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 solution?

Short answer

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

Step-by-step solution

(Define entropy)

Entropy (S) is a measure of the randomness or disorder of a system. The larger the entropy of a system, the more disordered it is.

(Evaluate entropy)

According to the definition, when the temperature of a material increases, the molecules in the material move more chaotically and randomly, leading to an increase in entropy. So, the entropy of the system will increase when the temperature increases. #b) Effect of volume increase on the entropy of a gas#

(Define entropy for a gas)

Entropy of a gas is also related to the randomness of the positions and velocities of the gas particles.

(Evaluate entropy of the gas)

When the volume of the gas increases, the gas particles have more places to move around, thereby increasing the randomness of their positions and velocities. Consequently, the entropy of the gas increases. So, the entropy of the system will increase when the volume of the gas increases. #c) Entropy change during the mixing of ethanol and water#

(Define entropy for mixing of substances)

The change in entropy when two substances are mixed is related to the randomness of the particle arrangement at a microscopic level in the mixture.

(Evaluate entropy of the mixture)

When equal volumes of ethanol and water are mixed, the molecules of the two substances become more randomly distributed, increasing the entropy of the system. So, the entropy of the system will increase when equal volumes of ethanol and water are mixed to form a solution.

Key concepts

Entropy change

Entropy is a key concept in thermodynamics that reflects the level of disorder or randomness in a system. When we talk about entropy change, we're investigating how this disorder is affected by various modifications within the system. Usually, when the entropy of a system increases, the arrangement of molecules becomes more chaotic. This is because, with more disorder, there are various configurations or possible states the system can be in. Conversely, a decrease in entropy is associated with a more orderly and less complex state. Analyzing how different factors such as temperature, pressure, volume, and mixing of substances affect entropy helps us understand the spontaneous nature of physical processes. For instance, when ice melts into water at a constant temperature, the entropy increases because the structure becomes more disordered.

Temperature effect on entropy

Temperature plays a significant role in the entropy of a system. When the temperature of any system is increased, the kinetic energy of its molecules also increases. This increase leads to more chaotic and rapid molecular motion. Imagine particles in a pot of boiling water, dancing energetically compared to their calmer state in a glass of iced water.
As temperature rises:

• Molecules move faster.
• The overall disorder or randomness increases.
• Entropy of the system becomes higher.

In essence, higher temperatures create more possible configurations for the molecules, hence increasing entropy. A classic example of temperature affecting entropy is when a solid turns into a liquid or gas. In such cases, the molecular arrangement becomes less rigid, leading to higher entropy.

Volume effect on gas entropy

For gases, entropy is closely linked to the volume available to the gas particles. When the volume of a gas expands, the particles have more space to spread out and move around. This increase in available space causes the gas particles to occupy positions more randomly, thereby increasing the entropy.
Key points about volume impact:

• More volume provides more room for particle movement.
• Random distribution of particles leads to increased entropy.
• The higher the entropy, the more disordered the gas system becomes.

For example, if a gas is contained in a balloon and the balloon stretches, the gas particles disperse within the newly available space, raising the average entropy through enhanced randomness.

Mixing and entropy

Mixing substances often leads to an increase in entropy due to the enhanced randomness in the arrangement of particles. For instance, when ethanol and water are mixed, the individual molecules intersperse, creating a mixture with the molecules spread more randomly than when they were separate.
Key aspects of mixing:

• Molecules disperse among each other upon mixing.
• Increased randomness in molecular arrangements heightens entropy.
• Mixed systems tend to be more stable due to increased disorder, which is thermodynamically favorable.

The heightened disorder from mixing means the system achieves a more probable and thus more stable state, thereby leading to an increase in the overall entropy of the system. This inherent increase in disorder upon mixing is one reason why such processes are often spontaneous and irreversible.