method of initial rates, rate
  laws can be deduced by graphical methods.

• If we rewrite the second-order concentration-time
  equation in a slightly different form, it can be
  identified as the equation of a straight line.

y mx b
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Graphing Kinetic Data

• In addition to the method of initial rates, rate
  laws can be deduced by graphical methods.

• If we rewrite the first-order concentration-time
  equation in a slightly different form, it can be
  identified as the equation of a straight line.

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Half-life

• The half-life of a reaction is the time required
  for the reactant concentration to decrease to
  one-half of its initial value.

• For a first-order reaction, the half-life is
  independent of the initial concentration of
  reactant.

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Half-life

• The half-life of a reaction is the time required
  for the reactant concentration to decrease to
  one-half of its initial value.

• Solving for t1/2 we obtain

• Figure 14.8 illustrates the half-life of a
  first-order reaction.

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Figure 14.8 A graph illustrating that the
half-life of a first-order reaction is
independent of initial concentration.
Half life, t1/2, is the time it takes for the
R to decrease by 1/2.
This is exactly like radioactive decay.
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Half-life

• Sulfuryl chloride, SO2Cl2, decomposes in a
  first-order reaction to SO2 and Cl2.

• At 320 oC, the rate constant is 2.2 x 10-5 s-1.
  What is the half-life of SO2Cl2 vapor at this
  temperature?

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A model of SO2CI2(g)
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Half-life

• Sulfuryl chloride, SO2Cl2, decomposes in a
  first-order reaction to SO2 and Cl2.

• At 320 oC, the rate constant is 2.20 x 10-5 s-1.
  What is the half-life of SO2Cl2 vapor at this
  temperature?

• Substitute the value of k into the relationship
  between k and t1/2.

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Half-life

• Sulfuryl chloride, SO2Cl2, decomposes in a
  first-order reaction to SO2 and Cl2.

• At 320 oC, the rate constant is 2.20 x 10-5 s-1.
  What is the half-life of SO2Cl2 vapor at this
  temperature?

• Substitute the value of k into the relationship
  between k and t1/2.

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Half-life

• For a second-order reaction, half-life depends on
  the initial concentration and becomes larger as
  time goes on.

• Each succeeding half-life is twice the length of
  its predecessor.