A rate law describes the behavior of a reaction. The rate of a reaction is a function of temperature (through the rate constant) and concentration.
Power Law Model
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k is the specific reaction rate (constant) and is given by the Arrhenius Equation:
k = Ae-E/RT, where E = activation energy (cal/mol)
R = gas constant (cal/mol*K)
T = temperature (K)
A = frequency factor
Activation Energy
Example: If the rate law for the non-elementary reaction
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is found to be
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then the reaction is said to be 2nd order in A, 1st order in B, and 3rd order overall.
Elementary Reactions
A reaction follows an elementary rate law if the stoichiometric coefficients are the same as the individual reaction order of each species. For the reaction in the previous example (above), the rate law would be:
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Rate Laws
Reversible Reactions
The net rate of formation of any species is equal to its rate of formation in the forward reaction plus its rate of formation in the reverse reaction:
ratenet = rateforward + ratereverse
At equilibrium, ratenet
0 and the rate law must reduce to an equation that is thermodynamically consistent with the equilibrium constant for the reaction.
Example: Consider the exothermic, heterogeneous reaction
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At low temperature, the rate law for the disappearance of A is
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[Recall PA=CART]
At high temperature, the exothermic reaction is significantly reversible:
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What is the corresponding rate law? Let's see.
If the rate of formation of A for the forward reaction (A + B
C) is
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then we need to assume a form of the rate law for the reverse reaction that satisfies the equilibrium condition. If we assume the rate law for the reverse reaction (C
A + B) is
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and:
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Does this rate law satisfy our requirement that, at equilibrium, it must reduce to an equation that is thermodynamically consistent with KP? Let's see.
From Appendix C we know that for a reaction at equilibrium:
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At equilibrium, rnet
0, so:
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Solving for KP gives:
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The conditions are satisfied.