Calculate standard entropy change in the reaction $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ Given : \(S_{m}^{\circ}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{~S}\right)=87.4, S_{m}^{\circ}(\mathrm{Fe}, S)=27.3\) \(S_{m}^{\circ}\left(\mathrm{H}_{2}, g\right)=130.7, S_{m}^{\circ}\left(\mathrm{H}_{2} \mathrm{O}, l\right)=69.9 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\)

Thermodynamics is a branch of physical science that deals with the relations between heat and other forms of energy. In the context of chemistry, thermodynamics helps us understand how energy is transferred during chemical reactions and how it influences the properties of substances. One fundamental concept in thermodynamics is the principle of entropy, which is a measure of the disorder or randomness in a system. The second law of thermodynamics states that for any spontaneous process, the total entropy of the system and its surroundings always increases.

In practical terms, calculating the entropy change, such as the standard entropy change (\(\Delta S^\circ\)), for a reaction offers insights into the feasibility of the reaction and the amount of energy that might be dispersed into the surroundings. This is critical in predicting how reactions occur and designing processes that take these energy changes into account.

Chemical reactions involve the transformation of one or more substances into different substances, and thermodynamics allows chemists to predict if and how a reaction will proceed. Entropy change is a significant aspect of chemical reactions because it gives an idea of the energy distribution. A reaction may be favorable if it increases the entropy of the surroundings, often releasing energy. Conversely, reactions that lead to a decrease in entropy are typically non-spontaneous unless energy is provided.

The computation of the entropy change is especially important for understanding endothermic and exothermic reactions. For instance, our exercise shows a negative entropy change (\(-215.2 \, \mathrm{JK}^{-1} \mathrm{mol}^{-1}\)) indicating that the reaction might not proceed spontaneously under standard conditions, as it leads to a decrease in the system's disorder.

Physical chemistry is the study of how matter behaves on a molecular and atomic level and how chemical reactions occur. Within this field, thermodynamics plays an essential role, providing quantitative data about the changes that occur during reactions. Standard entropy change calculations, like the one we've discussed, help in determining the direction and spontaneity of chemical reactions.

Understanding these concepts is fundamental for students who wish to apply physical chemistry principles to real-world scenarios in industries such as pharmaceuticals, energy, and materials science. The ability to perform accurate calculations of entropy changes is a skill that ties together the theoretical and practical aspects of physical chemistry.

Students preparing for competitive exams like the Joint Entrance Examination (JEE) in India need to have a strong understanding of thermodynamics, including entropy and Gibbs free energy. Proficiency in calculating entropy changes for chemical reactions is crucial, as it forms a key concept not only in physical chemistry but also in engineering applications.

For effective JEE exam preparation, students should practice a variety of entropy calculation problems. This will help them develop the necessary problem-solving skills and apply the thermodynamic principles confidently. Furthermore, understanding the theoretical underpinnings of these calculations, as explained in the previous sections, is vital for a deep and intuitive grasp of the subject matter required to excel in such competitive exams.