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) + 3O2(g)   2CO2(g)  + 3H2O(g)

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

 Chemical Species ΔfH (KJ/mol) ΔS (J/molK) C2H5OH(g) -278 160 O2(g) 0 205 CO2(g) -393 214 H2O(g) -242 189

Calculate the ΔH of the system:

ΔH = ∑ΔfH(products) – ∑ΔfH(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) 6CO2(g)    C6H12O6(aq) + 6O2(g)

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

 Chemical Species ΔfH (KJ/mol) ΔS (J/molK) C6H12O6(aq) -2801 209 O2(g) 0 205 CO2(g) -393 214 H2O(l) -286 70

Calculate the ΔH of the system:

ΔH = ∑ΔfH(products) − ∑ΔfH(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.