Entropy

&

Gibbs Energy

Total Entropy and Gibbs Energy

What is Equilibrium in terms of Entropy?

In thermodynamics, a chemical system is the matter in a reaction; the reactants and products. The entropy of a chemical system is indicated by the number of possible arrangements for that matter, meaning the mixing up or disorder of its particles. In terms of energy, entropy is the dispersal of energy into microstates - the more occupied microstates a system has, the higher its entropy. If we consider a chemical reaction together with its surroundings, for example in solution, total entropy (Ssystem + Ssurroundings) is at its maximum when the system is at equilibrium.

What is Equilibrium in terms of Gibbs Energy?

This entropy maximum is also a Gibbs free energy minimum - recall that a system with no Gibbs energy has no ability to do work, so it makes sense that a state of equilibrium represents the endpoint of a reaction. In other words, during the progress of a spontaneous reaction, Gibbs energy decreases as reactant atoms rearrange to maximise the overall entropy of the system and its surroundings.

Phase Transitions (Changes of State) and Gibbs Energy

Sometimes the surrounding environment does work to increase the entropy of the system, such as in the endothermic changes of state. Molecules have more freedom of movement in the new state, even if the surrounding molecules had to lose some of their kinetic energy, thereby losing entropy. For reversible reactions, the endothermic direction is favoured at high temperatures - the loss of entropy in the surroundings is small while the rise in entropy of the system is comparatively large. The loss of entropy of the surroundings is equal to the gain in entropy of the system at the transition temperature (e.g. boiling/melting point).

Let’s find the boiling point of water using standard enthalpies and entropies. We know that phase transition points are temperatures at which the change becomes spontaneous, where ΔG goes from positive to negative.

ΔG = 0 = ΔH - TΔS

I found the following information in the IBDP data booklet and organised it into a table for easy reference:

ΔH⦵f (H2O, l) = -286 kJmol-1

ΔH⦵f (H2O, g) = -242 kJmol-1

S⦵ (H2O, l) = +70 JK-1mol-1

S⦵ (H2O, g) = +189 JK-1mol-1

The boiling of water can be expressed in an equation:

H2O (l) → H2O (g)

And we can use Hess’ Law to calculate the enthalpy of vaporisation of water:

ΔH⦵f (H2O, g) – ΔH⦵f (H2O, l) = ΔH⦵vap (H2O)

-242 - (-286) = +44 kJmol-1

ΔSsystem is the difference between the entropy of liquid water and the entropy of steam:

S⦵(H2O,g) – S⦵(H2O,l) = ΔSsystem

189 – 70 = 119 JK-1mol-1

Don’t forget entropy is given in joules and enthalpy is given in kilojoules!

So 119 JK-1mol-1 becomes 0.119 kJK-1mol-1.

To find the boiling point:

ΔH - TΔS = ΔG

44 - T(0.119) = 0

44 / 0.119 = 370 K

370 kelvin is 970C. Can you suggest why we did not get 1000C?

Allotrope Transitions and Gibbs Energy - Tin Pest

Tin can be mixed with copper to form the alloy, bronze. It was one of the first metals that ancient peoples produced, worked and traded on a large scale. It is usually soft and malleable, but in cold temperatures and over a period of months, it can transform from the metallic allotrope, white tin, into the dull, brittle semi-conductor, grey tin. The process became known as tin pest because of grey tin’s powdery appearance making it look diseased. Pipes in Medieval church organs; the uniform buttons of Napoleon’s soldiers as they marched into a Russian winter; cans containing food for British explorers hoping to be the first men to reach the South Pole; Allied Liberty ships in the North Atlantic during the second world war: they are all rumoured to have suffered from tin pest and this affliction even affected the outcome of some of their stories. (The tetragonal crystal structure of white tin has many slip systems that allow the material to be deformed without shattering, while the diamond cubic structure of grey tin has fewer slip systems and cannot be deformed.)

Find the transition temperature, when white tin transforms into grey tin, using the following data:

You should arrive at 13oC. Don’t forget to convert your units! I think 13oC is surprisingly high in the sense that ‘tin pest’ is not a problem we hear about very often. The truth is that this allotropic transformation only readily occurs in pure samples, and nearly all the tin we use is alloyed with other metals.

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