Free Energy

Gibbs Free Energy Change (ΔG)

A thermodynamic quantity used to determine whether a process is spontaneous under the specified conditions.

Spontaneous Process

A process that is thermodynamically favored to proceed in a particular direction under the specified conditions.

Nonspontaneous Process

A process that is not thermodynamically favored to proceed in a particular direction under the specified conditions.

ΔG and Spontaneity

A process is spontaneous in the forward direction when ΔG < 0, at equilibrium when ΔG = 0, and nonspontaneous in the forward direction when ΔG > 0.

Negative ΔG

A negative Gibbs free energy change indicates that the forward process is thermodynamically spontaneous under the specified conditions.

Positive ΔG

A positive Gibbs free energy change indicates that the forward process is thermodynamically nonspontaneous under the specified conditions.

Zero ΔG

A Gibbs free energy change of zero indicates equilibrium.

Gibbs Free Energy Equation

ΔG = ΔH − TΔS.

Enthalpy Change (ΔH) in the Gibbs Equation

The enthalpy contribution to Gibbs free energy in the relationship ΔG = ΔH − TΔS.

Entropy Change (ΔS) in the Gibbs Equation

The entropy contribution to Gibbs free energy whose effect on ΔG depends on temperature through the term −TΔS.

Temperature in the Gibbs Equation

T is the absolute temperature in kelvins and determines the magnitude of the entropy contribution TΔS.

Why Must Temperature Be in Kelvins in ΔG = ΔH − TΔS?

The thermodynamic equation uses absolute temperature, so T must be expressed in kelvins.

Temperature Dependence of Spontaneity

The signs and magnitudes of ΔH and ΔS determine whether changing temperature can change the sign of ΔG and therefore the spontaneity of a process.

ΔH < 0 and ΔS > 0

A process with negative ΔH and positive ΔS has ΔG < 0 at all temperatures and is spontaneous at all temperatures.

Why Is ΔH < 0 and ΔS > 0 Always Favorable?

Both the negative ΔH term and the negative −TΔS term favor a negative ΔG.

ΔH > 0 and ΔS < 0

A process with positive ΔH and negative ΔS has ΔG > 0 at all temperatures and is nonspontaneous at all temperatures.

Why Is ΔH > 0 and ΔS < 0 Always Unfavorable?

Both the positive ΔH contribution and the positive −TΔS contribution favor a positive ΔG.

ΔH > 0 and ΔS > 0

A process with positive ΔH and positive ΔS can become spontaneous at sufficiently high temperature.

Why Can ΔH > 0 and ΔS > 0 Become Spontaneous at High Temperature?

As temperature increases, the favorable negative term −TΔS can become large enough to overcome the positive ΔH term.

ΔH < 0 and ΔS < 0

A process with negative ΔH and negative ΔS can be spontaneous at sufficiently low temperature.

Why Can ΔH < 0 and ΔS < 0 Become Nonspontaneous at High Temperature?

When ΔS is negative, −TΔS is positive and grows with temperature, eventually potentially overcoming the favorable negative ΔH.

Always-Spontaneous Sign Combination

ΔH < 0 and ΔS > 0.

Never-Spontaneous Sign Combination

ΔH > 0 and ΔS < 0.

High-Temperature-Spontaneous Sign Combination

ΔH > 0 and ΔS > 0.

Low-Temperature-Spontaneous Sign Combination

ΔH < 0 and ΔS < 0.

Transition Temperature

The temperature at which a process changes between spontaneous and nonspontaneous behavior because ΔG becomes zero.

Condition at the Transition Temperature

At the transition temperature, ΔG = 0.

Transition Temperature Equation

When ΔG = 0, the equation ΔG = ΔH − TΔS gives T = ΔH/ΔS.

Deriving T = ΔH/ΔS

Set ΔG = 0 in ΔG = ΔH − TΔS, giving 0 = ΔH − TΔS, and solve for T.

