Relationship Between Equilibrium and Rate Constants
In a simple reaction such as the isomerization:
there are two reactions to consider, the forward reaction in which the species A is converted into B and the backward reaction in which B is converted into A. If both reactions are elementary reactions, then the rate of reaction is given by
where kf is the rate constant for the forward reaction and kb is the rate constant for the backward reaction and the square brackets, denote concentration. If only A is present at the beginning, time t=0, with a concentration 0, the sum of the two concentrations, t and t, at time t, will be equal to 0.
The solution to this differential equation is
and is illustrated at the right. As time tends towards infinity, the concentrations t and t tend towards constant values. Let t approach infinity, that is, t→∞, in the expression above:
In practice, concentration changes will not be measurable after . Since the concentrations do not change thereafter, they are, by definition, equilibrium concentrations. Now, the equilibrium constant for the reaction is defined as
It follows that the equilibrium constant is numerically equal to the quotient of the rate constants.
In general they may be more than one forward reaction and more than one backward reaction. Atkins states that, for a general reaction, the overall equilibrium constant is related to the rate constants of the elementary reactions by
Read more about this topic: Dynamic Equilibrium
Famous quotes containing the words relationship, equilibrium and/or rate:
“Artists have a double relationship towards nature: they are her master and her slave at the same time. They are her slave in so far as they must work with means of this world so as to be understood; her master in so far as they subject these means to their higher goals and make them subservient to them.”
—Johann Wolfgang Von Goethe (1749–1832)
“There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.”
—Ralph Waldo Emerson (1803–1882)
“At the rate science proceeds, rockets and missiles will one day seem like buffalo—slow, endangered grazers in the black pasture of outer space.”
—Bernard Cooper (b. 1936)