Question

Do you expect a large or small value of the equilibrium constant for a reaction with the following values of \(\Delta G^{\circ}\) ? (a) \(\Delta G^{\circ}\) is positive. (b) \(\Delta G^{\circ}\) is negative.

Short answer

(a) Small K; (b) Large K.

Step-by-step solution

Understand the Relationship Between ΔG° and K

The equilibrium constant, \( K \), is related to the standard change in free energy, \( \Delta G^{\circ} \), by the equation: \( \Delta G^{\circ} = -RT \ln K \), where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin. This relationship suggests that the sign and magnitude of \( \Delta G^{\circ} \) have a direct impact on the size of \( K \).

Analyze ΔG° Positive Case

If \( \Delta G^{\circ} \) is positive, \( K \) is less than 1 because the natural logarithm \( \ln K \) must be negative in order for \( \Delta G^{\circ} \) to be positive. This indicates that the reactants are favored at equilibrium, leading to a small value of \( K \).

Analyze ΔG° Negative Case

If \( \Delta G^{\circ} \) is negative, \( K \) is greater than 1 because the natural logarithm \( \ln K \) must be positive in order for \( \Delta G^{\circ} \) to be negative. This suggests that the products are favored at equilibrium, resulting in a large value of \( K \).

Conclusion of Analysis

From the above analysis, we can conclude the trends: a positive \( \Delta G^{\circ} \) corresponds to a small \( K \), while a negative \( \Delta G^{\circ} \) corresponds to a large \( K \).

Key concepts

Free Energy Change

In chemistry, free energy change, often denoted as \( \Delta G^{\circ} \), is a crucial concept that helps predict the direction of a chemical reaction. \( \Delta G^{\circ} \) represents the change in Gibbs free energy under standard conditions, which is essential for understanding spontaneity. When the value of \( \Delta G^{\circ} \) turns out to be negative, this signifies that the reaction can occur spontaneously, as the system releases energy.

In contrast, a positive \( \Delta G^{\circ} \) indicates the reaction is non-spontaneous under standard conditions, requiring an input of energy to proceed. This can be summarized as:

• Negative \( \Delta G^{\circ}:\) Spontaneous reaction favoring product formation.
• Positive \( \Delta G^{\circ}:\) Non-spontaneous reaction favoring reactants, hence an input of energy is necessary.

Understanding free energy change allows chemists to determine which reactions are energetically feasible and which may require additional conditions or energy to occur.

Thermodynamics

The field of thermodynamics deals with energy transformations in chemical processes. It provides the framework for analyzing how heat, work, and energy are interrelated through different states of a system.

In the context of equilibrium and reactions, thermodynamics gives insight into the conditions under which a reaction proceeds. It uses concepts like enthalpy, entropy, and free energy to describe these transformations.

• Enthalpy (\( H \)): A measure of heat content in a system, reflected in energy absorbed or released during reactions.
• Entropy (\( S \)): A measure of disorder or randomness, indicating the distribution of energy within a system.
• Free Energy (\( G \)): A derived quantity combining enthalpy and entropy to determine feasibility of processes.

The pivotal equation \( \Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ} \) captures how these factors combine to influence reaction spontaneity, with temperature \( T \) playing a critical role. Thermodynamics thus serves as the foundation for understanding any chemical equilibrium by linking the system's microscopic properties to observable macroscopic behaviors.

Reaction Equilibrium

Reaction equilibrium is a key concept in chemistry, where a reaction reaches a state where the rate of forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time.

The equilibrium state is marked by the equilibrium constant \( K \), a dimensionless number that provides insight into the extent of reaction: whether reactants or products are favored.

• If \( K > 1 \), the reaction favors products, meaning products are more stable at equilibrium.
• If \( K < 1 \), reactants are favored, indicating reactants remain largely unreacted.

Understanding \( K \) helps predict shift in equilibrium and the effect of different conditions on the balance. Whether a change in conditions, such as temperature or pressure, shifts the equilibrium position, is also dictated by Le Chatelier’s Principle, an essential tool for anticipating system response to external changes. Thus, the concept of reaction equilibrium aids in designing and controlling chemical processes across many industries.