Problem 45 - Chemistry The Molecular Nature of Matter

Question

Sketch the shape of the free energy curve for a chemical reaction that has a positive \(\Delta G^{\circ}\). Indicate the composition of the reaction mixture corresponding to equilibrium.

Step-by-Step Solution

Answer

The free energy curve for a reaction with positive \(\Delta G^{\bullet}\) starts at a low position for reactants, peaks at the activated complex, then ends at a high position for products. Equilibrium is indicated by the lowest point between reactants and products on the graph.

Step 1: Identify Key Concepts

Understand that the free energy, denoted as \(\Delta G^{\bullet}\), determines the spontaneity of a reaction. A positive \(\Delta G^{\bullet}\) indicates a non-spontaneous process at standard conditions. The graph will have a higher free energy for products compared to reactants, indicating that reactants are favored at equilibrium.

Step 2: Sketch the Free Energy Curve

Draw a coordinate system with the reaction progress on the x-axis and free energy on the y-axis. Sketch the curve starting at a lower free energy level for reactants, rising to a peak representing the activated complex (transition state), and then descending to a higher free energy level for the products, indicating the endothermic nature of the reaction.

Step 3: Indicate the Equilibrium Composition

Mark the point on the curve directly between the reactants and products at a free energy minimum -- the lowest point of the curve. This point represents the state of equilibrium, where the rate of the forward reaction equals the rate of the reverse reaction, and no net change in the concentration of reactants and products occurs.

Step 4: Label the Graph

Label the y-axis as 'Free Energy' and the x-axis as 'Reaction Progress'. Mark the initial free energy level of reactants on the y-axis, the final free energy level of products, and the free energy of activation (the peak of the curve). Indicate the state of equilibrium with a dotted line or a point.

Key Concepts

Chemical Reaction Spontaneity

Understanding the spontaneity of a chemical reaction is crucial in predicting whether a reaction will proceed without external influence. Spontaneous reactions are those that occur naturally, given the initial conditions, without continuous input of energy.

The key to determining if a reaction is spontaneous lies in the Gibbs free energy change (abla G), a thermodynamic quantity representing the balance between enthalpy (heat content) and entropy (disorder) of the system throughout the reaction. A negative abla G value indicates a spontaneous reaction under standard conditions, while a positive value suggests a non-spontaneous process.
It is essential to note that the term 'spontaneous' does not comment on the reaction rate; a reaction may be spontaneous yet occur very slowly.

Gibbs Free Energy

Gibbs free energy, denoted as abla G, is a cornerstone concept in thermodynamics that helps predict reaction spontaneity and equilibrium. Gibbs free energy represents the maximum amount of work that a thermodynamic system can perform at a constant temperature and pressure.

The equation abla G = abla H - Tabla S combines the system's enthalpy (abla H), temperature (T), and entropy (abla S), thus integrating both energetic and disorder aspects. For a reaction to be spontaneous, the change in Gibbs free energy should be negative (abla G < 0). At equilibrium, the free energy is at its lowest value, and abla G = 0, implying that no net work can be extracted from the system.

Reaction Equilibrium

Reaction equilibrium is the state at which chemical reactions occur at a constant rate in both directions, resulting in no overall change in the concentration of reactants and products. This dynamic state can be represented on a free energy curve as the lowest point between the energy levels of reactants and products.

When a reaction system reaches equilibrium, it has achieved the minimum Gibbs free energy available under given conditions. At this point, referred to as the equilibrium composition, the forward and reverse rates are equal, and the reaction mixture's composition remains constant over time, provided the system is undisturbed. The position of equilibrium is affected by changes in temperature, pressure, and concentration, as described by Le Chatelier's Principle.

Endothermic Reaction

An endothermic reaction is a process that absorbs energy from its surroundings, typically in the form of heat. This energy uptake results in a greater enthalpy (abla H) for the products compared to the reactants. On a free energy curve, an endothermic reaction would feature reactants at a lower energy level than the products, indicating that energy input is required for the reaction to proceed.

The sign of abla H is positive in endothermic reactions, and the products have a higher potential energy. This is often shown by a peak on the graph that corresponds to the activated complex, where the energy is highest before transitioning to products. It's important to remember that endothermic reactions can still be spontaneous if the increase in entropy (abla S) is enough to drive a negative change in Gibbs free energy (abla G).