Gibbs Free Energy, Enthalpy and Entropy

In a practical and frequently used form of Gibbs free energy change equation, ΔG is calculated from a set values that can be measured by scientists: the enthalpy and entropy changes of a reaction, together with the temperature at which the reaction takes place.

ΔG=ΔH−TΔS

Let’s take a step back and look at each component of this equation.

• ∆H is the enthalpy change. Enthalpy in biology refers to energy stored in bonds, and the change in enthalpy is the difference in bond energies between the products and the reactants. A negative ∆H means heat is released in going from reactants to products, while a positive ∆H means heat is absorbed. (This interpretation of ∆H assumes constant pressure, which is a reasonable assumption inside a living cell).
• ∆S is the entropy change of the system during the reaction. If ∆S is positive, the system becomes more disordered during the reaction (for instance, when one large molecule splits into several smaller ones). If ∆S is negative, it means the system becomes more ordered.
• Temperature (T) determines the relative impacts of the ∆S and ∆H terms on the overall free energy change of the reaction. (The higher the temperature, the greater the impact of the ∆S term relative to the ∆H term.) Note that temperature needs to be in Kelvin (K) here for the equation to work properly.
• Reactions with a negative ∆G release energy, which means that they can proceed without an energy input (are spontaneous). In contrast, reactions with a positive ∆G need an input of energy in order to take place (are non-spontaneous). As you can see from the equation above, both the enthalpy change and the entropy change contribute to the overall sign and value of ∆G. When a reaction releases heat (negative ∆H) or increases the entropy of the system, these factors make ∆G more negative. On the other hand, when a reaction absorbs heat or decreases the entropy of the system, these factors make ∆G more positive.

By looking at ∆H and ∆S, we can tell whether a reaction will be spontaneous, non-spontaneous, or spontaneous only at certain temperatures.

If a reaction both releases heat and increases entropy, it will always be spontaneous (have a negative ∆G), regardless of temperature.

Similarly, a reaction that both absorbs heat and decreases entropy will be non-spontaneous (positive ∆G) at all temperatures.

Some reactions, however, have a mix of favorable and unfavorable properties (releasing heat but decreasing entropy, or absorbing heat but increasing entropy). The ∆G and spontaneity of these reactions will depend on temperature, as summarized in the table at right.

[Why can these terms predict spontaneity?]

At this point, you may be wondering why this set of terms (∆H, ∆S, and T) can predict reaction spontaneity.

According to the Second Law of Thermodynamics, a reaction will be spontaneous only if it increases the overall entropy of the universe. So, why mess around with ΔH and T?

In the ΔG equation shown above, ΔS (the entropy change of the system) is clearly entropy-related, and an increase in entropy favors spontaneity.

However, ΔH and T are also entropy-related, albeit in an indirect way. Released heat can increase (and absorbed heat can decrease) the entropy of the surroundings, and the magnitude of the change depends on temperature. Thus, all three terms of the ΔG equation actually relate to a reaction’s effect on the entropy of the universe.

For a more thorough and rigorous explanation of the relationship between ∆G and the entropy of the universe, check out this video on thermodynamics.