Non-equilibrium Systems - Learn

Non-equilibrium Systems

Reversible Reactions

Non-equilibrium Systems

A non-equilibrium system is one where all the reactants combine to form products and the reaction goes to completion. These reactions are considered irreversible and usually occur when the reaction releases a lot of energy or occur spontaneously.

Irreversible reactions can be analysed and determined by considering the enthalpy and entropy of the system and their impact on the Gibbs free energy of that chemical system.

Gibbs Free Energy

Gibbs free energy (ΔG°) is used to determine whether a reaction will occur spontaneously.

ΔG° = ΔH° – TΔS°

Where:

if ΔG° is positive, the reaction is non-spontaneous.

if ΔG° is negative, the reaction is spontaneous

Reactions that have ΔG° close to zero can occur in both directions when both reactants and products are present. These will form equilibrium systems.

Two examples of non-equilibrium systems include combustion and photosynthesis.

During combustion reactions, the entropy of the system increases and the enthalpy decreases. This combination dictates that combustion reactions are spontaneous. The Gibbs free energy is also largely negative and non-equilibrium.
During photosynthesis, the entropy of the system decreases and the enthalpy increases. This combination dictates that the photosynthesis reaction is non-spontaneous. The Gibbs free energy is also largely positive and non-equilibrium.

Combustion

We can analyse combustion reactions to illustrate their spontaneous and irreversible nature. Given the standard enthalpy of formation values and entropy values we can calculate the Gibbs free energy

Example 1: The combustion of ethanol is illustrated by the chemical equation below:

C₂H₅OH_(g) + 3O_2(g) 2CO_2(g) + 3H₂O_(g)

Determine if the combustion of ethanol is a spontaneous reaction given the following data at 25 C:

Chemical Species	Δ_fH (KJ/mol)	ΔS (J/molK)
C₂H₅OH_(g)	-278	160
O_2(g)	0	205
CO_2(g)	-393	214
H₂O_(g)	-242	189

Answer:

Calculate the ΔH of the system:

ΔH = ∑Δ_fH_(products) – ∑Δ_fH_(reactants)

ΔH = [(2×−393)+(3×−242)]−[(−278)+(3×0)]

ΔH = −1234 Kj mol^-1

Calculate the ΔS of the system:

ΔS = ∑ΔS_(products) – ∑ΔS_(reactants)

ΔS = [(2×214)+(3×189)]−[160+(3×205)]

ΔS = 220 JK^-1mol^-1 (0.22 K JK^-1mol^-1)

Calculate the Gibbs free energy:

ΔG° = ΔH° – TΔS°

ΔG° = −1234−(293×0.22)

ΔG° = −1298.5 Kj mol^-1

The Gibbs free energy for the combustion of ethanol is largely negative. This reflects the spontaneous and non-equilibrium nature of combustion reactions.

Photosynthesis

A similar process can be used to analyse photosynthesis.

Example 2: Photosynthesis is a complex series of reactions which is conveniently summarised as:

6H₂O_(l) 6CO_2(g) C₆H₁₂O_6(aq) + 6O_2(g)

Use the following information to illustrate the non-spontaneous nature of the photosynthesis reaction at 25 C:

Chemical Species	Δ_fH (KJ/mol)	ΔS (J/molK)
C₆H₁₂O_6(aq)	-2801	209
O_2(g)	0	205
CO_2(g)	-393	214
H₂O_(l)	-286	70

Calculate the ΔH of the system:

ΔH = ∑Δ_fH_(products) − ∑Δ_fH_(reactants)

ΔH = [(−2801)+(6×0)]−[(6×−393)+(6×−286)]

ΔH = 1273 Kj mol^-1

Calculate the ΔS of the system:

ΔS = ∑ΔS_(products) − ∑ΔS_(reactants)

ΔS = [(209)+(6×205)]−[(6×70)+(6×214)]

ΔS = −265 JK^-1mol^-1 (−0.265 K JK^-1mol^-1)

Calculate the Gibbs free energy:

ΔG° = ΔH° – TΔS°

ΔG° = 1273 −(293×−0.265)

ΔG° = 1350 Kj mol^-1

The Gibbs free energy for the photosynthesis process is largely positive. This reflects the non-spontaneous and non-equilibrium nature of photosynthesis.

Photosynthesis is a non-equilibrium reaction because it takes place in an open system (oxygen that is produced can quickly leave the plant). It also requires enzymes and light for the reaction to occur and overcome its non-spontaneous nature.