Question

Which of the following statement is true about ideal solutions? (a) the volume of mixing is zero (b) the enthalpy of mixing is zero (c) both \(\mathrm{A}\) and \(\mathrm{B}\) (d) none of these

Short answer

(c) both A and B

Step-by-step solution

Understand Ideal Solutions

An ideal solution is a solution in which the intermolecular interactions between different types of molecules are the same as between the same types. This means that ideal solutions follow Raoult's Law and do not have any energy change when mixed.

Examine the Volume of Mixing

For an ideal solution, when the components are mixed, there is no volume change. Therefore, the volume of mixing is zero. This means statement (a) is true.

Examine the Enthalpy of Mixing

Since ideal solutions have uniform intermolecular interactions, the enthalpy change for mixing is also zero, as there is no absorption or release of heat. Thus, statement (b) is true as well.

Determine Which Statements are True

Since both the volume of mixing and the enthalpy of mixing are zero in ideal solutions, both statements (a) and (b) are correct. This means option (c), which states both (a) and (b) are true, is the correct answer.

Key concepts

Volume of Mixing

When we talk about the volume of mixing in the context of ideal solutions, it refers to a simple concept: the total volume of the solution after mixing is the same as the sum of the volumes of the individual components before mixing. This implies no volume change or expansion occurs when different substances are combined.

For ideal solutions, the interactions between molecules of different types are similar to those that occur between molecules of the same type. This results in no net macroscopic effects as far as volume is concerned. Therefore, the volume of mixing is zero.

Let's break it down: * No volume contraction means no noticeable shrinkage in volume. * No volume expansion means no noticeable increase in size. * This observation is crucial because it reinforces the idea that the solution behaves completely predictably and maintains its physical space as a combination of its individual parts.

In summary, ideal solutions demonstrate a perfect additive property regarding volume, which is why it remains unchanged.

Enthalpy of Mixing

The enthalpy of mixing focuses on the thermal energy exchange between molecules when two substances are combined to form a solution. In simpler terms, when you mix components to form an ideal solution, no heat is absorbed or released.

To put this into perspective, consider that in an ideal solution: * Molecular interactions are uniform and consistent. * There's no preferability or aversion among different molecules when forming new interactions.

This means the system's total energy remains unchanged. If you're wondering how this works, think of it like combining two puzzle pieces that fit perfectly—in this perfect match, no energy is needed for adjustments.

This is why the enthalpy change for an ideal solution is zero. There are no additional forces needed to overcome, and no heat exchange occurs, indicating a completely balanced energetic environment.

Raoult's Law

Raoult's Law is a foundational principle in understanding ideal solutions. It states that the partial vapor pressure of a component in a solution is directly proportional to the mole fraction of that component in the solution.

Mathematically, it can be expressed as:\[ P_i = X_i \times P_i^0 \]where:* \(P_i\) is the partial vapor pressure of the component.* \(X_i\) is the mole fraction of the component in the solution.* \(P_i^0\) is the vapor pressure of the pure component.In an ideal solution:* Each component's partial pressure contributes predictably to the total vapor pressure.* The total vapor pressure is the sum of the partial pressures of individual components.

This concept highlights that, due to identical interactions as in their pure states, components in an ideal solution don't deviate from expected behavior. Everything is highly predictable and conforms well to theoretical expectations, making Raoult's Law a robust tool for analyzing such systems. Understanding this helps in predicting how solutions will behave under various conditions, essential for anyone studying chemistry.