5.6.2. Entropy and Spontaneity

The first law of thermodynamics tells us about the relationship between the heat absorbed and the work performed on or by a system. It puts no restrictions on the direction of heat flow. However, the flow of heat is unidirectional from higher temperature to lower temperature. In fact, all naturally occurring processes whether chemical or physical will tend to proceed spontaneously in one direction only.

The first law of thermodynamics indicates that energy is conserved in a system – it can neither be created nor destroyed. However, this law does not tell us if a process will occur naturally (spontaneously). Spontaneous processes are those that occur naturally without needing to be driven by an outside force. For instance, when a solid melts or a gas expands into a larger volume, these are spontaneous processes that occur without external influence.

Consider the way a ball rolls down a hill. The ball will move downwards due to gravity without any input needed from you, showing that some processes happen naturally without external help, analogous to spontaneous reactions in nature.

But heat will not flow from colder body to warmer body on its own, the gas in a container will not spontaneously contract into one corner or carbon dioxide will not form carbon and dioxygen spontaneously. These and many other spontaneously occurring changes show unidirectional change. We may ask ‘what is the driving force of spontaneously occurring changes? What determines the direction of a spontaneous change? In this section, we shall establish some criteria for these processes whether these will take place or not.

Spontaneous processes move towards states of lower energy or higher disorder (entropy). However, it's important to note that not all spontaneous processes lead to a decrease in energy. For example, some reactions can absorb energy (endothermic) and still be spontaneous if they increase the entropy of the system significantly. Understanding what drives these changes involves examining the underlying balance between entropy and enthalpy.

Imagine stirring sugar into a cup of coffee. The sugar dissolves (spontaneous) without needing heat from the surroundings, and the process ends when the sugar is fully integrated, leading to increased disorder in the system, which corresponds to increased entropy.

Let us first understand what do we mean by spontaneous reaction or change? You may think by your common observation that a spontaneous reaction is one which occurs immediately when contact is made between the reactants. Take the case of combination of hydrogen and oxygen. These gases may be mixed at room temperature and left for many years without observing any perceptible change. Although the reaction is taking place between them, it is at an extremely slow rate. It is still called spontaneous reaction.

A spontaneous reaction is defined by its ability to proceed towards product formation without external influence; however, this doesn't mean it happens quickly. An example is the reaction between hydrogen and oxygen to form water, which may take a long time to initiate at room temperature without a spark. Thus, spontaneity considers whether a reaction can occur naturally, not how quickly it happens.

Think of rust forming on iron left in a damp environment. The process is slow, but it demonstrates a spontaneous reaction resulting from the interaction of elements and environmental conditions, illustrating that time and spontaneity don't always align.

We may summarize it as follows: A spontaneous process is an irreversible process and may only be reversed by some external agency. If we examine the phenomenon like flow of water down hill or fall of a stone on to the ground, we find that there is a net decrease in potential energy in the direction of change.

A spontaneous process tends to lead towards an increase in entropy (chaos or disorder), while energy tends to decrease. Entropy is a measure of disorder, and systems naturally evolve to states with higher entropy and lower energy. This brings us to understand the essence of what makes processes happen naturally – the pursuit of chaos.

Imagine a neatly arranged stack of colored blocks. If you let them tumble over, they scatter everywhere, representing an increase in disorder (entropy). This is easy and happens naturally. To put them back in order (decrease the entropy), you need to force them into place, requiring energy or work.

Thus, the postulate that driving force for a chemical reaction may be due to decrease in energy sounds ‘reasonable’ as the basis of evidence so far! Now let us examine the following reactions: these reactions though endothermic, are spontaneous.

While a decrease in energy (enthalpy) often drives reactions, it's important to realize that endothermic reactions can also be spontaneous if they lead to an increase in entropy. Therefore, both factors – energy change and disorder – explain spontaneity. This intertwining creates a clear concept: spontaneity arises from the balance between energy and entropy.

An example is ice melting on a hot day. The melting requires heat (endothermic), but the chaos created as molecules break away into the liquid state represents entropy increase, making the process spontaneous under those conditions.

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