\(K_{\mathrm{c}}\) for the reaction; \(A+B \Longrightarrow P+Q\), is \(2.0 \times 10^{-2}\) at \(25^{\circ} \mathrm{C}\) and it is \(2.0 \times 10^{-1}\) at \(50^{\circ} \mathrm{C}\). Predict whether the forward reaction is exothermic or endothermic.

In physical chemistry, one of the fundamental concepts is the equilibrium constant, denoted as \( K \). This numeric value is essential for understanding the balance between the reactants and products in a chemical reaction at a specific temperature and pressure. The equilibrium constant for a reaction, such as \( A+B \rightleftharpoons P+Q \), is a measure of the ratio of the concentration of the products to the concentration of the reactants at equilibrium, with each raised to the power of their respective coefficients in the balanced equation.

For example, for the reaction given, \(K_c\) at \(25^\circ C\) is \(2.0 \times 10^{-2}\) and at \(50^\circ C\) it is \(2.0 \times 10^{-1}\), indicating that the position of equilibrium shifts with temperature changes. An increase in \(K_c\) with temperature implies that the product formation is favored at higher temperatures. In the context of IIT-JEE exams, understanding how to calculate and interpret \(K_c\) is crucial for problem-solving in physical chemistry.

Le Chatelier's Principle is a guiding concept when predicting how a system at equilibrium responds to outside changes. According to this principle, if an external condition is changed, the system will adjust itself to counteract the effect of the change and re-establish equilibrium.

For instance, consider the reaction mentioned above, where the equilibrium constants at two different temperatures indicate a shift in the reaction. When the temperature is increased from \(25^\circ C\) to \(50^\circ C\), and \(K_c\) increases, this suggests that the reaction shifts toward the products to counterbalance the added heat — the system's attempt to absorb the excess temperature and maintain equilibrium. Students preparing for competitive exams like the IIT-JEE should be adept at using Le Chatelier's Principle to predict the outcome of perturbations in a chemical system.

Chemical reactions can be broadly classified into two categories based on heat exchange with the surroundings: endothermic and exothermic. Endothermic reactions absorb energy, usually in the form of heat, from their surroundings. Conversely, exothermic reactions release energy.

In the context of the given exercise, the increase in \(K_c\) with an increase in temperature indicates that the reaction absorbs heat from the surroundings as it proceeds to form more products. This is a hallmark of an endothermic reaction. It is essential for IIT-JEE aspirants to grasp the idea that an increase in temperature drives endothermic reactions forward, whereas it inhibits exothermic reactions, due to the exothermic reaction releasing heat that would otherwise increase the temperature.