Entropy and Spontaneity of The Reaction

Spontaneous reactions are self driven reactions; they take place immediately without any assistance from external source. They have the potential to proceed without any help from outside. What is their driving force? What makes them to proceed by themselves? If we take examples from our day to day experiences, we will be able to understand the concept of spontaneity. When we toss a coin in the air it drops on the ground, here the dropping of coin is spontaneous reaction. Similarly, falling of water in a waterfall is an example of spontaneous reaction. Did you notice that these reactions are spontaneous in one direction only? Coin drops spontaneously but doesn’t jump up spontaneously; water falls from hills but doesn’t climb up spontaneously. In this post we will try to decipher the mystery of spontaneous reactions.

Spontaneity in chemical reactions is also unidirectional. Second Law of Thermodynamics explains it quite well. It also gives us an idea about the direction of energy or heat flow. As per this law heat flows from hotter to colder bodies or you can say that energy flows from higher level to lower level.

It means that if energy decreases on occurring of a reaction, then it may be a spontaneous reaction. You might think that if a reaction doesn’t require heat to start and is exothermic, it must be spontaneous. Let’s check this assumption:

You must have observed rust on iron rods, pipes or nails. Rust is an oxide of iron which is made by the reaction of Oxygen with Iron.

4Fe (s) + 3O₂ (g) ⟶ 2Fe₂O₃(s)    ..... Δ_rH^ө = -1648 kJ mol^-1

It is an exothermic reaction and spontaneous too. It seems that our assumption is going in right direction. Let’s take another example of exothermic reaction, formation of water.

H₂ (g) + ½ O₂(g) ⟶ H₂O (l)      ..... Δ_rH^ө= -285.8 kJ mol^-1

Even though formation of water is an exothermic reaction, if you mix Hydrogen and Oxygen gas at room temperature you won’t see any identifiable change even after years. Here we are proved wrong. It is not necessary that if a reaction is exothermic then it must be spontaneous too.

Another example of spontaneous reaction from our daily life is dissolution of table salt in water. Let’s see its chemical reaction:

NaCl (s) ⟶ Na⁺ (aq) +  Cl^- (aq) ..... Δ_rH^ө= +4 kJ mol^-1

It’s an endothermic reaction. But it occurs spontaneously. So how can we predict the spontaneity of any reaction if it doesn’t depend on heat of the reaction?

For this, we need another thermodynamic property ‘ENTROPY’ which is denoted by “S”. Entropy is the degree of randomness or you can say it’s a measure of freedom of the molecules. Let’s take the example of different phases of water to understand the concept of entropy.

In ice - molecules are held together by H-bonding and are bound to stay in one place. They have no freedom at all that means they have least entropy.

In water - molecules stay together because of H-bonding but they can move too. They have more freedom than they have in ice. That means entropy of water is more than ice.

In steam - molecules are too far apart to form H-bonds and they can move freely in any direction. So you can see that in vapour phase molecules are most free and therefore out of all phases of water, steam has the highest entropy.

What is Entropy?

Let’s take previous examples of spontaneous reactions and study them from the viewpoint of entropy.

For the formation of water, two gases H₂ and O₂ need to combine to form liquid H₂O. That means entropy of the system decreases in this reaction. That is why it is not spontaneous even if it is an exothermic reaction.

In the case of dissolution of salt, solid NaCl breaks into aqueous ions Na⁺(aq) and  Cl^-(aq) which are now free to move around. That means entropy of the system increases which favours spontaneity.

In both of the examples above, we have seen that there is a relation between the motion of molecules and its entropy. More freedom of motion means more entropy. Entropy doesn’t depend on path which means it’s a state function just like enthalpy and internal energy. Motion of molecules is related to the energy of molecules, and energy of molecules has direct relation to the heat. We can manipulate the energy by controlling the heat supply. So there must be some relation between entropy and heat.

Entropy (S) ∝ Heat (q)

How much motion can be generated by a given amount of heat depends on the temperature of the system. Let’s take an everyday example. A hot cup of coffee on a cold day can energize you but a similar cup of coffee in a hot day can irritate you. Same amount of heat supplied at lower temperate can create more difference in entropy. Because at lower temperate molecules are at rest and a little heat can create chaos and generate more randomness. While at higher temperature molecules are already in chaotic motion and heat can give more energy but doesn’t create more randomness because they are already in that state.  So we can conclude that change in entropy is inversely proportional to the temperature.

ΔS = q_rev/ T

When a system is in equilibrium, it’s entropy is maximum and change in entropy ΔS = 0.

For any spontaneous reaction total entropy change of the system and surrounding must be more than zero.

ΔS_total = ΔS_system + ΔS_surrounding  > 0

Now check the spontaneity of the formation of rust.

4Fe (s) + 3O₂ (g) ⟶ 2Fe₂O₃(s)    ..... Δ_rH^ө = -1648 kJ mol^-1

We have observed it time and again that rust formation is a spontaneous reaction even though entropy change given for this reaction is  -549.4 JK^-1mol^-1at 298K.

The discussion of spontaneity we had so far contradicts this observation. We discussed that for spontaneity total entropy must be greater than zero. How can this reaction be spontaneous when the entropy of the system is negative? Well, we did forget something, didn't we? Let’s work out the entropy change of the surrounding. This reaction is exothermic which means 1648 kJ mol^-1 amount of heat is absorbed by the surrounding.

ΔS_surr = Δ_rH^ө/ T

ΔS_surr = 1648 kJ mol^-1/ 298K

ΔS_surr = 5.53 kJ mol^-1K^-1= 5530 Jmol^-1K^-1

Now calculate the change in total entropy

ΔS_total = ΔS_system + ΔS_surrounding

ΔS_total = -549.4 JK^-1mol^-1+ 5530 Jmol^-1K^-1

ΔS_total = 4980.6 JK^-1mol^-1

The total entropy increases by the rusting which favours spontaneity. This is in accordance with the Second Law of Thermodynamics which tells us that on the transformation of energy from one form to another form entropy always increases and energy always decreases.

You have seen that enthalpy alone isn’t the deciding factor for a process to be spontaneous; you have to consider the entropy as well. As we saw in the example of rusting, it is quite confusing to decide the spontaneity of the reaction by just seeing the enthalpy and entropy of the system. To ease this problem, one more thermodynamic term has been introduced which is called the “Gibbs free energy”. In the next post we will discuss Gibbs free energy and will try to find out how we can predict spontaneity of any reaction by using it.

This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.