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 between, relationship, equilibrium and/or rate:
“It would be a fallacy to deduce that the slow writer necessarily comes up with superior work. There seems to be scant relationship between prolificness and quality.”
—Fannie Hurst (1889–1968)
“We must introduce a new balance in the relationship between the individual and the government—a balance that favors greater individual freedom and self-reliance.”
—Gerald R. Ford (b. 1913)
“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)
“You are more than entitled not to know what the word ‘performative’ means. It is a new word and an ugly word, and perhaps it does not mean anything very much. But at any rate there is one thing in its favor, it is not a profound word.”
—J.L. (John Langshaw)