Chemical reactions in nature tend to proceed towards a state of equilibrium. Gibbs free energy helps us predict and understand this behavior. Let's explore how these concepts are interconnected.

The Fundamentals of Gibbs Free Energy

Gibbs free energy (G) represents the energy available in a system to perform useful work at constant temperature and pressure. The change in Gibbs free energy (ΔG) is given by:

$\Delta G = \Delta H - T\Delta S$

where:

The value of ΔG tells us about reaction spontaneity:

Standard Gibbs Free Energy

Standard Gibbs free energy change (ΔG°) refers to the change in Gibbs free energy under standard conditions (1 M concentration, 1 bar pressure, 298.15 K). It's calculated using:

$\Delta G° = \Delta H° - T\Delta S°$

The relationship between ΔG and ΔG° is given by:

$\Delta G = \Delta G° + RT\ln Q$

where:

Predicting Reaction Direction

The reaction quotient (Q) helps predict reaction direction:

The Link Between ΔG° and Equilibrium Constant

At equilibrium, ΔG = 0, leading to:

$0 = \Delta G° + RT\ln K$ $\Delta G° = -RT\ln K$

This relationship reveals important insights:

Worked Example

Consider the reaction: $2NO_2(g) \rightleftharpoons N_2O_4(g)$ Given ΔG° = -20 kJ/mol at 298 K

Part A: Calculate ΔG when [NO₂] = 0.010 mol L⁻¹ and [N₂O₄] = 0.10 mol L⁻¹

Solution: $\Delta G = \Delta G° + RT\ln Q$ $\Delta G = -20,000 + (8.314)(298)\ln\frac{0.10}{(0.010)^2}$ $\Delta G = -2.9 × 10^3 \text{ J mol}^{-1}$

Since ΔG < 0, the forward reaction is spontaneous.

Part B: Calculate the equilibrium constant (K)

Solution: $\Delta G° = -RT\ln K$ $-20,000 = -(8.314)(298)\ln K$ $\ln K = \frac{20,000}{(8.314)(298)}$ $K = 3,205$