SAT Subject Test Chemistry




Chemical Equilibrium


Relation of Minimum Energy (Enthalpy) to Maximum Disorder (Entropy)

Some reactions are said to go to completion because the equilibrium condition is achieved when practically all the reactants have been converted to products. At the other extreme, some reactions reach equilibrium immediately with very little product being formed. These two examples are representative of very large values and very small values, respectively. There are essentially two driving forces that control the extent of a reaction and determine when equilibrium will be established. These are the drive to the lowest heat content, or enthalpy, and the drive to the greatest randomness or disorder, which is called entropy. Reactions with negative ΔH’s (enthalpy or heat content) are exothermic, and reactions with posi tive ΔS’s (entropy or randomness) are proceeding to greater randomness.

The Second Law of Thermodynamics states that the entropy of the universe increases for any spontaneous process. This means that the entropy of a system may increase or decrease but that, if it decreases, then the entropy of the surroundings must increase to a greater extent so that the overall change in the universe is positive. In other words,


When the ΔS is positive for the system, it means greater disorder.

The following is a list of conditions in which Δis positive for the system:

1. When a gas is formed from a solid, for example,

CaCO3(s) → CaO(s) + CO2(g ).

2. When a gas is evolved from a solution, for example,

Zn(s)+ 2H+(aq) → H2(g) + Zn2+(aq).

3. When the number of moles of gaseous product exceeds the moles of gaseous reactant, for example,

2C2H6(g) + 7O2 → 4CO2(g) + 6H2O(g).

4. When crystals dissolve in water, for example,

NaCl(s) → Na+(aq)+ Cl(aq).

Looking at specific examples, we find that in some cases endothermic reactions occur when the products provide greater randomness or positive entropy. This reaction is an example:

CaCO3(s)  CaO(s) + CO2(g)

The production of the gas and thus greater entropy might be expected to take this reaction almost to completion. However, this does not occur because another force is hampering this reaction. It is the absorption of energy, and thus the increase in enthalpy, as the CaCO3 is heated.

The equilibrium condition, then, at a particular temperature, is a compromise between the increase in entropy and the increase in enthalpy of the system.

The Haber process of making ammonia is another example of this compromise of driving forces that affect the establishment of an equilibrium. In this reaction

N2(g)+3H2(g)  2NH3(g)+heat

the forward reaction to reach the lowest heat content and thus release energy cannot go to completion because the force to maximum randomness is driving the reverse reaction.

Change in Free Energy of a System—the Gibbs Equation

These factors, enthalpy and entropy, can be combined in an equation that summarizes the change of free energy in a system. This is designated as ΔG. The relationship is

ΔG = ΔH − TΔS (is temperature in kelvins)

and is called the Gibbs free-energy equation.


Free energy, ΔG, depends on ΔH (enthalpy) and Δ(entropy).

The sign of ΔG can be used to predict the spontaneity of a reaction at constant temperature and pressure. If ΔG is negative, the reaction is (probably) spontaneous; if Δis positive, the reaction is improbable; and if ΔG is 0, the system is at equilibrium and there is no net reaction.

The ways in which the factors in the equation affect ΔG are shown in this table:

This drive to achieve a minimum of free energy may be interpreted as the driving force of a chemical reaction.


Know these relationships.