Question

State whether the entropy of the system increases or decreases in each of the following processes: (a) Pure gases are mixed to prepare an anesthetic. (b) Electronic-grade silicon is prepared from sand. (c) Dry ice (solid \(\mathrm{CO}_{2}\) ) sublimes.

Short answer

(a) Increases, (b) Decreases, (c) Increases.

Step-by-step solution

Process Analysis (a)

Consider the process where pure gases are mixed to prepare an anesthetic. Mixing pure substances typically increases the disorder or randomness in the system because the individual gas particles are more dispersed.

Determine Entropy Change (a)

Mixing pure gases increases the entropy of the system because the combined gas molecules have more possible positions and arrangements than the individual pure gases.

Process Analysis (b)

Consider the process of preparing electronic-grade silicon from sand. This involves purifying silicon, which is a process that reduces the disorder.

Determine Entropy Change (b)

Preparing electronic-grade silicon from sand decreases the entropy of the system because the silicon becomes more ordered than the original, impure sand.

Process Analysis (c)

Consider the process where dry ice (solid \(\text{CO}_2\)) sublimes. Sublimation involves the transition of a solid directly into a gas, bypassing the liquid phase.

Determine Entropy Change (c)

The sublimation of dry ice increases the entropy of the system because a gas has more possible molecular arrangements and greater randomness than a solid.

Key concepts

Entropy Increase

Entropy is a measure of disorder or randomness in a system. It helps us understand why certain processes occur naturally. When we mix pure gases to prepare an anesthetic, we are essentially increasing the randomness of the system. The individual gas molecules have more freedom to move and can occupy more possible positions. This increased freedom leads to a higher entropy.
Here's why. When pure gases mix, they go from being in an organized, separate state to a disorganized, mixed state. More disorder means more entropy. Therefore, the entropy of the system increases when gases mix.
In simpler terms, think about a deck of cards. If the deck is ordered, it has low entropy. Once shuffled, the deck's disorder increases, just like with mixed gases.

System Disorder

System disorder is directly related to entropy. When we talk about disorder, we mean the number of ways a system can be arranged. More arrangements equal higher disorder and thus higher entropy.
Consider the process of purifying electronic-grade silicon from sand. Sand has lots of impurities, meaning it's highly disordered. To make electronic-grade silicon, we must remove these impurities. This process reduces the system's disorder, leading to lower entropy.
When the silicon is purified, its molecules are arranged in a more ordered manner than in the original mixture. This increased order means there's less randomness, hence a decrease in entropy. Simply put, purifying silicon makes it highly organized, reducing its entropy.
Imagine tidying up a messy room; as you organize it, disorder decreases.

Sublimation Process

Sublimation is a fascinating process where a solid changes directly to a gas, skipping the liquid phase. A common example is dry ice, solid \(\text{CO}_2\). When dry ice sublimes, it goes from a highly ordered solid state directly to a much more disordered gaseous state.
This transition significantly increases entropy because gas molecules have much more freedom to move around than solid molecules. Solid \(\text{CO}_2\) has fixed positions in a crystalline structure, whereas gaseous \(\text{CO}_2\) molecules are free to travel around in space, leading to increased disorder.
So, when dry ice turns into gas, the system's entropy increases because the gas phase is much more random and disorganized compared to the solid phase. It's like if ice cubes in a tray turn directly into steam; there's way more room for the steam molecules to move around, increasing entropy.
In summary, sublimation always increases the system's entropy because it leads from a more ordered state (solid) to a less ordered state (gas).