Entropy and spontaneity

In order to find out some other factor that may be responsible for the feasibility of a process, let us examine endothermic reactions. The simplest process occurring without any energy change (where DH is almost zero) may be illustrated with the help of following experiment.

fig 4.4 (a) - Before mixing

fig 4.4 (b) - After mixing

Let us consider two containers connected by means of a valve. The containers are perfectly insulated so that no heat enters or leaves the system. While one container is filled with a liter of helium gas, the other is filled with a liter of neon gas. The two gases are non-reacting (being inert gases). When the valve is opened, it is observed that the two gases get mixed together spontaneously. During the mixing, there is a negligible energy change and, therefore, the criterion of decrease of energy for feasibility of process does not help. If we look closely to the final and initial states of system, we observe that in the initial state the two gases are orderly filled separately in the two containers. On the other hand, after mixing, helium and neon are distributed between both the containers. In other words, each gas occupies a large volume in the final state and, thereby, number of possible locations for the molecules of each gas is increased. This means that there is more disorder or randomness on mixing. Thus, the gases mix to achieve more randomness. Once mixed the gases cannot separate because to do so they will involve decrease in randomness due to lesser volume. Thus, it may be concluded that the process proceeds spontaneously in a direction in which the randomness or disorder of the system increases.

Some common examples of processes which occur in the direction of increased randomness are given below:

(i) Conversion of solids into liquids. The melting of solids into liquids (DH, +ve) results in the increase of randomness.

(ii) Evaporation of water. The evaporation of water also results in the increase of randomness because the molecules in the vapour state have more randomness than in the liquid state.

(iii) Dissolution of ammonium chloride in water. Solid ammonium chloride has less randomness while in solution ammonium chloride particles move freely as NH₄⁺ and Cl^- ions and hence, randomness increases.

Thus, in all the above endothermic processes, there is always increase in randomness. Since the above reactions are spontaneous, the tendency to achieve maximum randomness is another factor which determines the spontaneity of a process.

Driving force as the overall tendency for a process

It can be summarized that the spontaneous processes occur because of the two tendencies:

(i) Tendency of a system to acquire a state of minimum energy.

(ii) Tendency of a system to acquire a state of maximum randomness.

The overall tendency for a process to take place by itself is called the driving force. Regarding these two tendencies it is very important to keep in mind the following points:

a) The two tendencies act independent of each other.

b) The two tendencies may work in the same or in opposite directions in a process.

Thus, when there is no change in energy the second tendency is the governing factor For e.g., reaction will be spontaneous or non-spontaneous depending upon whether randomness factor favors or opposes. On the other hand, if there is no change in randomness, the energy factor is the controlling factor. However, this is not so simple in actual practice as both the tendencies operate simultaneously. In these cases, the significance of the magnitude of these tendencies becomes important Obviously, the tendency with the greater magnitude determines whether the process is feasible or not.