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# Gibbs free energy: whether a process is spontaneous

## Enthalpy: exothermic and endothermic reactions

Enthalpy (H) is a state function that includes both internal energy (the energy associated with potential energy and kinetic energy of all molecules) and the work done by or on the system. Enthalpy change, denoted as ΔH, is a thermodynamic quantity that measures the heat energy exchanged during a chemical or physical process at constant pressure. It represents the difference in enthalpy between the reactants and products involved in a reaction. We can obtain that the heat released from the system is equal to the enthalpy change of the system in the case of constant pressure.

ΔU = ΔQ + ΔW = ΔQ – PΔV ⇒ ΔU + PΔV = ΔQ ⇒ ΔH=ΔQ

U is the energy of the system, Q is the heat released externally, W is the work done by the system externally, and H = U + PV is the enthalpy of the system.

We classify chemical reactions as exothermic and endothermic reactions according to the enthalpy change.

In an exothermic reaction, the overall enthalpy change (ΔH) is negative, indicating that the reaction releases heat energy to the surroundings. This energy is often observed as an increase in temperature or as the generation of light or heat. The burning of fuels like gasoline or wood, are classic examples of exothermic reactions.

Endothermic reactions have a positive enthalpy change (ΔH), indicating that the reaction absorbs heat energy from the surroundings. The dissolution of ammonium nitrate in water is a typical heat absorption reaction. In ancient times it was used to make cold drinks in summer.

## Entropy: disorder or randomness of a system

Entropy is a fundamental concept in thermodynamics that measures the degree of disorder or randomness in a system. A system with high entropy has many possible configurations and is more disordered, while a system with low entropy has few possible configurations and is less disordered.

In most cases, systems tend to spontaneously transition towards a more disordered state. For instance, when two different metals are contacted closely for a long time, they will diffuse into each other at their interface, leading to increased disorder. However, there are instances where a transition occurs towards a less disordered state. For example, water freezing below 0°C is such a case. Its entropy decreases, but this comes at the cost of releasing heat to the surroundings.

## Gibbs free energy determine whether a process is spontaneous

Although we already know the concepts of enthalpy and entropy, it is not yet possible to tell whether a process will occur spontaneously or not. In general, reactions that release heat and become chaotic will occur spontaneously. However, there are some exceptions, such as the above mentioned heat absorption reactions and the physical process of condensing vapor into water (entropy becomes low).

In order to consider enthalpy and entropy at the same time, we introduce a concept called Gibbs free energy(also known as the Gibbs function, Gibbs energy). It is named after the American physicist Josiah Willard Gibbs, who developed the concept.

Gibbs free energy is related to the enthalpy (H) and entropy (S) of a system through the equation:

ΔG = ΔH - TΔS

where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

ΔG < 0: The process is spontaneous. The system releases energy and the reaction is exergonic.

ΔG > 0: The process is non-spontaneous. The system requires an input of energy, and the reaction is endergonic.

ΔG = 0: The system is at equilibrium. The free energy change is zero, indicating that there is no net transfer of energy.

If ΔH < 0, ΔS > 0, the process is spontaneous. If ΔH > 0, ΔS < 0, the process is not spontaneous. If ΔH > 0, ΔS > 0, or ΔH < 0, ΔS < 0, Whether a chemical reaction is spontaneous or not is determined by temperature. When the temperature is low, enthalpy is the primary consideration. When the temperature is high, entropy becomes the primary consideration.