Entropy Formula

Entropy is not a very familiar topic to most of the people. Also, in this topic, we will learn about entropy, entropy formula, its derivation and solved example. Moreover, you will explore the second law of the thermodynamics where entropy is introduced. Furthermore, you will inspect the formula for entropy and find out how to use it in a variety of cases.

Entropy

Entropy refers to the number of ways in which a system can be arranged. Moreover, the higher the entropy the more disordered the system will become. Furthermore, we can understand it more easily with the help of an example. Suppose you sprayed perfume in one corner of the room. So, what will happen next? We all know that the smell will spread in the entire room and the perfume molecule will eventually fill the room.

In another example, you grab a ball and put it on a table. Moreover, the question here is in how many ways you can arrange this ball? The answer is one. After some time you put another ball on the table. So, now you can arrange the balls in two ways. Furthermore, the more you increase the ball the more ways it can be arranged.

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The Second Law of Thermodynamics

The second law of thermodynamics says that every process involves a cycle and the entropy of the system will either stay the same or increase. Also, even when the cyclic process is changeable then the entropy will not change. Moreover, when the process is unalterable then the entropy will increase.

For example, watching a movie is a changeable process because you can watch the movie from backward. On the other hand, blowing a building, frying an egg is an unalterable change. Besides, some other example of changeable phase is the melting of metals. In addition, some microscope process is reversible.

Entropy Formula

Entropy is a thermodynamic function that we use to measure uncertainty or disorder of a system. Moreover, the entropy of solid (particle are closely packed) is more in comparison to the gas (particles are free to move). Also, scientists have concluded that in a spontaneous process the entropy of process must increase. Furthermore, it includes the entropy of the system and the entropy of the surroundings.

Besides, there are many equations to calculate entropy:

1. If the happening process is at a constant temperature then entropy will be

\(\Delta S_{system}\) = \(\frac{q _{rev}}{T}\)

Derivation of Entropy Formula

\(\Delta S\) = is the change in entropy

\(q_{rev}\) = refers to the reverse of heat

T = refers to the temperature in Kelvin

2. Moreover, if the reaction of the process is known then we can find \(\Delta S_{rxn}\) by using a table of standard entropy values.

\(\Delta S_{rxn}\) = \(\Sigma \Delta S_{products} – \Sigma \Delta S_{reactants}\)

Derivation

\(\Delta S_{rxn}\) – refers to the standard entropy values

\(\Sigma \Delta S_{products}\) = refers to the sum of the \(\Delta S_{products}\)

\(\Sigma \Delta _{reactants}\) – refers to the sum of the \(\Delta S_{reactants}\)

3. Is the Gibbs free energy (\(\Delta G\)) and the enthalpy (\(\Delta H\)) can also be used to find \(\Delta _S\).

\(\Delta G\) = \(\Delta H\) – T\(\Delta _S\)

Solved Example on Entropy Formula 

Example 1

Substance	\(S^{\circ}\frac{j}{k\cdot mol}\)
\(H_{2(g)}\)	130.6
\(F_{2(g)}\)	202.7
\(HF_{2(g)}\)	173.5

 

Find the entropy change for the following reaction using the table of entropy values.

\(H_{2 (g)} + F_{2 (g)}\) \(\rightarrow\) \(2HF_{g}\)

Solution:

\(\Delta S_{rxn}\) = \(\Sigma \Delta S_{products} – \Sigma \Delta S_{reactants}\)

\(\Delta S_{rxn}\) = \(2 \times 173.5) – (130.6 + 202. 7)

\(\Delta S_{rxn}\) = \(13.7\frac{j}{k\cdot mol}\)

So, the answer is \(13.7\frac{j}{k\cdot mol}\).