- Physical Chemistry I
Spring 2012, Unique 52135
Lecture Summary, 18-20 April 2012
rate laws: Any chemical reaction can
be broken down into a series of steps which proceed in order from
reactant to product. These steps are called elementary
reactions in equilibrium, and the rate law from each step can
be written down from the stoichiometrically balanced elementary
reaction. These elementary reactions demonstrate that during
the reaction, short-lived, high energy products are formed and then
consumed essentially immediately. These are called intermediates,
and are not shown in either the reactants or products. By
writing down a correct series of elementary reactions, and then
figuring out what happens to the intermediates, we can solve a rate
law analytically. By comparing this rate law to the
experimentally observed rate law, we can determine if our series of
elementary steps and our assumption about the intermediates are
correct. If our solved rate law does not match the
experimentally determined rate law, then we have either written down
an incorrect series of elementary reactions, or made an incorrect
assumption about the nature of the intermediates, or both.
Principle of Detailed Balance: Since our elementary equations are in equilibrium and all species are represented by the stoichiometric amounts:
k(1) / k(-1) = [P] / [R] = K(c)
or the ratio of the forward and backward rate constants is equal to the equilibrium constant of that elementary reaction. This is called the principle of detailed balance.
Steady-State Approximation: The steady-state approximation says that the intermediate generated by the rate-determining step of the reaction will be consumed essentially as soon as it is formed:
d[I] / dt = 0
This can happen in two ways. Either the backwards reaction that created [I] in the first place is very fast or the forward reaction that consumes [I] and takes it further to products is very fast. That in turn means that one rate constant in the reaction will be significantly greater than all the others, and it dominates any equation we set up for the rate of the reaction.
Fast Equilibrium: The steady-state approximation is usually most useful for reactions in which the first elementary step is the slowest (i.e. rate determining). Sometimes that is not the case, and the intermediate created in the first or first few elementary steps builds up over time before it is consumed:
[I] = K(c)[R]
Both the SSA and FE assumptions allow us to solve for [I] in terms of [R] and/or [P], which in turn will solve for a rate law. This rate law always must be compared to the experimentally observed rate law to determine if it is correct. If not, then one or more of our assumptions has been wrong, and we need to rethink the problem.