The Direction of Spontaneous Reactions

Certain processes occur spontaneously – for example cooling of a hot object to the temperature of the surroundings, and expansion of a gas to fill the volume available to it. Though these processes can be made to go the other way (heating an object up, confining a gas to a smaller volume), they do not occur spontaneously, and can only be brought about by doing work upon the system of interest.

It is useful to be able to predict whether or not a process will be spontaneous, but to do so we need to find some property of a system that will determine the direction of spontaneous change. Initially, one might consider the internal energy, U, of a system and hypothesise that it tends to a minimum. However, the First Law of Thermodynamics states that total energy is conserved in any process. This means firstly that the energy of an isolated system cannot change in any process, in disagreement with our expectation.

There is a second, more fundamental problem with the hypothesis: if the energy of a system decreases in a spontaneous change, then by the First Law the energy of the surroundings must increase by the same amount, but both processes are spontaneous. Thus it is clear that changes in the internal energy of a system cannot be the signpost of spontaneous change.

We shall see that in fact the direction of change is related to the distribution of energy in the system – a spontaneous change is always accompanied by a dispersal of energy into a less ordered form.

We can use this idea to illustrate the two examples given above:

  1. Objects do not spontaneously become warmer than their surroundings because this would require the accumulation of excess thermal energy (in the form of thermal motion) in the object. It is exceptionally unlikely that this could occur by transmission of energy from randomly vibrating atoms in the surroundings, so may be considered impossible. The opposite process, dispersal of the object’s thermal energy into the random vibrational motion of the surroundings, is a consequence of the tendency towards increased chaos.
  2. Gases do not spontaneously contract because to do so requires the chaotic motion of the gas particles to become ordered and localised in one part of the container. This is also so overwhelmingly improbable that it can be considered impossible. The opposite process, spontaneous expansion, is a natural consequence of increasing disorder.

The distinction between spontaneous and non-spontaneous processes is formalised in the Second Law of Thermodynamics.