The rate of reaction

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The rate of reaction
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Rate Law

• Relation between rate of reaction and
  concentration of the reactants

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Three important problems

• Determination of rate law and rate constant from
  experimental data.
• Construct reaction mechanism that are consistent
  with rate law.
• Value of rate constant and their temperature
  dependence

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Determination of rate law

• Isolation method Add large excess
• Methods of initial rate measurement of rate of
  reaction for several different initial
  concentration of reactants.

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Integrated Rate Laws
Consider a simple 1st order rxn A ? B

Differential form
How much A is left after time t? Integrate
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Integrated Rate Laws

• The integrated form of first order rate law

Can be rearranged to give
A0 is the initial concentration of A
(t0). At is the concentration of A at some
time, t, during the course of the reaction.
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Integrated Rate Laws

• Manipulating this equation produces

which is in the form
y mx b
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First-Order Processes

• If a reaction is first-order, a plot of ln At
  vs. t will yield a straight line with a slope of
  k.

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Second-Order Processes

• Similarly, integrating the rate law for a
  process that is second-order in reactant A

Rearrange, integrate
y mx b
also in the form
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Second-Order Processes

• So if a process is second-order in A, a plot of
  1/A vs. t will yield a straight line with a
  slope of k.

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Half-Life

• Half-life is defined as the time required for
  one-half of a reactant to react.
• Because A at t1/2 is one-half of the original
  A,
• At 0.5 A0.

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Half-Life

• For a first-order process, set At0.5 A0 in
  integrated rate equation

NOTE For a first-order process, the half-life
does not depend on A0.
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Half-Life- 2nd order

• For a second-order process, set
• At0.5 A0 in 2nd order equation.

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Outline Kinetics
First order Second order Second order
Rate Laws
Integrated Rate Laws complicated
Half-life complicated
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Reaction order and reaction mechanism
Most important application of studying the order
of a reaction is to establish the mechanism of
reaction. Reactions proceed in one or more
elementary steps. In elementary step
molecularity order of reaction
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Overall order of reaction corresponds to
stoichiometric equation gt The reaction mechanism
most probably involves one elementary step that
is identical to stoichiometric equation.
When the reaction order does not corresponds to
the stoichiometry of the reaction, the reaction
certainly involves more than one elementary
reaction.
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When the reaction order does not corresponds to
the stoichiometry of the reaction, the reaction
certainly involves more than one elementary
reaction.
Elementary Reaction

• Reversible elementary reaction
• A ? B
• (ii) Consecutive elementary reaction
• A ? B ? C
• (iii) Parallel Reaction
• A

B
C
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Consecutive Reaction
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Consecutive Reaction
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Consecutive Reaction
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Consecutive Reaction

• Rate of formation of the final product P depends
  on only the smaller of two rate constants.

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Consecutive Reaction
This is the basis of steady-State approximation.
P
Conc
A
I
Time
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Consecutive Reaction
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Case II when
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When are consecutive and Single-Step reactions
distinguishable ?
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Parallel Reaction
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Parallel Reaction
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Thermodynamic vs. Kinetic Control
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Parallel Reaction
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Reversible Reaction
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Reversible reaction
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Reversible reaction
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Higher order reversible Reaction
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