Kinetics

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Kinetics

• Sparks Chapter 7, pp. 207 - 215
• Additional McBride Chap. 1 . (1.2g)

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Rate Equations

• Forward rate
• Good where only the forward reaction is
  important ignore back reaction.
• e.g. A B ----gt C D

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• Far away from equilibrium where only the forward
  reaction is important
• Where kf is the forward rate constant and a and b
  are the reaction orders with respect to A and B.
• Nearer equilibrium the reverse rates must be
  considered

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Zero order

• a 0, b 0
• If at t 0, A0 A
• R kf

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• A0 - A -kt

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Zero order rate plot
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Typical zero order reaction

• The quantity of reaction sites is fixed.
• Catalytic reactions when the reactants are
  sufficiently concentrated to keep the reactions
  sites saturated.
• In this case increasing the concentration of
  reactants will not change the rate of reaction.

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First order

• a1, b0 (or B constant, pseudo first order )

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First order decay

• e.g. radioactive decay or degradation of many
  pesticides.

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• Half-life
• Applies only to first order reactions
• ln 0.5 kt

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Second Order

• Sum of the coefficients on the reactant
  concentrations 2.
• A and first order in B or
• second order in one component.

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Second order decay
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In Class Exercise

• A pesticide in soil has a 1/2 life of 69 days
• What is the reaction rate constant?
• How long will it take to reduce 100 mg/kg to 24
  g/kg?

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Answer

• k 0.693/69 .0010 d-1
•  25/100 1/4 2 half- lives
• time 2 (69) 138 days

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Effect of Temperature

• Arrhenius Equation
• A constant for each reaction,
• EA activation energy,
• R gas constant.

where T is in degrees Kelvin Activation
energy
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• where T is in degrees Kelvin
• EA Activation energy

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Arrhrenius plot
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• The activation energy represents an energy hump
  that must be overcome to get the reaction to go.
• See McBride (1994), Fig.1.6.
• Q10 for biological reactions in soil
• Biologically catalyzed reactions in soil
  generally double to triple in rate with 10oC rise
  in natural temperature ranges. (Q10 2-3)

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Activation Energy
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Quick Summary

• The rates of reactions can usually be defined by
  zero, first, or second order rate equations.
• In soils first order reactions are common.
• The temperature dependence of reactions rates is
  given by the the Arrhenius equation

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