Gibbs Energy and Spontaneity

For a system which is not isolated from its surroundings,

ΔS_total = ΔS_system + ΔS_surrounding

At constant temperature and pressure, if q_p is the heat given out by the system to the surroundings,

ΔS_surrounding = -q_p/T = – ΔH_system/T

ΔS_total = ΔS_system – ΔH_system/T

TΔS_total = TΔS_system – ΔH_system

– TΔS_total = ΔH_system – TΔS_system

Gibbs energy is defined as

G = H - TS

For a change in Gibbs energy,

ΔG = ΔH - Δ(TS)

ΔG = ΔH - TΔS - SΔT

For a change at constant temperature, ΔT= 0,

ΔG = ΔH - TΔS

Since H, T and S are state functions, it follows that G is also a state function.

ΔG = – TΔS_total

For a process occurring at constant temperature and pressure, if

• ΔG < 0 (negative), the process is spontaneous
• ΔG > 0 (positive), the process is non-spontaneous
• ΔG = 0 (zero), the process is at equilibrium