Compare the values of ∆G and ∆G° when: (a) Q < 1. (b) Q = 1. (c) Q > 1. Does the thermodynamic tendency for the reaction to occur increase or decrease as Q increases?

Verified step by step guidance

1. insert step 1> Identify the relationship between \( \Delta G \) and \( \Delta G^\circ \) using the equation: \( \Delta G = \Delta G^\circ + RT \ln Q \), where \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( Q \) is the reaction quotient.
2. insert step 2> For case (a) when \( Q < 1 \), note that \( \ln Q \) is negative, which makes \( \Delta G < \Delta G^\circ \). This implies that the reaction is more spontaneous than under standard conditions.
3. insert step 3> For case (b) when \( Q = 1 \), \( \ln Q = 0 \), so \( \Delta G = \Delta G^\circ \). This means the reaction's spontaneity is the same as under standard conditions.
4. insert step 4> For case (c) when \( Q > 1 \), \( \ln Q \) is positive, which makes \( \Delta G > \Delta G^\circ \). This implies that the reaction is less spontaneous than under standard conditions.
5. insert step 5> As \( Q \) increases, \( \Delta G \) becomes larger, indicating that the thermodynamic tendency for the reaction to occur decreases.

Key Concepts

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. It indicates the spontaneity of a reaction: if ∆G is negative, the reaction is spontaneous; if positive, it is non-spontaneous. The value of ∆G changes based on the reaction's conditions, including the concentrations of reactants and products.

Standard Gibbs Free Energy Change (∆G°)

Standard Gibbs Free Energy Change (∆G°) refers to the change in Gibbs Free Energy under standard conditions (1 bar pressure, 1 M concentration for solutes, and a specified temperature, usually 298 K). It provides a reference point for predicting the direction of a reaction. Unlike ∆G, which varies with the reaction's progress, ∆G° remains constant for a given reaction at specified conditions.

Reaction Quotient (Q)

The Reaction Quotient (Q) is a dimensionless number that reflects the ratio of the concentrations of products to reactants at any point in a reaction. It is used to determine the direction in which a reaction will proceed to reach equilibrium. When Q < 1, the reaction favors products; when Q = 1, the system is at equilibrium; and when Q > 1, the reaction favors reactants, indicating that as Q increases, the tendency for the reaction to occur decreases.