It’s all Gibberish

The universe is lazy. During any change (a chemical reaction, for instance), the system will always favor a path which drags it down to a low potential-energy configuration. If you’re into the sciences, it’s likely that you’ve observed this bias in topics ranging from torque to binding energy of nuclei. So, if being lazy is deep-seated in our universe (and its beings), is there a way to possibly measure it?

Gibbs Energy.

 

I like to visualize Gibbs Free Energy as a measure of laziness of any system (say, our universe). Qualitatively, Gibbs Energy tells us whether a reaction is thermodynamically feasible (or the amount of free energy available post-reaction). Quantitatively, it is given by,

Change in Gibbs Energy, ∆G = ∆H – T∆S

Here, ∆H indicates the change in enthalpy (or change in energy) for that reaction. T is the temperature in Kelvin. ∆S quantifies entropy (or randomness of a system). A negative value of ∆G indicates a spontaneous or feasible reaction (or a reaction which is favored by the lazy system).

diagram2
Gibbs Energy dropping with temperature Source: University of Cambridge

Um. How does ∆G drop to negative values?

To answer this, we need to understand how ∆H and ∆S vary with reactions. Consider the reaction,

A + B → A-B

Here, a bond ‘-‘ is formed between A and B, let’s assume they approach lower potential energy. Since energy is conserved, the remainder changes to kinetic energy which appears as heat. Since the system has lost heat to its surroundings, ∆H is negative. Also, after the reaction, the disorder (or randomness) has decreased due to a relative decrease in the number of entities after the reaction. This indicates that ∆S is negative. Playing around with these values in reactions, along with temperature, decides the sign of ∆G.

CNX_Chem_07_02_Morse1
Notice how the potential energy drops when a bond is formed Source: LumenLearning

But. Why should a negative value indicate spontaneity? 

Again, consider the reaction,

A + B → A-B

The reactants drop to lower potential energies after the bond formation. Since the universe is lazy, it favors a low energy configuration which is more stable. A helpful analogy would be that of two magnets which when kept at a distance pull on each other spontaneously to overcome the magnetic potential energy and attain a stable configuration. Similarly, since our original reaction achieves greater stability on completion, it is, understandably, spontaneous.

The same idea can be discussed mathematically in terms of Gibbs Energy as follows.

Here ∆S is negative (due to a decrease in disorder) and it’s quite likely that ∆H is highly negative (because heat evolves). In,

∆G = ∆H – T∆S

If the temperature is moderate to low, using basic arithmetic, you might realize ∆G is negative. Hence, theoretically, too, the reaction is spontaneous.

Similarly, if, for any other process, ∆S is highly positive (disorder increases), the reaction may become spontaneous because ∆G might become negative (according to the expression). But why does the universe favor randomness and disorder? It lies in the fact that mobile particles favor bobbing around because in that way they can pour energy into the system (by releasing heat of collision, for instance) and bring about a decrease in their internal potential energy.

Thus, this is the reason why lower potential energy (-∆H) and higher disorder (+∆S) is favored by our universe and how it tries to become more stable. So. Yeah. The next time you feel lazy, you have our entire universe to blame!

-Shamoil Khomosi

 

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