Problem 13 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate whether each statement is true or false: (a) A solute will dissolve in a solvent if solute-solute interactions are stronger than solute-solvent interactions. (b) In making a solution, the enthalpy of mixing is always a positive number. (c) An increase in entropy favors mixing.

Step-by-Step Solution

Answer

Statement (a) is false because a solute will dissolve in a solvent if solute-solvent interactions are stronger than solute-solute interactions. Statement (b) is false because the enthalpy of mixing can be either positive or negative, not always positive. Statement (c) is true since an increase in entropy, which represents an increase in disorder, favors mixing.

Step 1: Statement (a) analysis

To determine if statement (a) is true or false, we need to understand when a solute will dissolve in a solvent. A solute will dissolve in a solvent if solute-solvent interactions are stronger than solute-solute interactions. In this case, the statement says a solute will dissolve if solute-solute interactions are stronger, which is not correct. Therefore, statement (a) is false.

Step 2: Statement (b) analysis

To determine if statement (b) is true or false, we need to understand the concept of enthalpy of mixing. The enthalpy of mixing refers to the energy change when two substances mix together, which can be either positive (endothermic) or negative (exothermic). The statement claims that the enthalpy of mixing is always a positive number, which is not true. It can be either positive or negative depending on the substances involved. Hence, statement (b) is false.

Step 3: Statement (c) analysis

To determine if statement (c) is true or false, we need to understand the concept of entropy. Entropy is a measure of the randomness or disorder of a system. An increase in entropy means that the system becomes more disordered or random, which is generally favored in reactions. In the context of mixing, an increase in entropy implies that the molecules become more dispersed, which favors mixing. So, statement (c) is true.

Key Concepts

Solubility

Solubility is a key concept in solution chemistry that explains how well a solute can dissolve in a solvent. Imagine you have sugar and water, where sugar is the solute and water is the solvent.
The principle behind solubility is that substances with similar molecular interactions tend to dissolve in each other better. In simple terms, "like dissolves like."

• If the solute-solvent interactions are stronger than the solute-solute interactions, the solute will dissolve. This means that the molecules have a stronger attraction to the solvent than to each other.
• Conversely, if solute-solute interactions are stronger, solubility is less likely because the molecules prefer to stick together rather than mix with the solvent.

Having this understanding will help you identify which substances are likely to dissolve in others.

Enthalpy of Mixing

Enthalpy of mixing is the energy change that occurs when two substances mix. This process can be either endothermic or exothermic.
Let's break it down:

• Endothermic mixing: In this scenario, mixing absorbs energy from the surrounding environment, resulting in a positive enthalpy change. This usually occurs when solute-solvent interactions are weaker compared to solute-solute and solvent-solvent interactions.
• Exothermic mixing: Here, mixing releases energy into the surroundings, leading to a negative enthalpy change. It happens when solute-solvent interactions are strong, as this releases energy and stabilizes the system.

It’s important to note that the enthalpy of mixing can be either positive or negative, disproving the mistaken idea that it is always positive.

Entropy

Entropy is a measure of disorder or randomness in a system. It is a natural tendency for systems to move towards a state of higher entropy, meaning more disorder.
So, what does this mean for mixing?

• Increase in entropy: When two substances mix, the overall entropy of the system typically increases because the molecules become more spread out and disordered.
  This increased randomness is favorable and drives the mixing process forward.
• The concept aligns with the second law of thermodynamics, which states that the entropy of an isolated system will increase over time.

An increase in entropy is a significant factor that favors the mixing of two substances.