Animated Solution for Chemistry - Chemical Thermodynamics: During which of the following processes, does entropy decrease ? A. Freezing of water to ice at $0^{\circ }\text{C}$. B. Freezing of water to ice at $-10^{\circ }\text{C}$. C. ${\text{N}}_2(g)+3{\text{H}}_2(g)⟶2{\text{NH}}_3(g)$ D. Adsorption of $\text{CO}(g)$ and lead surface. E. Dissolution of $\text{NaCl}$ in water.

Decoding Entropy

Imagine a perfectly organized library where every book is in its exact place. Now, imagine a tornado sweeping through that library. The resulting chaos is a perfect analogy for entropy. In thermodynamics, entropy (denoted by $S$) is the fundamental measure of randomness, disorder, or the number of microstates available to a system.

The universe naturally tends toward higher entropy, but in specific localized processes, we can force a system to become more organized. When a system goes from a chaotic state to a highly ordered state, its randomness decreases, which mathematically means the change in entropy is negative ($\Delta S<0$). In this problem, we are tasked with acting as thermodynamic detectives to identify which of the five given processes result in a decrease in entropy.

Freezing Water

Let's begin by examining processes A and B. Both of these processes describe the freezing of liquid water into solid ice. The only difference is the temperature: one occurs at $0^{\circ }\text{C}$ and the other at $-10^{\circ }\text{C}$.

Does the temperature change the fundamental nature of the phase transition? Absolutely not. In liquid water, molecules possess enough kinetic energy to slide past one another, constantly breaking and reforming hydrogen bonds. It is a dynamic, relatively disordered state. However, when water freezes, these molecules are forced to lock into a rigid, hexagonal crystal lattice. Their translational freedom is entirely stripped away. Because the system transitions from a disordered liquid to a highly ordered solid, the randomness plummets. Therefore, for both processes A and B, the entropy strictly decreases ($\Delta S<0$).

Gas Reactions

Next, we turn our attention to process C, the famous Haber process for synthesizing ammonia:

When dealing with chemical reactions entirely in the gas phase, there is a brilliant shortcut to determine the sign of the entropy change: simply count the moles of gas. Gases are the most chaotic state of matter. If a reaction produces fewer gas molecules than it consumes, it is effectively destroying chaos.

Let's calculate the change in the number of gaseous moles ($\Delta n_g$):

Because the number of gas molecules decreases from four to two, the system has fewer particles bouncing around. The randomness is reduced, meaning the entropy decreases ($\Delta S<0$).

Adsorption

Process D involves the adsorption of carbon monoxide gas ($\text{CO}$) onto a solid lead surface.

Before adsorption, the $\text{CO}$ molecules are in the gas phase, enjoying three degrees of translational freedom. They can move anywhere within their container. However, during adsorption, these molecules collide with the lead surface and form weak bonds (physisorption) or strong bonds (chemisorption) with the metal atoms. They are essentially trapped on a two-dimensional plane. This massive loss of freedom and mobility translates directly to a massive loss of randomness. Thus, adsorption is always accompanied by a decrease in entropy ($\Delta S<0$).

Dissolution

Finally, let's look at process E: the dissolution of solid sodium chloride ($\text{NaCl}$) in water.

We start with a highly ordered, perfectly alternating 3D lattice of sodium and chloride ions. When dropped into water, the polar water molecules surround the ions and rip the lattice apart. The ions are now free to swim randomly throughout the entire volume of the liquid. We have taken a perfectly ordered solid and turned it into a chaotic soup of moving ions. Because the disorder of the system has drastically increased, the entropy change here is positive ($\Delta S>0$).

Let's summarize our thermodynamic investigation. We found that processes A, B, C, and D all involve a transition from a more chaotic state to a more ordered state, resulting in a decrease in entropy. Process E was the sole exception, resulting in an increase in entropy.

The question asks us to identify the processes where entropy decreases. Our findings perfectly align with the combination of A, B, C, and D. Therefore, the correct option is (a).