Problem 36 - Chemistry: The Central Science in SI Units, Global Edition

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?

Step-by-Step Solution

Answer

(a) The entropy of the system increases when the temperature increases, as particles gain kinetic energy and move more randomly. (b) The entropy of the system increases when the volume of a gas increases, as there are more possible positions for the gas particles, increasing disorder. (c) The entropy of the system increases when equal volumes of ethanol and water are mixed to form a solution, as the dispersion of molecules increases disorder due to the larger volume and more possible arrangements.

Step 1: (a) Effect of increasing temperature on entropy

As the temperature of a system increases, the particles within the system gain kinetic energy. This increase in kinetic energy causes the particles to move faster and more randomly. Since entropy is a measure of disorder, the entropy of the system increases when the temperature increases.

Step 2: (b) Effect of increasing volume of a gas on entropy

When the volume of a gas increases, the number of possible positions for the gas particles also increases. The increase in the number of possible positions means that there is a higher degree of disorder or randomness in the system. Thus, the entropy of the system increases when the volume of a gas increases.

Step 3: (c) Effect of mixing equal volumes of ethanol and water on entropy

When we mix equal volumes of ethanol and water to form a solution, both the molecules of ethanol and water are dispersed within each other. This dispersion of the ethanol and water molecules increases the disorder of the system. This is because there is now a larger volume for the particles to move, and more possible arrangements for the particles relative to each other. As a result, the entropy of the system increases when we mix equal volumes of ethanol and water to form a solution.

Key Concepts

Temperature and Entropy

Temperature and entropy are closely linked in the world of thermodynamics. When the temperature of a system rises, it affects the particles within the system.
Increased temperature gives these particles more kinetic energy, which means they move faster and more chaotically.

• As particles move more randomly, there is an increase in the overall disorder of the system.
• This disorder is measured quantitatively by entropy.
• Therefore, as the temperature increases, the entropy of the system also increases.

This is why we often associate higher temperatures with increased randomness and disorder in a system. Understanding this relationship helps explain many processes, from the melting of ice to the boiling of water, where entropy plays a crucial role.

Volume and Entropy

The connection between volume and entropy is fundamental in understanding gases and their behaviors. When the volume of a gas increases, it allows the particles within that gas more space to move around.

• More space means that particles have more positions they can occupy.
• This increase in positional possibilities corresponds to an increase in entropy.
• With more available space, the system becomes more random and disordered.

Thus, when a gas expands, the increase in volume leads to a corresponding increase in the entropy of the system. This concept is crucial in explaining behaviors like the natural expansion of gases and how they fill their containers.

Mixing and Entropy

Mixing and entropy involve combining different substances, leading to an increase in system disorder. Consider mixing equal volumes of ethanol and water. As they combine, the molecules of each substance become interspersed with the others.

• The molecules now have more potential positions and arrangements.
• This intermingling increases the disorder or randomness within the solution.
• The mixed solution overall exhibits a higher entropy.

Such processes are common in everyday life, from cooking mixtures to chemical reactions, demonstrating that when different substances mix, their combined entropy is usually higher than when they are separate.