The quantum casino: tutorials

The role of energy

Energy also has a role to play in the entropy or randomness of a chemical system, by which we mean a quantity of substance or substances (such as a reaction mixture). Energy exists in ‘packets’ called quanta. This means that it is similar to molecules. You cannot have half a molecule and, similarly, you can have any whole number of quanta of energy but not 1½ or 3.25 quanta. Quanta are like marbles rather than plasticine. Like the distribution of atoms in space, the distribution of quanta of energy between molecules is also random because, like molecules, energy quanta do not ‘know’ where they are supposed to be – ‘energy doesn’t care’.  We can simulate this distribution.

We can see that the more quanta of energy and the more molecules there are in a system, the more ways there are to distribute them.

This can be shown simply by the following examples but can be shown more generally by the simulation. Tables 4, 5 and 6 show the possible arrangements of four quanta between two molecules, five quanta between two molecules and three quanta between three molecules respectively.

 Molecule 1 Molecule 2 0 4 1 3 2 2 3 1 4 0

Table 4 Two molecules, four quanta – five arrangements

 Molecule 1 Molecule 2 0 5 1 4 2 3 3 2 4 1 5 0

Table 5 Two molecules, five quanta – six arrangements

 Molecule 1 Molecule 2 Molecule3 3 0 0 0 0 3 0 3 0 1 1 1 1 2 0 2 1 0 1 0 2 2 0 1 0 1 2 0 2 1

Table 6 Three molecules, three quanta – 10 arrangements

The distribution of energy quanta also contributes to entropy because of the relationship S = k lnW. The more heat energy we put into anything, the more its entropy increases because there are more quanta and thus more ways, W, to distribute them. Most chemical reactions involve a change of heat energy (enthalpy), either given out from the reactants to the surroundings or taken in from the surroundings into the products. So we must also take this into account when we are considering the entropy change of a chemical reaction. It is not just the chemical reaction that matters but the surroundings as well.

 The role of energy

 Home Videos Tutorials The direction of chemical reactions Entropy The Second Law of Thermodynamics Is the Second Law wrong? The role of energy The system and the surroundings Total entropy change The Gibbs free energy ∆G and temperature Reversible reactions Why is free energy 'free'? Simulations Entropy and disorder Arranging objects The distribution of energy The approach to equilibrium Equilibrium mixtures ∆G and temperature