Problem 27 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The equilibrium constants for the reaction: \(\mathrm{A}_{2} \rightleftharpoons 2 \mathrm{~A}\) at \(500 \mathrm{~K}\) and \(1000 \mathrm{~K}\) are \(1 \times 10^{-10^{2}}\) and \(1 \times 10^{-5}\), respectively. The reaction is (a) Exothermic (b) Very slow (c) Very fast (d) Endothermic

Step-by-Step Solution

Answer

The reaction is endothermic as the equilibrium constant increases with temperature.

Step 1: Understand the Direction of Equilibrium Shift with Temperature

The change in equilibrium constant, K, with temperature gives information about the nature of the reaction in terms of heat exchange. According to Le Chatelier's Principle, if the equilibrium constant increases with an increase in temperature, the reaction absorbs heat, while if the equilibrium constant decreases with an increase in temperature, the reaction releases heat.

Step 2: Analyze the Given Equilibrium Constants

Compare the given equilibrium constants at two different temperatures. At 500 K, the equilibrium constant is much smaller (\(1 \times 10^{-10^2}\) or essentially zero) than at 1000 K (\(1 \times 10^{-5}\)). This indicates that as the temperature increases, the reaction shifts to produce more products, suggesting that the forward reaction is endothermic.

Step 3: Conclude the Nature of the Reaction

Since the reaction shifts to favor the production of products at a higher temperature, it indicates that heat is absorbed in the process. Thus, the reaction is endothermic.

Key Concepts

Le Chatelier's Principle

Imagine a seesaw in balance, each side holding its weight steadily. Suddenly, if you add more weight on one side, the seesaw will tilt, seeking a new balance. This is similar to how Le Chatelier's Principle describes the behavior of chemical reactions reaching a state of balance, or equilibrium. When a reaction at equilibrium is subjected to a change in concentration, pressure, or temperature, the equilibrium will shift to counteract the imposed change and restore a new balance.

Applied to our context, when the temperature of a reactant system is increased, the equilibrium position will shift in the direction that absorbs this added heat. Similarly, if the temperature is decreased, the system will adjust to produce more heat. Understanding this principle helps predict how changes in conditions affect the composition of the equilibrium mixture.

Endothermic Reactions

Just like putting ice cubes into a drink to absorb the heat and cool the liquid, endothermic reactions absorb heat from their surroundings. These reactions require energy, usually in the form of heat, for the reaction to proceed. As a result, the temperature of the surroundings decreases as the reaction occurs.

In the case of the reaction \(\mathrm{A}_{2} \rightleftharpoons 2 \mathrm{~A}\), the increase in the equilibrium constant with temperature indicates that the reaction requires a heat input to favor the production of products, identifying it as an endothermic process. Substances undergoing endothermic reactions often feel cold to the touch because they are drawing in thermal energy from their environment.

Chemical Equilibrium

Chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate, leading to no net change in the amounts of products and reactants. Think of it as a tug-of-war where both teams are equally strong; they pull with the same force, and the rope doesn't move. This dynamic state does not mean the reaction has stopped, but rather that it is continuously occurring in both directions at an equal pace.

The position of equilibrium can be described by the equilibrium constant, K, which is a ratio of the concentrations of the products to the reactants, raised to their respective coefficients in the balanced equation. A larger K indicates a larger proportion of products at equilibrium, while a smaller K indicates a larger proportion of reactants.

Reaction Heat Exchange

Reaction heat exchange is concerned with how heat is transferred during a chemical reaction. It is a crucial part of understanding and controlling industrial chemical processes, where managing the temperature is essential for safety and efficiency. Reactions that release heat to the surroundings, warming them, are termed exothermic, and those that absorb heat, cooling their surroundings, are called endotheric.

The equilibrium constant's sensitivity to temperature changes helps chemists to deduce the heat exchange nature of the reaction. In our textbook problem, the increase of K with rising temperatures indicates that the reaction absorbs heat from the surroundings. Consequently, this allows us to infer that the forward reaction of transforming \(\mathrm{A}_{2}\) into \(2 \mathrm{~A}\) is endothermic.