A. Energy Requirements
Every reaction has an energy change associated with it. This energy change can be shown either as the enthalpy change ( H) or as the free energy change ( G). Free energy G is the energy available to do useful work. These two energy changes are related by the equation

G = H - T S

in which T is the temperature (K) at which the reaction is taking place and S is the associated entropy change.

1. Entropy
Entropy measures disorder. The entropy change accompanying a reaction measures how the reaction affects the orderliness of the system. Other factors being equal, it is the nature of matter to move toward a state of maximum disorder. When rocks are dumped from a truck, they do not spontaneously arrange themselves in a neat wall; rather, they land in an untidy pile. If you emptied a bag of red, white, and blue jelly beans onto a flat surface, they would not spontaneously settle into a replica of the flag but would become even more disordered than they were in the bag, for they would now be spread over a larger surface. In either case, energy must be added to decrease the entropy - to arrange the rocks into a neat fence or the jelly beans into a flag. See Figure 13.1 for another example of increase in entropy.

FIGURE 13.1 The concept of entropy: (a) order; (b) disorder

In our study of chemistry we have seen changes in entropy. In Chapters 9 and 10 we saw that the structure of a solid is usually well ordered, the structure of a liquid is less ordered, and that of a gas is quite random. From these facts, we can deduce that the change from a solid to a liquid is accompanied by an increase in entropy (Figure 13.2); so is a change from a liquid to a gas. When molecules containing many atoms break apart to form smaller molecules, there is also an increase in entropy.

FIGURE 13.2 Entropy in the three physical states: (a) crystalline solid (order); (b) liquid (less order); and (c) gas (very little order).

2. Free energy
The free energy change G associated with a reaction tells whether or not the reaction will occur under the specified conditions. For a reaction to occur spontaneously (that is, without the net addition of energy) and actually produce the products shown in its equation, the free energy change at the specified conditions must be negative. The three factors that play a role in determining the spontaneity of a reaction (that is, the sign of G) are: (1) whether the reaction as written is exothermic ( H < 0), (2) the temperature at which it is proposed to run the reaction, and (3) the entropy change S associated with the reaction. These factors are related by the equation given earlier:

G = H - T S

Careful examination of this equation allows us to make the following predictions:

1. If a reaction is exothermic ( H is negative) and the entropy S is positive (more disorder), the free energy change is always negative and the reaction is always spontaneous.

2. If a reaction is endothermic ( H positive) and the entropy change S is negative (less disorder), the free energy change is always positive and the reaction is never spontaneous.

3. If the enthalpy change H and the entropy change S are both positive or both negative, the spontaneity of the reaction depends on the temperature. These predictions are summarized in Table 13.1.

The phase changes of water illustrate the dependence of some free energy changes on temperature. When ice melts, the change is endothermic ( H is positive), and entropy increases ( S is positive) as the water molecules lose ordered arrangement of ice crystals. The T S factor for melting ice at 298 K is numerically larger than H; the free energy change G is then negative, so melting is spontaneous at that temperature.

Similarly, the freezing of water at temperatures below 273 K is an example of a spontaneous change that is exothermic and accompanied by a decrease in entropy (an increase in order).

3. Activation energy
A reaction that is spontaneous is always accompanied by the net release of free energy (energy available to do useful work). However, some spontaneous reactions require added energy to get started. The energy they finally release includes both this added energy and the calculated free energy of the reaction. We all know that paper burns in air (the reaction has a negative free energy), but the reaction does not take place until extra energy is added (the heat from a burning match). That added energy is called activation energy.

B. Requirements at the Molecular Level
Consider now what happens at the molecular level when a reaction takes place. Bonds between the atoms in the reacting molecules break, and new bonds form to combine the atoms in a different way. For this reaction to occur, the reacting molecules must collide. Together they must have enough kinetic energy (energy of motion) to overcome the repulsion between the clouds of electrons that surround the molecules. As they collide, the two reacting molecules must be oriented so that those atoms that will be bonded together in the product are next to each other. Without this molecular orientation, the molecules will retreat from the collision without reacting (Figure 13.3). A collision that takes place with enough energy and with the correct molecular orientation is called an effective collision. Needless to say, not all collisions are effective.

FIGURE 13.3 For a reaction between molecules to occur, the molecules must be correctly oriented when they collide.