δg° = -rt ln k

Definition

The equation $$ ext{δg°} = - ext{RT} ext{ln} K$$ relates the standard Gibbs free energy change (δg°) of a chemical reaction to the equilibrium constant (K) of that reaction. This relationship shows how the spontaneity of a reaction at standard conditions is influenced by the position of equilibrium, indicating that a more favorable (negative) δg° corresponds to a larger equilibrium constant, signifying a greater tendency for products to form. Essentially, it connects thermodynamics with chemical equilibrium, emphasizing that spontaneous reactions tend to favor product formation.

5 Must Know Facts For Your Next Test

1. The equation shows that if K is greater than 1, δg° is negative, indicating that the reaction is spontaneous under standard conditions.
2. If K is less than 1, δg° is positive, which means the reaction is non-spontaneous at standard conditions.
3. The term 'R' in the equation represents the universal gas constant, which has a value of 8.314 J/(mol·K).
4. Temperature (T) in Kelvin plays a crucial role in determining the spontaneity; as temperature increases, the impact on δg° and K can change.
5. This relationship highlights that equilibrium can be reached when δg° equals zero, signifying no net change in concentrations of reactants and products.

Review Questions

• How does the value of K relate to the spontaneity of a reaction as described by the equation δg° = -rt ln k?
  • The value of K indicates whether a reaction favors products or reactants at equilibrium. If K is greater than 1, it means there are more products than reactants at equilibrium, which corresponds to a negative δg°, indicating that the reaction is spontaneous under standard conditions. Conversely, if K is less than 1, it reflects more reactants than products, resulting in a positive δg°, suggesting non-spontaneity. Thus, this equation directly connects the concepts of spontaneity and chemical equilibrium.
• Discuss how temperature influences the relationship between Gibbs free energy and the equilibrium constant according to δg° = -rt ln k.
  • Temperature significantly affects both δg° and K in the equation. An increase in temperature can alter the value of K depending on whether a reaction is endothermic or exothermic. For endothermic reactions, increasing temperature generally increases K, making δg° more negative and favoring spontaneity. In contrast, for exothermic reactions, increasing temperature can decrease K, potentially making δg° positive. This interplay emphasizes the importance of temperature in determining reaction spontaneity through changes in Gibbs free energy.
• Evaluate how understanding δg° = -rt ln k can impact our approach to predicting reaction behaviors in real-world chemical processes.
  • Understanding this equation equips us with tools to predict how changes in concentration, temperature, or pressure can shift equilibria and influence spontaneity in real-world scenarios. For example, in industrial chemistry where maximizing product yield is crucial, knowing how to manipulate these variables using the principles derived from this equation helps chemists design efficient processes. Additionally, it aids in assessing reaction feasibility under different conditions by allowing predictions about whether reactions will proceed towards products or revert to reactants based on calculated Gibbs free energies and equilibrium constants.

Related terms

Gibbs Free Energy: A thermodynamic potential that measures the maximum reversible work obtainable from a closed system at constant temperature and pressure.

Equilibrium Constant (K): A number that expresses the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction, reflecting the extent to which a reaction proceeds.

Spontaneity: The tendency of a process or reaction to occur without the need for external energy input, often indicated by a negative change in Gibbs free energy.