 # Entropy Formula

Entropy is one of the important concepts which science students need to understand clearly. It is equally important in the study of Chemistry and Physics. More significantly, entropy has many definitions given in several ways. Thus, it can be applied in various stages or instances in a thermodynamic system. The concept of entropy basically talks about the spontaneous changes occurring in the everyday phenomenon or the tendency of the universe towards the disorder. The student will learn Entropy Formula with examples here. Let us begin it!

Table of content

## Entropy Formula

### What is Entropy?

Generally, the definition of entropy is as a measure of randomness or disorder of a system. It was introduced by a German physicist named Rudolf Claudius in the year 1850. From a thermodynamics viewpoint of entropy, we will not consider the microscopic details of a system.

Instead, entropy is used to describe the behavior of thermodynamic system-related terms such as temperature, pressure, entropy, and heat capacity. This description will take into consideration the state of equilibrium of the systems.

On the other hand, the statistical definitions are given in terms of the statistics of the molecular motions of a system. Thus entropy is a measure of the molecular disorder.

For example, the entropy of a solid, where the particles are not free to move, is always less than the entropy of a gas. Scientists have got the conclusion that if a process is to be spontaneous, the entropy of that process must increase. This includes both the entropies i.e. of the system and of the surroundings.

### Properties of Entropy:

• It is a thermodynamic function.
• It is a state function, as it depends on the state of the system and not the path which is followed.
• Entropy is represented by S.
• It’s SI unit is J per K. mol and the CGS unit is cal per K.mol.
• Entropy is an extensive property because it scales with the size or extent of the system.

The much disorder exists in an isolated system, hence entropy also increases. During chemical reactions, if reactants break into more products, then entropy also increases. A system at higher temperatures will have greater randomness than a system at a lower temperature. Therefore, it is clear that entropy increases with a decrease in regularity.

### Formula for Entropy:

We can calculate Entropy using many different equations:

Method-1: If the process is at a constant temperature then:

$$\Delta S_{System}$$ = $$\frac{q_{rev}}{T}$$

Where,

 $$\Delta S$$ change in entropy $$q_{rev}$$ reverse of the heat T Kelvin temperature

Method-2: If the reaction is known, then $$\Delta S_{reaction}$$ can be calculated using a table of standard entropy values.

$$\Delta S_{reaction}$$ = $$\sum \Delta S_{products} – \sum \Delta S_{reactants}$$

1. Gibbs free energy $$(\Delta G) and enthalpy (\Delta H) can also be used to calculate \Delta S$$.

$$\Delta G = \Delta H – T \Delta S$$

### Solved examples:

Q.1: Calculate the entropy change for the following reaction using the table of entropy values, as given:

$$H_2 (g) + F_2 (g) → 2HF (g)$$

 Substance S ( j per k.mol) $$H_2$$ 130.6 $$F_2$$ 202.7 HF 173.5

Solution: As we know:

$$\Delta S_{reaction}$$ = $$\sum \Delta S_{products} – \sum \Delta S_{reactants}$$

Thus substituting the values,

$$\Delta S_{reaction}$$ = $$2 \times 173.5 – (130.6 + 202.7)$$

= 13.7 j per K.mol

Thus entropy change will be 13.7 j per K.mol

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