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## Difference Between Gibbs Free Energy and Helmholtz Free Energy

Gibbs Free Energy vs Helmholtz Free Energy

Some things happen spontaneously, others do not. The direction of change is determined by the distribution of energy. In spontaneous change, things tend to a state in which the energy is more chaotically dispersed. A change is spontaneous, if it leads to greater randomness and chaos in the universe as a whole. The degree of chaos, randomness, or dispersal of energy is measured by a state function called the entropy. The second law of thermodynamics is related to entropy, and it says, “the entropy of the universe increases in a spontaneous process.” Entropy is related to the amount of heat generated; that is the extent to which energy has been degraded. In fact, the amount of extra disorder caused by a given amount of heat q depends on the temperature. If it is already extremely hot, a bit of extra heat doesn’t create much more disorder, but if the temperature is extremely low, the same amount of heat will cause a dramatic increase in disorder. Therefore, it is more appropriate to write, ds=dq/T.

To analyze the direction of change, we have to consider changes in both system and the surrounding. The following Clausius inequality shows what happens when heat energy is transferred between the system and the surrounding. (Consider the system is in thermal equilibrium with the surrounding at temperature T)

dS – (dq/T) ≥ 0………………(1)

Helmholtz free energy

If the heating is done at constant volume, we can write the above equation (1) as follows. This equation expresses the criterion for a spontaneous reaction to take place in terms of state functions only.

dS – (dU/T) ≥ 0

The equation can be rearranged to get the following equation.

TdS ≥ dU (equation 2); therefore, it can be written as dU – TdS ≤ 0

The above expression can be simplified by the use of the term Helmholtz energy ‘A’, which can be defined as,

A = U – TS

From the above equations, we can derive a criterion for a spontaneous reaction as dA≤0. This states that, a change in a system at constant temperature and volume is spontaneous, if dA≤0. So change is spontaneous when it is corresponding to a decrease in the Helmholtz energy. Therefore, these systems move in a spontaneous path, to give lower A value.

Gibbs free energy

We are interested in Gibbs free energy than the Helmholtz free energy in our laboratory chemistry. Gibbs free energy is related with the changes happening at constant pressure. When heat energy is transferred at constant pressure, there is only expansion work; therefore, we can modify and rewrite the equation (2) as follows.

TdS ≥ dH

This equation can be rearranged to give dH – TdS ≤ 0. With the term Gibbs free energy ‘G’, this equation can be written as,

G = H – TS

At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs free energy. Therefore, dG≤0.

 What is the difference between Gibbs and Helmholtz free energy? • Gibbs free energy is defined under constant pressure, and Helmholtz free energy is defined under constant volume. • We are more interested at Gibbs free energy in laboratory level than the Helmholtz free energy, because they are occurring at constant pressure. • At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs free energy. In contrast, at constant temperature and volume, reactions are spontaneous in the direction of decreasing Helmholtz free energy.

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• Tushar

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