Chemical Kinetics

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Chemical Kinetics

• Chapter 3

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Chemical Reactions

• Elements combine to form compounds by chemical
  reaction (atomic shuffle or rearrangement),
  follow
• Law of conservation of mass
• Law of constant proportions - compounds made up
  of same elemental components in same proportion
  by weight
• Law of multiple proportions - ratios of wt of 1
  element combining with fixed amt of another is in
  small whole nos.

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Types of Chemical Reactions

• Proton transfers (acid base reactions)
  neutralization, alkalinity measurements
• Electron transfer (oxidation/reduction)
  chlorination, ozonation, biological treatment
• Electron sharing (covalent, ionic bonding) ion
  exchange, precipitation, softening
• Metathesis - rearrangement of atoms, ions
  precipitation, softening

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Chemical Equations

• Used to describe chemical reactions
• aA bB-----gt cC dD
• products reactants
• Balanced equation (including redox reactions)
• Reaction quantities

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Chemical Kinetics

• Approaches in evaluating a chemicals fate and
  treatment kinetics and equilibrium
• Kinetics deals with the rates of reactions.
• Kinetic approach is appropriate when the reaction
  is slow relative to our time frame or when we are
  interested in the rate of change of
  concentration.
• Rate Change in concentration/time

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Factors that affect reaction rate

• Concentration of reactants
• Increasing concentration of reactants often
  increase the rate of reaction
• Temperature
• Increasing the temperature generally increases
  the rate of reaction
• Catalysts
• Catalysts increase the rate of reaction without
  themselves being consumed

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The Rate Law

• Rate law used to predict the rates of chemical
  and biological processes.
• The rate law describes the relationship between
  the rate of a reaction and the concentration of
  the reactants.

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Reaction Rate

• Rate (R ) kAaBb
• The rate constant, k
• Relates rate and concentration at a particular
  temperature

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The reaction order

• The rate law describing the decrease in
  concentration of chemical C with time

where C is concentration of C t is time k is
rate constant dependant on the order of the
reaction n, reaction order
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Zero-order Reaction

• If n is zero,
• This is the rate law describing a zero-order
  reaction.

Unit conc/time (moles/L-s)
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First-Order Reaction

• If n1,
• This is the rate law for a first-order reaction.
• E.g. radioactive decay.

(Unit of time-1,e.g. s-1)
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Example 13

• How long will it take the CO concentration in a
  room to decrease 99 after the source of CO is
  removed and the windows are opened? Assumed the
  first-order rate constant for CO removal (due to
  dilution by incoming clean air) is 1.2 h-1.

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Pseudo-First-Order Reactions

• The rate law for this reaction is
• If the concentration of A does not change
  significantly during the reaction i.e.
• , the
  concentration of A may be assumed to be
  constant can be incorporated into the rate
  constant, k.
  

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• Then, the rate law becomes
• where k is the pseudo-first-order rate constant
  and equals kA0a.
• The rate law for disappearance of substance B
• If b1,

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Example 14

• An engineer is modeling the transport of a
  chemical contaminant in groundwater. The
  individual has a mathematical model that only
  accepts first-order degradation rate constants
  and a handbook of "subsurface chemical
  transformation half- lives." Subsurface
  half-lives for benzene, TCE, and toluene are
  listed as 69, 231, and 12 days, respectively.
  What are the first-order rate constants for all
  three chemicals?

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Half-life

• The half-life, t½, is defined as the time
  required for the concentration of a chemical to
  decrease by one half (e.g. C0.5C0.
• For zero-order reactions 0.5C0 C0-kt½
• For first-order reactions 0.5C0 C0e-kt

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Example 15

• After the Chernobyl nuclear accident, the
  concentration of 137Cs in milk was proportional
  to the concentration of 137Cs in the grass that
  cows consumed. The concentration in the grass
  was, in turn, proportional to the concentration
  in the soil. Assume that the only reaction by
  which 137Cs was lost from the soil was through
  radioactive decay and the half-life for this
  isotope is 30 years. Calculate the concentration
  of 137Cs in cow's milk after 5 years if the
  concentration in milk shortly after the accident
  was 12,000 Bq/L. (Note A Bequerel is a measure
  of radioactivity. One Bequerel equals one
  radioactive disintegration per second.)

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Effect of Temperature on Rate Constant

• Rate of molecular motion was a function of
  temperature.
• Higher the temperature, the faster the molecules
  move, which results in an increase in the number
  of collisions per unit time. A higher temp. also
  increases the energy of the collisions.
• As a result, a greater fraction of the collisions
  results in a chemical reaction.
• Thus, the rate of chemical reactions that depend
  on collision of two or more molecules will be
  increased by an increase in temperature.

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Arrhenius equation

• The Arrhenius equation is used to adjust rate
  constants for changes in temperature
• where k is the rate constant of a particular
  order
• A is termed as preexponential factor (same unit
  as k)
• Ea is the activation energy (kJ/mole)
• R is the gas constant
• T is a temperature (K)

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Rate Constant for CBOD

• The carbonaceous biochemical oxygen demand (CBOD)
  rate constant, kL, known at a particular
  temperature, is typically converted to other
  temperatures using the following expression
• is a dimensionless temperature coefficient.
• In fact, equals

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Example 16

• The rate constant for CBOD at 20oC is 0.1 day-1.
  What is the rate constant at 30oC? Assume
  1.072.