Problem 38 - Chemistry: The Central Science

Question

Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a selution?

Step-by-Step Solution

Answer

(a) The entropy of the system increases when the temperature of the system increases. (b) The entropy of the system increases when the volume of a gas increases. (c) The entropy of the system increases when equal volumes of ethanol and water are mixed to form a solution.

Step 1: (Understanding Entropy)

Entropy is a measure of the disorder or randomness of a system. In general, if a process results in an increase in the disorder of the system, the entropy will increase. Conversely, if a process results in a decrease in the disorder of the system, the entropy will decrease.

Step 2: (Effect of temperature on entropy)

(a) When the temperature of the system increases, the particles in the system have more energy, which allows them to move more vigorously and randomly. This results in an increase in the disorder of the system. Therefore, as the temperature of the system increases, the entropy of the system also increases.

Step 3: (Effect of gas volume on entropy)

(b) When the volume of a gas increases, the particles in the gas have more space to move, which results in more possible locations for them. This increases the disorder of the system. Hence, as the volume of the gas increases, the entropy of the system also increases.

Step 4: (Effect of mixing ethanol and water)

(c) When equal volumes of ethanol and water are mixed, the interactions between the ethanol and water molecules result in a more disordered system. The mixing process increases the number of possible microstates and arrangements of the molecules, leading to an increase in the disorder. Therefore, when equal volumes of ethanol and water are mixed to form a solution, the entropy of the system increases. In conclusion, (a) The entropy of the system increases when the temperature of the system increases. (b) The entropy of the system increases when the volume of a gas increases. (c) The entropy of the system increases when equal volumes of ethanol and water are mixed to form a solution.

Key Concepts

Temperature Effect on Entropy

Entropy is all about disorder and randomness in a system. When you increase the temperature of a system, you're giving more energy to its particles. This extra energy means the particles move around faster and in a less orderly fashion.
So, the system becomes more disordered. Think of it like making popcorn. As the kernels get hotter, they start popping all over the place! Much like that popcorn popping, an increase in temperature causes the system's entropy to go up.
The increase in temperature doesn't just speed things up; it also opens up more ways for the particles to arrange themselves. More possible arrangements equate to more entropy. This is because the energy input allows the system to explore more possible microstates. In summary, higher temperature means a messier system, which means higher entropy.

Gas Volume and Entropy

When we talk about gases, volume and entropy are closely linked. Imagine releasing a balloon full of air into an empty room. As you let the air out, it fills the room, spreading out and finding new places to go.
This idea captures the essence of how an increase in volume affects gas entropy. As volume increases, gas particles spread over a larger area. It's like giving them a bigger playground!
With more room to roam, there's a boost in disorder. The more volume you have, the more possible ways the particles can be arranged. This increase in possible arrangements leads to an increase in the number of microstates—and hence, an increase in entropy.
So, expanding the volume of a gas is much like breaking down boundaries, letting particles explore and wander, ultimately increasing the system's entropy.

Mixing Substances and Entropy

Mixing substances like ethanol and water is like mixing colors to paint a picture. When you combine equal volumes of two substances, you disrupt the separate order each had before mingling. This mixing process makes the system more disordered.
When ethanol and water are mixed, their molecules start interacting. These new interactions lead to many possible arrangements—or microstates—in the solution. Each of these possible microstates contributes to an increase in randomness or disorder.
While particles were limited to their type of substance before, mixing gives them a broader range of partners to interact with. So, mixing becomes a dance with a lot more potential moves, resulting in elevated entropy.
In essence, any interaction that broadens the spectrum of possible arrangements will increase entropy. This holds true for most substance mixtures, making mixing a sure way to boost disorder in a system.