Question

The free energy change of the reaction \(\mathrm{A}(g) \longrightarrow \mathrm{B}(g)\) is zero under certain conditions. The standard free energy change of the reaction is \(-42.5 \mathrm{~kJ}\). Which statement must be true about the reaction? a. The concentration of the product is greater than the concentration of the reactant. b. The reaction is at equilibrium. c. The concentration of the reactant is greater than the concentration of the product.

Short answer

The correct statement is b. The reaction is at equilibrium.

Step-by-step solution

Understanding Free Energy Change

Free energy change (eq 0eq)egeq 0eq)eq0eq 0 indicates the direction in which a reaction is spontaneous. A negative value means the reaction is spontaneous under standard conditions, while a value of zero indicates the reaction is at equilibrium.

Analyzing the Standard Free Energy Change

The standard free energy change (= -42.5 =−42.5 eq−42.5 ==−42.5 kJ) given is negative, which implies that the forward reaction, from A to B, is spontaneous under standard conditions.

Determining the True Statement

If the free energy change of the reaction is zero (= 0eq 0eq0eq 0), it means the system has reached equilibrium. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of reactants and products remain constant.

Key concepts

Free Energy Change

When evaluating the direction of chemical reactions, free energy change is a vital concept. It is denoted by the symbol \( \Delta G \). In simple terms, it tells us about the amount of energy that is available (or not) to do work during a chemical process when temperature and pressure are constant. The standard free energy change \( \Delta G^\circ \) is the change in free energy of a reaction under standard conditions, which include a temperature of 298K (25°C), a pressure of 1 atm, and all substances in their stable states.

As depicted in the textbook exercise, a reaction with a standard free energy change of \( -42.5 \text{ kJ} \) indicates that the reaction is spontaneous under those standard conditions. It means that the reaction will proceed without the addition of external energy. However, when the exercise states that the free energy change of the reaction is zero, this signifies that the system has reached a state of balance — the equilibrium point — where no further net change occurs in the concentrations of reactants and products over time. This balance point is not static but rather a dynamic condition where the rate of the forward reaction equals the rate of the backward reaction. Hence, understanding free energy guides us in predicting the feasibility and spontaneity of chemical processes.

Spontaneous Reaction

A spontaneous reaction is one that occurs without external intervention, usually releasing energy to the surroundings. It's a bit like rolling a ball down a hill; once it starts, it doesn't need help to continue. The free energy change informs us of the spontaneity. A negative \( \Delta G \) indicates a spontaneous reaction under the given conditions, while a positive \( \Delta G \) means the reaction is non-spontaneous and requires energy input.

It's crucial to realize that 'spontaneous' does not mean immediate. Some spontaneous reactions may occur so slowly that they seem nonexistent without a catalyst. For example, the rusting of iron is spontaneous but can take a long time. In contrast, other spontaneous reactions, like the combustion of gasoline, happen rapidly and release energy quickly. Moreover, the concept of spontaneity is dependent on conditions such as temperature and pressure, emphasizing why a deep understanding of free energy is essential for both chemists and students alike.

Equilibrium Constant

When a chemical reaction reaches a state where the forward and reverse reactions proceed at equal rates, we say it’s in equilibrium. To quantify this state, we use the equilibrium constant, symbolized as \( K_{eq} \). This constant is a dimensionless number derived from the concentrations (or partial pressures) of the products and reactants at equilibrium. The general form of the equilibrium constant expression for a reaction \( aA + bB \longleftrightarrow cC + dD \) is given by:\[ K_{eq} = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

The higher the value of \( K_{eq} \), the more product-favored the equilibrium position. Conversely, a lower \( K_{eq} \) suggests a more reactant-favored position. It's noteworthy to understand that while \( K_{eq} \) gives us valuable information on the position of equilibrium, it does not tell us about the rate at which equilibrium is achieved. Moreover, \( K_{eq} \) is temperature-dependent and constant only at a particular temperature. The fascinating fact here is that even though the concentrations of reactants and products do not change at equilibrium, the reaction is not halted—it is dynamically proceeding in both directions with no net effect on concentration.