**Free Energy vs Standard Free Energy**

**What is Free energy?**

The amount of work that a thermodynamic system can perform is known as free energy. Free energy can be described using two terms, Helmholtz free energy and Gibbs free energy. In chemistry, when we use the word “free energy” that means Gibbs free energy. In physics, free energy refers to Helmholtz free energy. Both terms are described below.

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. But, in fact, the amount of extra disorder caused by a given amount of heat q depends on the temperature. If it is already very hot, a bit of extra heat does not create much more disorder, but if the temperature is very low, the same amount of heat will cause a dramatic increase in disorder. It is, therefore, 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)*

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),*and therefore, it can be written as

*dU – TdS ≤0*

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

*一个= 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 is related with the changes happening at constant pressure. When heat energy is transferred at constant pressure, there is only expansion work; therefore, we modify and write 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 Standard Free Energy?**

Standard free energy is the free energy defined at standard conditions. The standard conditions are temperature, 298 K; pressure, 1 atm or 101.3 kPa; and all solutes at 1 M concentration. Standard free energy is denoted as Go.

• In chemistry, free energy is referred to Gibbs free energy. It is related with the changes happening at constant pressure. Standard free energy is the free energy defined at standard conditions. •因此，在298K温度和1个ATM压力下给出标准的自由能，但是自由能值可能会根据温度和压力而变化。 |

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