Life, the universe and everything

Entropy has already been discussed in terms of disorder. The tendency of the universe to move towards disorder is a consequence of there being an infinite number of possible disordered states and very few ordered states. The probability of adoption of disorder is just too great for it not to happen.

For any process, physical or chemical, there is a before and after. We can consider a process to have two parts, a system and a surroundings (everything else that is not the system). The two parts together make up the whole universe.

If the process results in an increase in entropy in the universe then it is possible. There are two ways that universal entropy can increase.

1. The system produces a greater number of particles
2. The system releases energy that goes to increasing the disorder of the surroundings.

The entropy of the universe = the entropy of the system + the entropy of the surroundings, and any change in the universal entropy must be a consequence of either change in the entropy of the surroundings, the system or both.

ΔS(universe) = ΔS(system) + ΔS(surroundings)

Therefore:

ΔS(universe) - ΔS(surroundings) = ΔS(system)

Entropy change in the system can be gauged in terms of the number of particles with degrees of freedom (specifically gases). Change in the entropy of the surroundings is caused by release of energy.

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Gibbs Free Energy

From the previous sub-section we se that there are two ways that the overall entropy of the universe can increase. Increasing the number of particles in the system, or releasing energy from the system that increases the entropy of the surroundings.

The effect of energy on the entropy change is dependent on the temperature of the surroundings. They are equated by the relationship:

ΔS(surroundings) = q/T

That is, the entropy change is the energy (q) released by the system (transferred to the surroundings) divided by the absolute temperature.

We call the energy released by chemicals in the course of a reaction, the enthalpy change (negative as the reaction is exothermic), so the relationship can also be written:

ΔS(surroundings) = -ΔH/T

If this is substituted into the universal entropy relationship:

ΔS(universe) = ΔS(surroundings) + ΔS(system)

we get:

ΔS(universe) = -ΔH/T + ΔS(system)

Multiplying through by -T gives:

-TΔS(universe) = ΔH - TΔS(system)

Gibbs recognised the importance of this relationship and defined a state symbol 'G' that represents the '-TΔS(universe)', which he called ' Free Energy of the system'.

G = -TΔS(universe)

It should be appreciated that when the universal entropy increases G must take a negative value.

Hence, Gibbs' free energy is related to the entropy of the universe. For any process to be possible, the change in Gibbs' free energy must be negative.

ΔG = ΔH - TΔS

When the entropy of the universe increases it means that the Gibbs Free Energy of the system decreases

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Spontaneity

The term 'spontaneity' has a connotation of immediacy in common speech usage. However, in chemistry it means something rather different. A process is spontaneous if there is no thermodyanic reason why it cannot take place. It is a word that means that the process is possible.

Gibbs free energy must be negative for the entropy of the universe to increase. Conversely if the Gibbs free energy of a process is positive it means that the process cannot take place (under the specified conditions). A negative Gibbs free energy value indicates a spontaneous process and, in the reverse case, positive Gibbs free energy indicates non-spontaneity.

Gibbs free energy ΔG	Spontaneity
positive ΔG > 0	non-spontaneous
negative ΔG < 0	spontaneous

REM Spontaneous = possible in 'chemistry speak'

Example: For the reaction: 3HC  CH(g) → C6H6(g) ΔH = - 597.3 kJ and ΔS = - 0.33 kJ K-1. This reaction A. is spontaneous at 300 K and becomes non-spontaneous at higher temperatures. B. is spontaneous at 300 K and becomes non-spontaneous at lower temperatures. C. is non-spontaneous at 300 K and becomes spontaneous at higher temperatures. D. is non-spontaneous at 300 K and becomes spontaneous at lower temperatures. Using Gibbs free energy equation at 300k: ΔG = ΔH - TΔS ΔG = -597.3 - 300 x (-0.33) ∴ ΔG = -597.3 + 99 = - 498.3 Hence the reaction is spontaneous at this temperature. However, as the temperature increases the term TΔS becomes more negative making the term -TΔS more positive. Hence ΔG gets less negative as the temperature rises until eventually it becomes non-spontaneous.

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Special cases

There are one or two things to take into account when dealing with Gibbs free energy.

1 Spontaneity does not imply that the reaction goes ahead, it simply considers the possibility, or feasibility, of a particular reaction, or process.

Kinetic control Although a reaction, or process, may be spontaneous thermodynamically, it does not mean that it necessarily happens. One example is the oxidation of sugar. C12H22O11(s) + 6O2(g) 12CO2(g) + 11H2O(l) Thermodynamically, this is very favourable with a large negative ΔG value. However, sugar is a perfectly stable substance, which can remain on a table for years without being oxidised by the surrounding air. The reason is that the reaction has a high activation energy. The process is said to be 'kinetically controlled'.

2 Standard Gibbs free energies are calculated for a specific set of standard conditions. It may be that the reaction proceeds normally under other circumstances.

Changing conditions The reaction between HCl and MnO2 is thermodynamically unfeasible, i.e. non-spontaneous as the value for the standard Gibbs free energy change is positive. However, this is precisely the reaction that is used to generate chlorine in the laboratory. 4HCl(aq) + MnO2(s) MnCl2(aq) + Cl2(aq) + 2H2O(l) Thermodynamically, the reaction appears non-spontaneous as the conditions require heat and stronger concentrations than 1 mol dm-3 for the HCl. These are non-standard conditions. Under these non-standard conditions the Gibbs free energy value becomes negative and the reaction spontaneous.

3 As soon as a reaction starts, the conditions change. This may cause a spontaneous reaction to become non-spontaneous.

Changing conditions As reactions proceed the reactants are used up and their concentrations decrease. The enthalpy and entropy values that produce the Gibbs free energy value are calculated for molar quantities. ΔG = ΔH - TΔS As the relative amounts of the reactants change so does the value of the Gibbs free energy.

4 When the Gibbs free energy value equals zero, the system is at equilibrium. This follows on from number 3 (above).

Equilibrium As reactions proceed the reactants are used up and their concentrations decrease. At the same time the products concentrations increase. The forward reaction gradually becomes less spontaneous and the reverse reaction less non-spontaneous. If there are still reactants remaining when ΔG becomes zero, then an equilibrium is established. ΔG = ΔH - TΔS = 0 Use can be made of this fact to find the temperature at which such equilibria are established.

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