Equilibrium Constant: Why is k Defined?

[pivoxa15]

Why is the equilibrium constant, k defined the way it is?

There are other expressions that would also be constant at the chemical equilibrium. These expressions could contain terms that are concentrations of the chemicals at eqiulibrium which will always be constants. So multiply a bunch of constants and get a constant, every time.

 

[Gokul43201]

It follows from the expression for the reaction free energy. Consider, for example, the equilibrium A <--> B, where both are ideal gases. Then, the reaction free energy change, defined by
$$\Delta G(reac) = \left( \frac{\partial G} {\partial x} \right) _{p,T}$$

where x is the reaction co-ordinate, is clearly equal to difference in chemical potentials of A and B (follows directly from definition of the Gibb's Free Energy). Then, the reason for the particular form of the equilibrium constant is seen to come from the variation of the chemical potential with p,T.

$$\mu_ i = \mu_ i^0 + RT~ ln~p_i ~ \implies \Delta G (reac) = \mu _B - \mu _A = \Delta G^0(reac) +RT ~ln(p_B/p_A)$$

At equilibrium, $$\Delta G(reac) = 0$$

Plug this in above, and you have,
$$\Delta G^0(reac) = -RT ~ ln(p_B/p_A)_{equil}$$

This is the motivation to define $K = (p_B/p_A)_{equil}$, for this particular system. The definition can be generalized to solutions and to systems with more components.

In a more simplistic argument, one might say that the above definition provides, by means of comparing the ionic product with the equilibrium constant, a direct means of relating to le Chatelier's principle. In other words, it preserves the sanctity of forward and backward reactions, and hence, provides a simple relationship between the equilibrium constant and the forward and reverse rate constants, through the definition of equilibrium as experiencing equal forward and reverse rates.

 

[ravenprp]

The equilibrium constant, k, is defined as the ratio of the forward rate constant to the reverse rate constant at equilibrium. This definition is based on the law of mass action, which states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants.

By defining k in this way, it allows us to quantitatively describe the ratio of products to reactants at equilibrium. This is important because it helps us understand the direction and extent of a chemical reaction. A large value of k indicates that the equilibrium lies towards the products, while a small value of k indicates that the equilibrium lies towards the reactants.

Moreover, this definition of k also takes into account the effect of temperature on the equilibrium constant. As temperature increases, the forward and reverse rates of a reaction may change, but the ratio of these rates, and thus the equilibrium constant, remains constant. This allows us to predict how changes in temperature will affect the equilibrium position of a reaction.

In essence, the definition of the equilibrium constant, k, is necessary to accurately describe the behavior of a chemical reaction at equilibrium. It allows us to quantitatively express the relationship between the concentrations of reactants and products, and how changes in temperature affect this equilibrium. Without this definition, it would be much more difficult to understand and predict the behavior of chemical reactions.