## Free Energy Changes in Chemical Reactions

#### Learning Objective

• Recall the possible free energy changes for chemical reactions.

#### Key Points

• If the free energy of the reactants is greater than that of the products, the entropy of the world will increase when the reaction takes place as written, and so the reaction will tend to take place spontaneously.
• If the free energy of the products exceeds that of the reactants, then the reaction will not take place.
• An important consequence of the one-way downward path of the free energy is that once it reaches its minimum possible value, net change comes to a halt.
• In a spontaneous change, Gibbs energy always decreases and never increases.

#### Term

• spontaneous changeA spontaneous process is the time-evolution of a system in which it releases free energy (usually as heat) and moves to a lower, more thermodynamically stable energy state.

## The Direction and Extent of Chemical Change

ΔG determines the direction and extent of chemical change. Remember that ΔG is meaningful only for changes in which the temperature and pressure remain constant. These are the conditions under which most reactions are carried out in the laboratory. The system is usually open to the atmosphere (constant pressure) and the process is started and ended at room temperature (after any heat that has been added or which was liberated by the reaction has dissipated.)

The importance of the Gibbs function can hardly be over-stated: it determines whether a given chemical change is thermodynamically possible. Thus, if the free energy of the reactants is greater than that of the products, the entropy of the world will increase and the reaction takes place spontaneously. Conversely, if the free energy of the products exceeds that of the reactants, the reaction will not take place.

In a spontaneous change, Gibbs energy always decreases and never increases. This of course reflects the fact that the entropy of the world behaves in the exact opposite way (owing to the negative sign in the TΔS term). Here is an example:

${H}_{2}O(\text {liquid}) \rightarrow {H}_{2}O (\text{ice})$

Water below zero degrees Celsius undergoes a decrease in its entropy, but the heat released into the surroundings more than compensates for this so the entropy of the world increases, the free energy of the H2O diminishes, and the process proceeds spontaneously.

An important consequence of the one-way downward path of the free energy is that once it reaches its minimum possible value, net change comes to a halt. This, of course, represents the state of chemical equilibrium. These relations are summarized as follows:

• $\Delta G : The reaction will occur spontaneously to the right. • [latex]\Delta G > 0$: The reaction will occur spontaneously to the left.
• $\Delta G = 0$: The reaction is at equilibrium and will not proceed in either direction.

## Conditions for Spontaneous Change

Recall the condition for spontaneous change:

ΔG = ΔH – TΔS < 0

where ΔG = change in Gibbs free energy, ΔH = change in enthalpy, T = absolute temperature, and ΔS = change in entropy

It is apparent that the temperature dependence of ΔG depends almost entirely on the entropy change associated with the process. (it is appropriate to say “almost” because the values of ΔH and ΔS are themselves slightly temperature dependent; both gradually increase with temperature). In particular, notice that in the above equation the sign of the entropy change determines whether the reaction becomes more or less spontaneous as the temperature is raised.

For any given reaction, the sign of ΔH can also be positive or negative. This means that there are four possibilities for the influence that temperature can have on the spontaneity of a process:

## Case 1: ΔH < 0 and ΔS > 0

Under these conditions, both the ΔH and TΔS terms will be negative, so ΔG will be negative regardless of the temperature. An exothermic reaction whose entropy increases will be spontaneous at all temperatures.

## Case 2: ΔH < 0 and ΔS < 0

If the reaction is sufficiently exothermic it can force ΔG to be negative only at temperatures below which |TΔS| < |ΔH|. This means that there is a temperature defined by $T = \frac{\Delta H}{\Delta S}$ at which the reaction is at equilibrium; the reaction will only proceed spontaneously below this temperature. The freezing of a liquid or the condensation of a gas are the most common examples of this condition.

## Case 3: ΔH > 0 and ΔS > 0

This is the reverse of the previous case; the entropy increase must overcome the handicap of an endothermic process so that TΔS > ΔH. Since the effect of the temperature is to “magnify” the influence of a positive ΔS, the process will be spontaneous at temperatures above $T = \frac{\Delta H}{\Delta S}$ . (Think of melting and boiling. )

## Case 4: ΔH > 0 and ΔS < 0

With both ΔH and ΔS working against it, this kind of process will not proceed spontaneously at any temperature. Substance A always has a greater number of accessible energy states, and is therefore always the preferred form.