Question

Use a solution of benzene in toluene to explain what is meant by an ideal solution.

Short answer

An ideal solution, like benzene in toluene, has no enthalpy or volume change upon mixing and follows Raoult's Law.

Step-by-step solution

Understanding an Ideal Solution

An ideal solution is one where the interactions between different molecules are the same as the interactions between like molecules. In simple terms, it means the forces between benzene-benzene molecules, toluene-toluene molecules, and benzene-toluene molecules are similar, resulting in no change in enthalpy when they are mixed.

Characteristics of Benzene-Toluene Solution

A benzene-toluene solution is commonly used as an example of an ideal solution. This is because benzene and toluene are both non-polar hydrocarbons with similar molecular sizes and structures, resulting in similar types and strengths of intermolecular forces (Van der Waals forces).

Applying Raoult's Law

In an ideal solution, Raoult's Law applies perfectly. It states that the partial vapor pressure of a component in a solution is equal to the product of the vapor pressure of the pure component and its mole fraction in the solution. Mathematically, for component A (benzene):\[ P_A = P_A^0 imes X_A \]where \( P_A \) is the partial pressure of benzene, \( P_A^0 \) is the vapor pressure of pure benzene, and \( X_A \) is the mole fraction of benzene in the solution.

Considering Enthalpy Change

In an ideal solution, there is no change in enthalpy upon mixing, meaning \( \Delta H_{mix} = 0 \). For the benzene-toluene solution, the energy required to break the benzene-benzene bonds and toluene-toluene bonds is equal to the energy released when benzene-toluene bonds form. Therefore, there is no net energy change.

Volume Change on Mixing

Ideal solutions show no volume change on mixing, i.e., \( \Delta V_{mix} = 0 \). For a benzene-toluene solution, this means that the total volume of the mixture is the sum of the volumes of benzene and toluene before mixing, indicating no contraction or expansion upon mixing.

Key concepts

Raoult's Law

Raoult's Law is a fundamental principle in the study of ideal solutions. It simplifies the understanding of how different components in a solution contribute to its overall behavior. In simple words, Raoult's Law focuses on vapor pressures. According to the law, the partial vapor pressure of a component in a solution is directly proportional to its mole fraction.

When we use Raoult's Law for a benzene-toluene solution, we can predict how much each component contributes to the total vapor pressure. The formula can be expressed mathematically:
\[ P_A = P_A^0 \times X_A \]where:

• \( P_A \) is the partial pressure of benzene in the solution
• \( P_A^0 \) is the vapor pressure of pure benzene
• \( X_A \) is the mole fraction of benzene within the solution

For the solution to behave ideally, each component must obey Raoult's Law perfectly, which becomes crucial in calculating the contribution of each component to the vapor phase above the solution.

Enthalpy Change

Enthalpy change is a key indicator in determining whether a solution behaves ideally. In an ideal solution, the enthalpy change upon mixing, denoted as \( \Delta H_{mix} \), is zero. This implies that the process of forming the solution neither absorbs nor releases energy.

Let's think of it this way: when benzene and toluene are mixed, the energy that is required to overcome the attractions between benzene-benzene and toluene-toluene molecules is perfectly matched by the energy released when benzene-toluene interactions are formed.
This balance of energy flows ensures that the enthalpy change remains zero. By understanding this, we can see why benzene and toluene form an ideal solution – their molecular interactions are just right to keep the mix energetically neutral.

Benzene-Toluene Solution

When you mix benzene and toluene, you are working with two very similar molecules. Both are hydrocarbons with non-polar characteristics, which means they are like twins in their behavior. This is why the benzene-toluene solution is often highlighted as a classic example of an ideal solution.

The similarity in their molecular sizes and structures leads to similar interactions, mainly through Van der Waals forces. These forces are relatively weak and non-specific, causing no appreciable energy change during the mixing. The lack of significant change makes it so you can't tell apart the mixed molecules based solely on energetic interactions, leading to what's called an ideal mixture.
Therefore, the benzene-toluene solution not only adheres to Raoult's Law generously but also exhibits zero enthalpy change and volume change upon mixing.

Volume Change on Mixing

In an ideal solution, the volume change upon mixing is zero, a concept denoted by \( \Delta V_{mix} = 0 \). But what does this mean in practical terms? Essentially, it means that when you mix two liquids like benzene and toluene, their total volume remains constant as if you simply added their individual volumes.

This no-change scenario indicates no expansion or contraction occurs when the two liquids are combined. Why does this happen? Because the molecular interactions in the mixture are identical to those in the pure liquids, causing no necessity for the molecules to either pack together more or spread apart.
This behavior is another distinctive trait of an ideal solution, reinforcing how benzene-toluene successfully maintains such predictability without altering its volumetric footprint upon mixing.