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:
“When any relationship is characterized by difference, particularly a disparity in power, there remains a tendency to model it on the parent-child-relationship. Even protectiveness and benevolence toward the poor, toward minorities, and especially toward women have involved equating them with children.”
—Mary Catherine Bateson (20th century)
“That doctrine [of peace at any price] has done more mischief than any I can well recall that have been afloat in this country. It has occasioned more wars than any of the most ruthless conquerors. It has disturbed and nearly destroyed that political equilibrium so necessary to the liberties and the welfare of the world.”
—Benjamin Disraeli (1804–1881)
“If we became students of Malcolm X, we would not have young black men out there killing each other like they’re killing each other now. Young black men would not be impregnating young black women at the rate going on now. We’d not have the drugs we have now, or the alcoholism.”
—Spike Lee (b. 1956)