# Boyleâ€™s Law

Chemical equilibrium is achieved when the rate of the forward and reverse reactions is equal and the concentrations of the reactants and products remain constant. Chemical equilibria are stable and dynamic in nature.

If the reactants and products in a system are in the same phase, the equilibrium is said to be homogeneous.

A phase is a homogeneous (same composition and properties throughout) part of a system, separated from other phases (or homogeneous parts) by bounding surfaces.

If more than one phase is present in a chemical equilibrium, it is said to be heterogeneous equilibrium.
1. Let us consider the following equilibrium reaction

Its equilibrium constant (Keq) will be

Concentrations of Y and Z are their respective number of moles per unit volume of the container (as the volume occupied by the gas is equal to the volume of the container). The concentration of X is the number of moles of X per unit volume of solid. As we know, the concentration of all pure solids (and pure liquids) is a constant as it is represented by d/M (where d and M represent the density and molar mass, respectively). This ratio of d/M will be a constant whether X is present initially or at equilibrium. This means that the concentration of X is not varying, but is a constant, which can be merged with Keq to give another constant called Kc.

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Thus, expression Kc involves only those species whose concentration changes during the reaction.

The distinction between Keq and Kc is that the expression of Keq involves all species (whether they are pure solids, pure liquids, gases, solvents, or solutions), while the expression Kc involves only those species whose concentration is a variable (such as gases and solutions). Thus, expression Kc is devoid of pure components (such as pure solids and pure liquids) and solvents.

Since LHS of the expression is a constant, the ratio PZ/PY would also be a constant, represented by KP. Therefore,

2. Now, let us change the phase of reactant X from pure solid to solution and add another gaseous product. The equilibrium reaction can now be represented as:

We have seen above that concentration of Y, Z, and A is a variable but what about the concentration of X now. Let us see. X in solution phase means some moles of X (solute) are dissolved in a particular solvent. The concentration of X is thus given as the number of moles of X per unit volume of solution (volume of the solution has major contribution from the volume of solvent; the volume of solute hardly contributes to it). Let the number of moles of X taken initially is a, which is dissolved in V liter of solvent. So, the initial concentration of X is a/V. Now at equilibrium, the moles of X reacted with Y is x. Thus, the concentration of X now becomes (a âˆ’ x)/V. This shows that the concentration of X changes during the reaction and X is thus a variable. Thus, the given expression of Keq involves all variable terms, so the ratio can also be referred as Kc. Therefore,

Now, if we try to express the concentration of X, Y, Z, and A in terms of partial pressures, we will be able to do it only for Y, Z, and A, but not for X, since it is a solution. As the concentration of X cannot be expressed in terms of its pressure or vapor pressure and constants, it should be kept as concentration term only in the equilibrium constant expression. Therefore,

The LHS of the expression is a constant (as Kc, R, and T all are constant), which implies that the RHS will also be a constant. But RHS of the expression can neither be called KP (as all are not partial pressure terms) nor Kc (as all are not concentration terms). So such expression that involves both partial pressure and concentration terms are referred as KPC. Therefore,

Thus, KP can exist only for that equilibrium which satisfies the following two conditions:
1. At least one of the reactant or product should be in gaseous phase.
2. No component of the equilibrium should be in the solution phase (because when solution is present, the equilibrium constant would be called KPC).
3. For the equilibrium of type: n1A(g) + n2B(g)  m1C(g) + m2D(g)KP = Kc(RT)Î”n

where

Î”n = Sum of stoichiometric coefficient of the gaseous product(s)

â€“ Sum of stoichiometric coefficient of the gaseous reactant(s)