If \(\Delta \mathrm{G}\) for the reaction \(\mathrm{P}^{+}+\mathrm{Q}^{-} \rightarrow \mathrm{P}^{2+}+\mathrm{Q}^{2-}\) is \(\mathrm{X}\) than \(\Delta \mathrm{G}\) for this reaction is? \(\frac{1}{2} \mathrm{P}^{+}+\frac{1}{2} \mathrm{Q}^{-} \rightarrow \frac{1}{2} \mathrm{P}^{2+}+\frac{1}{2} \mathrm{Q}^{2-}\) (a) \(\frac{x}{2}\) (b) \(2 \mathrm{X}^{2}\) (c) \(\sqrt{x}\) (d) \(2 \mathrm{X}\)

Thermodynamics is a branch of physics that deals with the relationships between heat, work, temperature, and energy. In chemistry, thermodynamics plays a key role in understanding how chemical reactions occur and the energy changes associated with them. One of the central concepts in thermodynamics related to chemical reactions is Gibbs Free Energy, often denoted as \( \Delta G \).

Gibbs Free Energy is a thermodynamic potential used to predict whether a chemical reaction will proceed spontaneously. The sign and magnitude of \( \Delta G \) reflect the system's stability; a negative \( \Delta G \) indicates a spontaneous process, while a positive value suggests a non-spontaneous reaction. Furthermore, \( \Delta G \) is an extensive property, meaning it depends on the amount of reacting substances. For example, if the amount of reactants is halved, as shown in the exercise, the \( \Delta G \) for the reaction is also halved, which simplifies the understanding of the relationship between the chemical quantities involved and the energy changes.

In educational content, emphasizing the significance of \( \Delta G \) in thermodynamics and its relation to reaction spontaneity can greatly help students in courses like NEET Chemistry where such concepts are critical.

A chemical reaction is a process where reactants are transformed into products through breaking and forming chemical bonds. During this transformation, energy is either absorbed or released primarily in the form of heat or light, which is crucial in the study of reaction energetics. For any chemical reaction, many thermodynamics-related quantities can be calculated, and among them, Gibbs Free Energy \( \Delta G \) is particularly significant.

The example in the textbook solution, \( \mathrm{P}^{+} + \mathrm{Q}^{-} \rightarrow \mathrm{P}^{2+} + \mathrm{Q}^{2-} \), illustrates this concept by asking students to understand how the \( \Delta G \) varies when the coefficients of the reaction are changed. Students should note that the stoichiometric coefficients are proportional to the amounts of reactants and products, hence directly influencing the value of \( \Delta G \) for the given reaction. Such exercises are designed to clarify that the extensive property nature of \( \Delta G \) connects it tightly with the stoichiometry of the reaction—a key concept for mastering the problem-solving aspect of NEET Chemistry and related to thermodynamics in general.

NEET, or the National Eligibility cum Entrance Test, is an examination that aspiring medical students in India must clear to gain admission to undergraduate medical courses. The chemistry section of NEET tests a student's understanding of various concepts, including physical, organic, and inorganic chemistry. Thermodynamics and specifically Gibbs Free Energy, is a recurring topic in the physical chemistry portion of NEET.

To excel in NEET Chemistry, students should grasp the fundamental principles and calculations related to \( \Delta G \) as it applies to chemical reactions. The exercise provided conveys such a concept by showing that the properties of \( \Delta G \) are directly influenced by the reaction's stoichiometry. Being able to strategically approach problems like these equips students with the analytical skills required to solve a variety of thermodynamics questions commonly seen in the exam. Additionally, when preparing educational materials for NEET Chemistry, including exercises that teach the extensive property nature of \( \Delta G \) and its calculations, contributes significantly to a student's ability to tackle multiple-choice questions with confidence and precision.