For the water gas reaction : $$ \mathrm{C}_{(\mathrm{s})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})} \rightleftharpoons \mathrm{CO}_{(\mathrm{g})}+\mathrm{H}_{2(\mathrm{~g})} $$ the standard Gibbs energy of reaction (at \(1000 \mathrm{~K}\) ) is \(-8.1 \mathrm{~kJ} \mathrm{~mol}^{-\mathrm{i}}\). Calculate its equilibrium constant.

Gibbs free energy change (abla G) is a thermodynamic quantity that indicates the spontaneity of a chemical reaction at constant temperature and pressure. A negative value of abla G implies that a reaction is spontaneous, meaning it can proceed without any additional energy input. For example, in the water gas reaction, a abla G of -8.1 kJ/mol hints that the reaction favors the production of carbon monoxide (abla CO) and hydrogen gas (abla H_2).abla G is also a key factor in determining the direction in which a reaction must shift to reach equilibrium.The relationship between abla G and the equilibrium constant (abla K_c) is given by the equation abla G^o = -RT ln(abla K_c). This fundamental equation bridges the gap between thermodynamics and equilibrium, enabling chemists to predict the position of equilibrium solely based on the Gibbs free energy change.

Physical chemistry is the branch of chemistry focused on the study of how matter behaves on a molecular and atomic level and how chemical reactions occur. It combines principles from physics and chemistry to understand the physical properties of molecules, the forces that act upon them, and the energy changes associated with chemical reactions.Understanding abla G and its application in calculating equilibrium constants is a key aspect of physical chemistry. Physical chemists use this knowledge to unravel complex reactions and to predict the behavior of substances under various conditions, akin to solving the water gas reaction in the exercise.

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of the reactants and products remain constant over time. It is a dynamic state, meaning that reactions are still occurring, but with no net change in reactant and product concentrations.The equilibrium constant (abla K_c) reflects the ratio of product and reactant concentrations at equilibrium. Each equilibrium position is associated with a specific abla K_c value, which is temperature-dependent and can be calculated from abla G using the mentioned formula. It is fundamental to predict the extent of a reaction and to determine the conditions necessary to favor the production of desired products, as in the water gas reaction.

IIT-JEE preparation involves a deep understanding of concepts like Gibbs free energy and chemical equilibrium, which are integral parts of the physical chemistry syllabus. To excel in the IIT-JEE and similar competitive exams, students must be adept at applying these concepts to solve complex problems.Practicing problems such as the calculation of equilibrium constants from the standard Gibbs free energy helps to reinforce these concepts. The step-by-step approach used in solving the water gas reaction problem is a vital solve strategy for students preparing for the IIT-JEE, where clear conceptual understanding along with the ability to perform quick, accurate calculations is key to success.

Reaction thermodynamics analyzes the energy changes during a chemical reaction and provides insights into the factors that influence reaction spontaneity and equilibrium. It deals with concepts such as enthalpy, entropy, and Gibbs free energy.In our exercise, the change in Gibbs free energy for the water gas reaction gives us quantitative insight into the reaction's spontaneity at a given temperature (abla 1000 K). By converting abla G to an equilibrium constant, we connect thermodynamic predictions with measurable equilibrium properties of the system, making thermodynamics a powerful tool in predicting and understanding the overall flow of energy during chemical reactions.