Question

A solution formed on mixing of two liquids is ideal if (a) \(\Delta V_{\operatorname{mix}}=0, \Delta H_{\operatorname{mix}} \neq 0\) (b) \(\Delta V_{\operatorname{mix}} \neq 0, \Delta H_{\operatorname{mix}}=0\) (c) \(\Delta V_{\operatorname{mix}}=0, \Delta H_{\operatorname{mix}}=0\) (d) \(\Delta V_{\operatorname{mix}}=0, \Delta H_{\operatorname{mix}} \neq 0\)

Short answer

The correct answer is (c) \(\Delta V_{\operatorname{mix}}=0, \Delta H_{\operatorname{mix}}=0\).

Step-by-step solution

Understanding the Variables

\(\Delta V_{\operatorname{mix}}\) represents the change in volume upon mixing while \(\Delta H_{\operatorname{mix}}\) represents the change in enthalpy upon mixing.

Identifying the Characteristics of an Ideal Solution

An ideal solution is marked by the fact that the change in volume and the change in enthalpy upon mixing both equal zero. This is because, in an ideal mixture, the attraction between the different types of molecules is the same as the attraction between the same types of molecules.

Selection of the Correct Option

Given the criteria for an ideal solution, the correct option is the one that indicates both the volume and enthalpy changes upon mixing are zero.

Key concepts

Change in Volume Upon Mixing

When two liquids are combined to form a solution, the total volume of the resulting mixture can sometimes differ from the sum of the individual volumes of the original liquids. This phenomenon is known as the change in volume upon mixing, denoted as
For an ideal solution, this change in volume is expected to be zero, symbolically represented as
This indicates that the volume of the mixture is exactly the same as the combined volumes of the pure components before mixing. In reality, the change in volume upon mixing is influenced by the molecular interactions occurring between different liquid molecules. Thus, for an ideal solution, it implies that the molecular interactions between unlike molecules are similar in magnitude to those between like molecules, resulting in no net change in volume.

Change in Enthalpy Upon Mixing

The change in enthalpy upon mixing, indicated by
refers to the heat absorbed or evolved when substances are combined to form a solution. For an ideal solution, this value is zero, which implies that the energy required to separate molecules of the pure substances is exactly balanced by the energy released when the different molecules mix and attract each other.
Thus, there is no overall energy change during the process of mixing. However, if there are differences in molecular interactions between solute and solvent or among solutes themselves, the enthalpy change will be non-zero. It is important to note that ideal behavior is an approximation and real solutions often have small but finite changes in enthalpy upon mixing.

Characteristics of Ideal Solutions

Ideal solutions exhibit properties that are defined by certain characteristics which are fundamentally theoretical in nature, providing a baseline for understanding solution behavior. Among these characteristics, the most important are:

• Zero change in volume upon mixing ( ) and zero change in enthalpy upon mixing (
• Consistent molecular attraction between different and identical molecules, leading to no net energy change during mixing.
• Behavior that follows Raoult's law, which states that the vapor pressure of each component in the solution is directly proportional to its mole fraction.

Ideal solutions are a simplified model often used as a starting point in thermodynamics to understand more complex solution behaviors.

Molecular Attraction in Mixtures

Understanding molecular attraction in mixtures is crucial for grasping how solutions form and behave. In the context of ideal solutions, the assumption is that molecular attractions between unlike molecules (solvent-solute interactions) are equal in strength to those between like molecules (solvent-solvent or solute-solute interactions). This means when different molecules come together to form a solution, they do not preferentially attract or repel each other.
Real-world mixtures, however, often exhibit positive or negative deviations from ideality. This happens when the interactions between unlike molecules are either stronger or weaker than those between their own kind. For instance, stronger solvent-solute interactions than solvent-solvent or solute-solute interactions may result in a negative change in volume upon mixing and a negative enthalpy change, indicating the release of heat upon mixing. Conversely, weaker interactions can result in positive values for these properties. Understanding these molecular attractions helps in predicting whether a given solution will behave ideally or deviate from ideal solution behavior.