Gibbs Free Energy (ΔG) is a fundamental thermodynamic quantity that helps predict reaction feasibility. It indicates whether a process will occur spontaneously under specific conditions, providing insights into reaction behavior.
Understanding Gibbs Free Energy and Reaction Spontaneity
The value of ΔG indicates a reaction’s spontaneity at constant temperature and pressure. A negative ΔG signifies a spontaneous reaction, meaning it can proceed without continuous external energy input. Conversely, a positive ΔG indicates a non-spontaneous reaction, which will not occur as written unless energy is supplied. If ΔG is zero, the system is at equilibrium, with no net change in reactant or product concentrations.
Many ΔG values are often reported under “standard conditions,” defined as 25°C (298.15 K), 1 atmosphere pressure for gases, and 1 M (molar) concentrations for solutions. These standard conditions provide a common reference point for comparing the spontaneity of different reactions. While ΔG can be calculated for non-standard conditions, ΔG° (standard Gibbs Free Energy change) is a frequently used reference point.
Calculating Delta G Using Standard Formation Values
One method to determine the standard Gibbs Free Energy change for a reaction (ΔG°rxn) uses the standard Gibbs Free Energies of Formation (ΔG°f) for the reactants and products. ΔG°f represents the change in Gibbs Free Energy when one mole of a compound forms from its elements in their standard states. Elements in their standard states, such as O₂ gas or solid carbon (graphite), have a ΔG°f value of zero.
The general formula for calculating ΔG°rxn from standard formation values is:
ΔG°rxn = ΣnΔG°f(products) – ΣmΔG°f(reactants).
Here, ‘n’ and ‘m’ are the stoichiometric coefficients from the balanced chemical equation. This approach allows for the determination of ΔG° without direct experimental measurement for every reaction.
For example, consider the reaction: CO(g) + 2H₂(g) → CH₃OH(l).
Using hypothetical ΔG°f values: CO(g) = -137.2 kJ/mol, H₂(g) = 0 kJ/mol, CH₃OH(l) = -166.3 kJ/mol.
ΔG°rxn = [1 mol × ΔG°f(CH₃OH(l))] – [1 mol × ΔG°f(CO(g)) + 2 mol × ΔG°f(H₂(g))]
ΔG°rxn = [1 mol × (-166.3 kJ/mol)] – [1 mol × (-137.2 kJ/mol) + 2 mol × (0 kJ/mol)]
ΔG°rxn = -166.3 kJ – (-137.2 kJ) = -29.1 kJ. This negative value indicates the reaction is spontaneous under standard conditions.
Calculating Delta G Using Enthalpy, Entropy, and Temperature
The fundamental equation for calculating Gibbs Free Energy change is ΔG = ΔH – TΔS. This equation relates ΔG to changes in enthalpy (ΔH), entropy (ΔS), and temperature (T). Enthalpy change (ΔH) represents the heat absorbed or released during a reaction, while entropy change (ΔS) measures the change in disorder or randomness within the system. Temperature (T) must always be expressed in Kelvin.
The signs of ΔH and ΔS influence spontaneity. If ΔH is negative (exothermic) and ΔS is positive (increased disorder), ΔG will always be negative, making the reaction spontaneous at any temperature. Conversely, if ΔH is positive (endothermic) and ΔS is negative (decreased disorder), ΔG will always be positive, meaning the reaction is never spontaneous. When both ΔH and ΔS have the same sign, temperature becomes a determining factor; a reaction with positive ΔH and positive ΔS can be spontaneous at high temperatures, while one with negative ΔH and negative ΔS can be spontaneous at low temperatures.
Ensure consistent units; if ΔH is in kilojoules, ΔS should also be in kilojoules per Kelvin (or converted from Joules).
For an example calculation, consider a reaction with ΔH = -50.0 kJ/mol and ΔS = -0.150 kJ/(mol·K) at a temperature of 300 K.
ΔG = ΔH – TΔS
ΔG = -50.0 kJ/mol – (300 K × -0.150 kJ/(mol·K))
ΔG = -50.0 kJ/mol – (-45.0 kJ/mol)
ΔG = -5.0 kJ/mol. The negative ΔG indicates spontaneity at 300 K.
Calculating Delta G Using the Equilibrium Constant
The standard Gibbs Free Energy change (ΔG°) is directly related to the equilibrium constant (K) of a reaction: ΔG° = -RTlnK. In this formula, R is the ideal gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and lnK is the natural logarithm of the equilibrium constant. The equilibrium constant (K) describes the ratio of products to reactants at equilibrium, providing insight into the extent to which a reaction proceeds.
A large negative ΔG° corresponds to a large K value, indicating that products are favored at equilibrium. Conversely, a large positive ΔG° leads to a small K value, signifying that reactants are favored. If ΔG° is zero, K equals 1, suggesting that products and reactants are present in roughly equal amounts at equilibrium under standard conditions.
To illustrate, if a reaction has an equilibrium constant (K) of 500 at 298 K:
ΔG° = -RTlnK
ΔG° = -(8.314 J/(mol·K)) × (298 K) × ln(500)
First, calculate ln(500) ≈ 6.2146.
Then, ΔG° = -(8.314 J/(mol·K)) × (298 K) × 6.2146
ΔG° ≈ -15400 J/mol, or -15.4 kJ/mol.