The accompanying diagram shows how the free energy, G, changes during a hypothetical reaction A(g) + B(g) → C(g). On the left are pure reactants A and B, each at 1 atm, and on the right is the pure product, C, also at 1 atm. Indicate whether each of the following statements is true or false. (a) The minimum of the graph corresponds to the equilibrium mixture of reactants and products for this reaction. (b) At equilibrium, all of A and B have reacted to give pure C. (c) The entropy change for this reaction is positive. (d) The ‘x’ on the graph corresponds to ΔG for the reaction. (e) ΔG for the reaction corresponds to the difference between the top left of the curve and the bottom of the curve.

Verified step by step guidance

1. Step 1: Understand the concept of Gibbs Free Energy (G) in a chemical reaction. Gibbs Free Energy is a thermodynamic potential that can be used to predict the direction of a chemical reaction and determine the equilibrium position. The change in Gibbs Free Energy (ΔG) indicates whether a reaction is spontaneous.
2. Step 2: Analyze statement (a). The minimum of the graph represents the point where the system is at its lowest free energy, which corresponds to the equilibrium state of the reaction. At this point, the forward and reverse reaction rates are equal, and the concentrations of reactants and products remain constant.
3. Step 3: Evaluate statement (b). At equilibrium, the reaction does not necessarily proceed to completion. Instead, it reaches a state where the concentrations of reactants and products are constant. Therefore, not all of A and B need to be converted to C for the system to be at equilibrium.
4. Step 4: Consider statement (c) regarding entropy change. The entropy change (ΔS) of a reaction can be positive if the disorder of the system increases. For a reaction involving gases, an increase in the number of gas molecules typically results in a positive entropy change. Analyze the stoichiometry of the reaction to determine the change in entropy.
5. Step 5: Examine statements (d) and (e) about ΔG. The 'x' on the graph likely represents a specific point on the reaction coordinate, not ΔG itself. ΔG for the reaction is the difference in free energy between the reactants and products, which is typically represented by the difference between the initial and final points on the graph, not the top left and bottom of the curve.

Key Concepts

Gibbs Free Energy (G)

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is a crucial concept in determining the spontaneity of a reaction; a negative ΔG indicates a spontaneous process, while a positive ΔG suggests non-spontaneity. The change in Gibbs Free Energy (ΔG) during a reaction reflects the difference in free energy between reactants and products.

Equilibrium in Chemical Reactions

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. At this point, the system has reached a state of balance, and the Gibbs Free Energy is at a minimum. It is important to note that equilibrium does not imply that reactants are completely converted to products; rather, it indicates a dynamic state where both reactants and products coexist.

Entropy (S) and its Role in Reactions

Entropy (S) is a measure of the disorder or randomness in a system. In chemical reactions, a positive change in entropy (ΔS) typically indicates an increase in disorder, which can favor spontaneity. The relationship between Gibbs Free Energy, enthalpy, and entropy is described by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin. Understanding how entropy changes during a reaction is essential for predicting the direction and feasibility of the reaction.