Dynamic equilibrium
In
In
Examples
In a new bottle of soda, the concentration of carbon dioxide in the liquid phase has a particular value. If half of the liquid is poured out and the bottle is sealed, carbon dioxide will leave the liquid phase at an ever-decreasing rate, and the partial pressure of carbon dioxide in the gas phase will increase until equilibrium is reached. At that point, due to thermal motion, a molecule of CO2 may leave the liquid phase, but within a very short time another molecule of CO2 will pass from the gas to the liquid, and vice versa. At equilibrium, the rate of transfer of CO2 from the gas to the liquid phase is equal to the rate from liquid to gas. In this case, the equilibrium concentration of CO2 in the liquid is given by Henry's law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.[1] This relationship is written as
where K is a temperature-dependent constant, P is the partial pressure, and c is the concentration of the dissolved gas in the liquid. Thus the partial pressure of CO2 in the gas has increased until Henry's law is obeyed. The concentration of carbon dioxide in the liquid has decreased and the drink has lost some of its fizz.
Henry's law may be derived by setting the
Dynamic equilibrium can also exist in a single-phase system. A simple example occurs with
At equilibrium the
In this case, the forward reaction involves the liberation of some
Dynamic equilibria can also occur in the gas phase as, for example when nitrogen dioxide dimerizes.
- ;
In the gas phase, square brackets indicate partial pressure. Alternatively, the partial pressure of a substance may be written as P(substance).[2]
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
where kf is the
The solution to this differential equation is
and is illustrated at the right. As time tends towards infinity, the concentrations [A]t and [B]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[3] that, for a general reaction, the overall equilibrium constant is related to the rate constants of the elementary reactions by
See also
References
Atkins, P.W.; de Paula, J. (2006). Physical Chemistry (8th. ed.). Oxford University Press.
- ^ Atkins, Section 5.3
- ISBN 0-521-28150-4.
- ^ a b Atkins, Section 22.4