# Free Energy Changes in Chemical Reactions

## ΔG determines the direction and extent of chemical change.

#### 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 in the direction written, but it will tend to proceed in the reverse direction.

• 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.

#### Terms

• A 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.

#### Figures

1. ##### Free Energy and Chemical Reactions

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.

## Free Energy Changes in Chemical Reactions

ΔG determines the direction and extent of chemical change. Please 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 we begin and end the process at room temperature (after any heat we have added or which is liberated by the reaction has dissipated.)

The importance of the Gibbs function can hardly be over-stated: it serves as the single master variable that 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 when the reaction takes place as written, and so the reaction will tend to take place spontaneously. Conversely, if the free energy of the products exceeds that of the reactants, then the reaction will not take place in the direction written, but it will tend to proceed in the reverse direction.

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:

${H}_{2}O(liquid) → {H}_{2}O (ice)$

Water below its freezing point 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 in Figure 1.

Recalling 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. (We 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 spontaniety 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. Anexothermic 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 negative only at temperatures below which |TΔS| < |ΔH|. This means that there is a temperature T = ΔH / ΔS 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 = ΔH / ΔS. (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.

#### Key Term Glossary

atmosphere
a layer of gases that may surround a material body of sufficient mass, such as the earth, and that is held in place by the gravity of the body
##### Appears in these related concepts:
Boiling
Boiling is the rapid vaporization of a liquid and occurs when a liquid is heated to its boiling point. A liquid's boiling point is the temperature at which the vapor pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding environment.
##### Appears in these related concepts:
chemical equilibrium
the state of a reversible reaction in which the rates of the forward and reverse reactions are the same
##### Appears in these related concepts:
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present at concentrations which have no further tendency to change with time.
##### Appears in these related concepts:
chemical reaction
A process involving the breaking or making of interatomic bonds, in which one or more substances are changed into others.
##### Appears in these related concepts:
condensation
the change of the physical state of matter from gaseous phase into liquid phase
##### Appears in these related concepts:
constant
Consistently recurring over time; persistent
##### Appears in these related concepts:
endothermic
of a chemical reaction that absorbs heat energy from its surroundings
##### Appears in these related concepts:
energy
a quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent
##### Appears in these related concepts:
enthalpy
In thermodynamics, a measure of the heat content of a chemical or physical system.
##### Appears in these related concepts:
Enthalpy
A measure of the total energy of a thermodynamic system.
##### Appears in these related concepts:
entropy
A thermodynamic property that is the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work.
##### Appears in these related concepts:
equilibrium
the state of a reaction in which the rates of the forward and reverse reactions are the same
##### Appears in these related concepts:
exothermic
of a chemical reaction that releases energy in the form of heat
##### Appears in these related concepts:
free energy
The difference between the internal energy of a system and the product of its entropy and absolute temperature.
##### Appears in these related concepts:
Freezing
Freezing or solidification is a phase transition in which a liquid turns into a solid when its temperature is lowered below its freezing point.
##### Appears in these related concepts:
freezing point
The temperature at which a liquid freezes, and the solid and liquid phases are in equilibrium; normally the same as the melting point.
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gas
Matter in a state intermediate between liquid and plasma that can be contained only if it is fully surrounded by a solid (or held together by gravitational pull); it can condense into a liquid, or can (rarely) become a solid directly.
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gibbs free energy
a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure
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Gibbs free energy
The difference between the enthalpy of a system and the product of its entropy and absolute temperature: a measure of the useful work obtainable from a thermodynamic system at constant temperature and pressure.
##### Appears in these related concepts:
heat
Heat is defined as the energy transferred from one system to another by thermal interaction.
##### Appears in these related concepts:
liquid
A substance that flows and keeps no definite shape, such as water. A substance whose molecules, while not tending to separate from one another like those of a gas, readily change their relative position, and which therefore retains no definite shape, except that determined by the containing receptacle; an inelastic fluid.
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Pressure
the amount of force that is applied over a given area divided by the size of this area
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product
a chemical substance formed as a result of a chemical reaction
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reactant
Any of the participants present at the start of a chemical reaction. Also a molecule before it undergoes a chemical change.
##### Appears in these related concepts:
spontaneous change
A 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.
##### Appears in this related concept:
state
The physical property of matter as solid, liquid, gas or plasma
##### Appears in these related concepts:
substance
Physical matter; material.
##### Appears in these related concepts:
surroundings
All parts of the universe that are not within the thermodynamic system of interest.
##### Appears in these related concepts:
system
the part of the universe being studied, arbitrarily defined to any size desired
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temperature
A measure of cold or heat, often measurable with a thermometer.