Determine whether the following statements are true or false. If false, explain why. (a) In an equilibrium reaction, the reverse reaction begins only when all reactants have been converted to products. (b) The equilibrium concentrations will be the same whether one starts with pure reactants or pure products. (c) The rates of the forward and reverse reactions are the same at equilibrium. (d) If the Gibbs free energy is greater than the standard Gibbs free energy of reaction, the reaction proceeds forward to equilibrium.

Understanding the equilibrium constant is crucial for grasping the nature of chemical equilibrium. This constant, represented by the symbol K, expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective stoichiometric coefficients. It is essential to note that K is only affected by temperature changes and is constant for a given reaction at a specific temperature.

When dealing with gas-phase reactions, the equilibrium constant can also be expressed in terms of partial pressures, K_p, which relates to the equilibrium constant for concentrations, K_c, through the ideal gas law. The beauty of the equilibrium constant lies in its ability to predict the direction of a reaction. If Q, the reaction quotient, is less than K, the reaction proceeds in the forward direction; if Q is greater, the reaction moves in the reverse direction until equilibrium is reached.

In practical terms, if you mix certain amounts of reactants and products, regardless of where the initial state was, the reaction will adjust itself until the ratio defined by the equilibrium constant is achieved. This explains why statement (b) from the exercise holds true: the equilibrium state, characterized by specific concentrations of reactants and products, does not depend on whether one starts with reactants or products.

Gibbs free energy, denoted by ΔG, is a thermodynamic function that describes the energy associated with a chemical reaction that can be used to do work at constant temperature and pressure. It is a pivotal concept because it determines the spontaneity of a reaction. If ΔG is negative, the reaction occurs spontaneously; if positive, the reaction is non-spontaneous under the current conditions.

Moreover, the standard Gibbs free energy (ΔG°) is a special case, referring to the free energy change when reactants and products are in their standard states. The relationship between ΔG, ΔG°, and the equilibrium constant is given by the equation ΔG = ΔG° + RTlnQ, where R is the gas constant, T is the temperature, and Q is the reaction quotient. At equilibrium, Q = K, and ΔG becomes zero, indicating a state of minimum energy and no net change in reactants and products. This illustrates why statement (d) from our exercise is not necessarily true: a reaction does not proceed just because ΔG is greater than ΔG°; it depends on whether ΔG itself is negative.

Reaction rates describe how fast reactants get converted into products in a chemical reaction. Factors influencing these rates include the nature of reactants, temperature, concentration, and the presence of a catalyst. In the context of equilibrium, the concept of reaction rates is particularly interesting because at the point of equilibrium, the rates of the forward and reverse reactions are equal.

This state of balance does not mean that reactions have stopped; rather, there is a dynamic process where reactants are constantly becoming products and vice versa. As such, equilibrium is not static but a highly active state. The result is that the macroscopic properties (concentration, color, pressure) of the system remain constant over time. Our exercise highlighted the importance of this concept in statement (c), which is correct in stating that at equilibrium the rates of the forward and reverse reactions are the same.

Dynamic equilibrium occurs in a closed system when the rates of the forward and reverse reactions are equal. At this point, the concentrations of reactants and products remain constant over time, not because no reactions are occurring, but because the reactions are proceeding at the same rate in both directions.

Due to the dynamic nature of equilibrium, it can be approached from either direction of the reaction: starting with reactants or with products. This continuity of motion is a delicate balance and the slightest change in conditions—like temperature or pressure—can shift the equilibrium position. However, as long as the system is closed and the conditions remain constant, the system will return to its equilibrium state even after disturbances, aligning with the principle of Le Chatelier's. Therefore, statement (a) from the exercise is incorrect because it implies a static situation, which is not representative of an equilibrium context where both forward and reverse reactions begin simultaneously.