Meaning of T = ΔH/ΔS

It gives the temperature at which the enthalpy and entropy contributions exactly balance so that ΔG = 0.

Phase-Transition Equilibrium

At the equilibrium temperature for a phase transition, the two phases coexist at equilibrium and the Gibbs free energy change for the transition is zero.

Boiling-Point Equilibrium

At the boiling point under the specified pressure, liquid and vapor are at equilibrium and ΔG for vaporization is zero.

Melting-Point Equilibrium

At the melting point under the specified pressure, solid and liquid are at equilibrium and ΔG for fusion is zero.

Thermodynamic Estimate of a Phase-Transition Temperature

If ΔH and ΔS for the transition are treated appropriately, the equilibrium transition temperature can be estimated using T = ΔH/ΔS.

Standard Gibbs Free Energy Change (ΔG°)

The Gibbs free energy change associated with a reaction under standard-state conditions.

ΔG vs. ΔG°

ΔG describes the free energy change under the actual current conditions, whereas ΔG° refers to standard-state conditions.

Reaction Quotient in Thermodynamics

The reaction quotient Q describes the current composition of the reaction mixture and contributes to the actual Gibbs free energy change.

Free Energy Under Nonstandard Conditions

The actual Gibbs free energy change is related to the standard Gibbs free energy change and the current reaction composition by ΔG = ΔG° + RT ln Q.

Free-Energy–Reaction-Quotient Equation

ΔG = ΔG° + RT ln Q.

R in ΔG = ΔG° + RT ln Q

R is the gas constant.

T in ΔG = ΔG° + RT ln Q

T is the absolute temperature in kelvins.

ln Q in the Free-Energy Equation

The natural logarithm of the reaction quotient accounts for how the current reaction composition affects ΔG.

Why Can ΔG Differ from ΔG°?

Actual reactant and product conditions may differ from their standard states, and the RT ln Q term accounts for this difference.

Composition and Reaction Driving Force

Changing the reaction composition changes Q and can therefore change ΔG and the thermodynamic driving force of the reaction.

ΔG < 0 and Reaction Direction

When ΔG is negative, the forward reaction is thermodynamically favored.

ΔG > 0 and Reaction Direction

When ΔG is positive, the reverse direction is thermodynamically favored relative to the forward direction.

ΔG = 0 and Reaction Direction

When ΔG is zero, there is no net thermodynamic driving force in either direction and the system is at equilibrium.

Q < K and Gibbs Free Energy

When Q < K, the forward reaction is favored as the system moves toward equilibrium, corresponding to ΔG < 0 for the forward reaction.

Q > K and Gibbs Free Energy

When Q > K, the reverse reaction is favored as the system moves toward equilibrium, corresponding to ΔG > 0 for the forward reaction.

Q = K and Gibbs Free Energy

When Q = K, the system is at equilibrium and ΔG = 0.

Thermodynamic Condition for Chemical Equilibrium

At chemical equilibrium, ΔG = 0.

Compositional Condition for Chemical Equilibrium

At chemical equilibrium, Q = K.

Kinetic Condition for Chemical Equilibrium

At chemical equilibrium, the forward and reverse reaction rates are equal.

Three Views of Chemical Equilibrium

Kinetic: forward rate = reverse rate; compositional: Q = K; thermodynamic: ΔG = 0.

Relationship Between Q and Equilibrium Direction

Q < K favors forward reaction, Q > K favors reverse reaction, and Q = K corresponds to equilibrium.

Equilibrium as a Thermodynamic Destination

A reaction mixture tends toward a composition where the thermodynamic driving force vanishes, corresponding to ΔG = 0 and Q = K.

Central Thermodynamic Picture of Equilibrium

The current composition determines Q, Q contributes to ΔG, the sign of ΔG determines the thermodynamically favored direction, and equilibrium is reached when Q = K and ΔG = 0.