Definitions

# Dynamic equilibrium

A dynamic equilibrium occurs when two opposing processes proceed at the same rate. A reversible chemical reaction will be at dynamic equilibrium when the rate of forward reaction is equal to the rate of the reverse reaction. While at dynamic equilibrium there is no change in the concentration of either the forward or reverse reactions. The word "dynamic" indicates that at equilibrium both the forward and reverse chemical reactions still occur rather than the reaction halting once equilibrium is reached.

An example of dynamic equilibrium, for a closed and partially filled water bottle water will evaporate from the surface of the water and the air in the bottle will begin to become saturated with water vapor. Eventually, the air will be completely saturated with water vapor, this water will then condense as its molecules collide with the surface of the water. When the rate of evaporation is equal to the rate of condensation the system is at dynamic equilibrium.

Although we have learned that the kinetics of a reaction may override predictions based purely on thermodynamics, the two aspects are not totally separated.The concept of dynamic equilibrium is not limited to simple changes of state such as that described above. It is often applied to the analysis of chemical reaction kinetics, to obtain useful information about the ratios of reactants and products which will form at equilibrium. It should be noted that at equilibrium the concentrations of the reactants and the concentrations of the products are constant.

The term also has applications across a wide range of disciplines. While it may be applied to less physical systems in these fields, it still relates to a stable situation maintained by balancing processes. For example: in economics it may be used to refer to the constant flux of capital in otherwise stable markets; in ecology, an unchanging population of organisms results from the balancing of birth rate against death rate.

This term can also be used to refer to a steady state (i.e., a state which isn't a true equilibrium, but does not change with time). This can only happen if the system is in contact with an environment which is not in equilibrium. A prime example is that of most stars - nuclear fusion provides an outward pressure to counteract the pressure of gravity, but neither the fusion continually produces energy, and the environment external to the star is certainly not in equilibrium, either.

NOTE that the previous two paragraphs contradict each other. For both the cases of economics (where the amount of capital in the environment is not in equilibrium) and of ecology (where the energy flow into the environment is required for organismal growth), the economic capital and the ecological population are "in contact with an environment which is not in equilibrium." Accordingly, both meet the definition of "steady state" as defined in the previous paragraph rather than "equilibrium" as defined beforehand.

## Equilibrium Constant K

If a system is in dynamic equilibrium, a constant ratio of concentrations for that equilibrium can be described.

In general, for the reaction aA + bB cC + dD, K is given by one of the following equilibrium constant expressions:

(i) $K_P = \left\{frac\left\{\left(P_C\right)^c\left(P_D\right)^d\right\}\left\{\left(P_A\right)^a\left(P_B\right)^b\right\}\right\}$

(ii) $K_C = \left\{frac\left\{\left[C\right]^c\left[D\right]^d\right\}\left\{\left[A\right]^a\left[B\right]^b\right\}\right\}$

where P indicates partial pressure and square brackets indicate concentration in molarity; that is, number of moles per litre of solution.

When both reactants and products are in the gaseous phase, the Equilibrium Constant is referred to as KP, and equation (i) is used; when reactants and products are all in solution, the Equilibrium Constant is referred to as KC, and equation (ii) is used.

The two can be related by the ideal gas law, $PV = nRT$,

where

$P$ is the absolute pressure of the gas,
$V$ is the volume of the gas,
$n$ is the number of moles of gas,
$R$ is the universal gas constant,
$T$ is the absolute temperature.