## Entropy Considerations ### What is entropy?

The easiest way to think of entropy is as a measure of disorder in a system. Alternatively, it is the spreading and sharing of thermal energy within a system. Entropy is energy in the system that is unusable for chemical change. Over time, entropy increases.

We use S to stand for entropy and S is the change in entropy.

### Free Energy

We have talked about the energy changes in chemical reactions and changes in state in terms of enthalpy. Remember that H is the change in heat energy at constant pressure.

We can classify chemical reactions as being spontaneous or non-spontaneous. In most spontaneous reactions heat is released from the system to the surroundings and H is a negative number. These are exothermic reactions.

Some reactions proceed at a given temperature even though they are endothermic. The surroundings get colder as heat is absorbed. How can a spontaneous reaction absorb heat when all chemical systems tend to move to lower energy states from higher states?

The answer is entropy.

A very useful energy term is G, or the Gibbs free energy. It is this that determines whether or not a reaction will proceed spontaneously in the forward direction. If the value of G is a negative number, the reaction is spontaneous as written. If the value of G is a positive number, the reaction will not occur as written and, in fact, the reverse reaction will be spontaneous. G = H - T S

The enthalpy change is usually the most important factor in the Gibbs free energy because the value of H is typically much greater than the value of S. However when the enthalpy change is small the entropy change can determine the spontaneity of the reaction.

### Entropy Changes in Solutions

How does this relate to solutions and intermolecular forces? Let's consider the case of water and table salt.  Water is a highly ordered material. You made models of parts of the ice/water lattice in class showing that each oxygen atom is connected to others around it through bridging hydrogen atoms (an extreme case of hydrogen bonding). When something dissolves in water, some of these O-H bonds are broken. This requires heat energy. The water molecules can then form attractive interactions to solute ions or molecules, releasing heat energy.

A crystal of NaCl is also highly ordered. The chloride anions form a cubic close packed lattice and the sodium cations fit into the octahedral holes in the lattice. Strong ionic bonding holds the anions and cations together in the crystal. When NaCl dissolves in water the strong ionic bonds are broken (requiring heat energy) and the ions interact with water molecules (releasing heat energy).

The solution of NaCl in water has much less order than the pure water and the crystalline salt. Entropy increases every time a solute dissolves in a solvent.

Examples:
• When NaCl dissolves in water the heat required just about balances the heat released so the temperature of the solution changes very little.

• When calcium chloride, CaCl2, dissolves in water, heat is released. This salt is used in hot packs.

• When ammonium nitrate, [NH4][NO3], dissolves in water the solution becomes colder. This salt is used in cold packs. Even though the enthalpy change is a positive number, the dissolution is spontaneous because the Gibbs free energy change, G, is negative due to the entropy term.

Professor Patricia Shapley, University of Illinois, 2011