In order to know what is Gibbs free energy, and where it comes out, we, first of all, must be fully acquainted with what is a spontaneous process, and what are the important criteria of spontaneity?

*WHAT IS SPONTANEOUS PROCESS?*

For a chemist, the main purpose of studying thermodynamics is to be able to predict whether or not a reaction will happen when some reactants are brought together. If a reaction takes place when we brought some reactant under given set of conditions (e.g. at a certain pressure, temperature, and concentration) is called spontaneous process. If doesn’t occur it is called non-spontaneous.

The feasibility of a process indicates the term spontaneity. For example in nature water flows down the hill without the help of any external force, heat flows from the higher temperature to the lower temperature etc. All these processes are spontaneous because of their feasibility, that is they can occur without the help of external work.

## DEFINITION:

So the spontaneous process can be defined as a process which has a natural tendency to occur of its own under the given set of conditions without the addition of external energy.

### WHAT ARE TWO IMPORTANT CRITERIA FOR SPONTANEITY?

Now we have learned what is a spontaneous process, then very obvious question arise in our mind that why some processes are spontaneous? So there are some forces which are responsible for the spontaneity of processes.

**♠1)** A tendency of a system to have a minimum energy:

In an exothermic reaction, heat is generated from the system. So the enthalpy of system decreases (ΔH=-ve) and the system comes to a lower energy state to maintain its equilibrium position.

~ Hence negative value of the change in enthalpy **(ΔH)** may be one of the criteria of spontaneity.

**♠2)** Tendency of a system to acquire maximum randomness:

Any liquids substance in its gaseous state is more random than its liquid state. Thus evaporation of such liquid is a spontaneous process since it takes place in the direction of more randomness this is due to according to the 2nd law of thermodynamics.

**⇒** The thermodynamic property entropy **(S)** is a measure of randomness of a system, and so one of the criteria of spontaneity. More the randomness of a system more will be the entropy.

## INTRODUCTION TO GIBBS FREE ENERGY

So we conclude that a reaction is more probably take place spontaneously if the enthalpy change** (ΔH)** is negative (exothermic reaction) and entropy change** (ΔS)** is positive. However, we see that there are various spontaneous processes in which entropy decreases** ( ΔS= – ve )** or enthalpy increases** ( ΔH = + ve)**. Therefore to explain, whether a reaction is spontaneous or not we have to simultaneously consider both **ΔS** and **ΔH**. Thanks to Willard Gibbs, who introduced an another thermodynamic state function now called Gibbs Free Energy represented by symbol **G**.

### WHAT IS GIBBS FREE ENERGY(G)?

Gibbs showed that by combining the effect of energy factor ΔH and randomness or entropy factor TΔS, which explains the spontaneity of a process more clearly. When a reaction takes place at constant temperature and pressure, ΔG represents that portion of the total energy, which is available that is free to do useful work. For example, if for a reaction ΔG is -300kJ then it is possible to obtain 300kJ of useful work from that reaction. Conversely, if ΔG is +300kJ, we have to supply at least much energy in the form of work to make the reaction possible.

### DEFINITION:

The Gibbs free energy is a thermodynamic quantity, which is the maximum amount energy available to a system during a process that can be converted into useful work.

Mathematically it can be defined by this equation: **G = H – TS**

where **H** is enthalpy i.e. the heat content, **S** is the system’s entropy, and **T** is the absolute temperature in kelvin, **K.**

## WHAT ARE THE CHARACTERISTICS OF GIBBS FREE ENERGY?

* ♦1)* It is also an extensive property.

*Other thermodynamic properties like enthalpy (H), energy (E), and entropy (S), it is also a state function.*

**♦2)***The value of the free energy (G) is independent of the path followed i.e. it is an exact differential.*

**♦3)***The absolute value of free energy (G) can’t be determined.*

**♦4)**#### IMPORTANCE OF FREE ENERGY CHANGE (ΔG)

From forth characteristics of G as mentioned above, we know that the absolute value of free energy (G) can’t be determined. This is because it is not possible to evaluate the absolute value of free energy we find the change in free energy from the initial stage to final stage for a process.

“The change in free energy is represented as **ΔG = ΔH – TΔS”**

This equation, which is called “Gibbs-Helmholtz” equation is very helpful in determining the spontaneity of a process.

#### WHAT IS THE RELATION BETWEEN SPONTANEITY AND FREE ENERGY CHANGE (ΔG)?

We know the total entropy change **(ΔS)** universe determine the spontaneity of process. The total entropy change during a process is given by **ΔS** universe = **ΔS** system + **ΔS** surrounding and is must be positive in order to be spontaneous. So all we have to do is to find the change in free energy of the system. We don’t need to consider the total entropy of the universe, which is very complicated. The spontaneity of a process in term of free energy change **(ΔG)** can be summarized as follows:

1). If **ΔG** is negative for a process then the process is spontaneous and it will occur in the forward direction.

2). If **ΔG** is zero for a process then the process is in equilibrium state. The reaction will not take place.

3). If** ΔG** is positive for a process then the reaction doesn’t proceed in the forward direction. It may occur in the reverse direction.

• Hence, free energy change **(ΔG)** must be negative for a process to in order to satisfy its spontaneity.

#### WHAT ARE THE CONDITIONS FOR FREE ENERGY CHANGE (ΔG) TO BE NEGATIVE?

In order to satisfy its spontaneity of a process, free energy change **(ΔG)** must be negative. From Gibbs-Helmholtz equation, we know that **ΔG** depends upon three factors **ΔH**, **ΔS**, and** T**. So the three important possible conditions for spontaneity of a process are

1). The change in entropy **( ΔS)** is positive and change in enthalpy **(ΔH)** is negative for any magnitude ΔH, ΔS, and T.

2). Both changes in entropy and enthalpy are negative, and magnitude of **ΔH** should be more than that of **TΔS **i.e. at low temperature.

3). Both changes in entropy **( ΔS)** and enthalpy** (ΔH)** are positive, and magnitude of **ΔH** should be less than that of **TΔS** i.e. at high temperature.

#### SUMMARY

**◊1)** For a spontaneous process, the entropy of the universe always increases, which is stated by 2nd law of thermodynamics as

**ΔS** universe = **ΔS** system + **ΔS** surrounding **> 0**

**◊2)** Gibbs-Helmholtz equation states that at constant **P** and constant **T**, Gibbs free energy represented as **ΔG** = **ΔH** – **TΔS**

**◊3)** Free energy change **(ΔG)** must be negative for a process to in order to satisfy its spontaneity.

**◊4)** The spontaneity of a process depends upon three factors **ΔH**, **ΔS**, and temperature.

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