Problem 32 - A Complete Resource Book in Chemistry for JEE Main

Question

Which pair of the following will not form an ideal solution? (a) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}\) (b) \(\mathrm{H}_{2} \mathrm{O}+\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}\) (c) \(\mathrm{CCl}_{4}+\mathrm{SiCl}_{4}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{14}+\mathrm{C}_{7} \mathrm{H}_{16}\)

Step-by-Step Solution

Answer

Pair (b) will not form an ideal solution.

Step 1: Understand Ideal Solutions

Ideal solutions are mixtures in which the enthalpy of mixing is zero, meaning interactions between mixed particles are similar, and the components follow Raoult’s Law throughout the range of concentrations. Usually, molecules in ideal solutions have similar size and similar intermolecular forces.

Step 2: Analyze Option (a)

Ethyl bromide (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\)) and ethyl iodide (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}\)) have comparable molecular sizes and similar types of interactions, such as van der Waals forces. Hence, they are more likely to form an ideal solution.

Step 3: Analyze Option (b)

Water (\(\mathrm{H}_{2} \mathrm{O}\)), a polar molecule capable of hydrogen bonding, mixed with butanol (\(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}\)), also forms hydrogen bonds. However, the significant difference in polarity can lead to non-ideal behavior.

Step 4: Analyze Option (c)

Carbon tetrachloride (\(\mathrm{CCl}_{4}\)) and silicon tetrachloride (\(\mathrm{SiCl}_{4}\)) have similar molecular structures and types of interactions (dispersion forces), so they are likely to form an ideal solution.

Step 5: Analyze Option (d)

Hexane (\(\mathrm{C}_{6} \mathrm{H}_{14}\)) and heptane (\(\mathrm{C}_{7} \mathrm{H}_{16}\)) are both nonpolar hydrocarbons and have similar intermolecular interactions, thus likely to form an ideal solution.

Step 6: Conclusion

The pair of water (\(\mathrm{H}_{2} \mathrm{O}\)) and butanol (\(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}\)) is more prone to behave as a non-ideal solution due to their differing polarity and potential for hydrogen bonding. Thus, they are the most likely pair not to form an ideal solution.

Key Concepts

Enthalpy of Mixing

Enthalpy of mixing is the thermal energy change that occurs when two substances are combined to form a solution. For ideal solutions, the enthalpy of mixing is zero. This means that when you mix the components, no heat is either absorbed or released. In other words, the attractive forces between different molecules in the mixture are the same as those in the pure components.
When mixing substances that form an ideal solution:

• The molecular sizes of the components are similar.
• The intermolecular forces are closely matched.

Examples of ideal solutions include mixtures like carbon tetrachloride with silicon tetrachloride, where both substances have comparable dispersion forces. Lack of change in enthalpy reflects that the energy penalty or gain for disruption of interactions is negligible. This characteristic allows some solutions to behave ideally according to chemical laws.

Raoult’s Law

Raoult’s Law is a fundamental principle for studying ideal solutions. It describes how the vapor pressure of a solvent is affected by the presence of a solute. Simply put, when a solute is dissolved in a solvent, the solvent's vapor pressure decreases proportionally to the mole fraction of the solvent in the solution.
This law states that the partial vapor pressure of each component in a liquid mixture is directly proportional to its mole fraction. Mathematically, it is given by:\[P_i = X_i \cdot P_i^0\]where:

• \(P_i\) is the partial vapor pressure of component \(i\).
• \(X_i\) is the mole fraction of component \(i\).
• \(P_i^0\) is the vapor pressure of the pure component \(i\).

Raoult’s Law applies best to ideal solutions where the solute-solvent interaction is similar to the solvent-solvent interaction. This law is supportive analysis for choices like hexane and heptane, which follow it closely due to their similar intermolecular interactions and sizes.

Intermolecular Forces

Understanding intermolecular forces is key to analyzing which solutions will behave ideally. These forces are interactions that hold molecules together. The main types include:

• Dipole-dipole interactions: Occur in polar molecules with permanent dipoles.
• Hydrogen bonds: High-strength dipole interactions seen in molecules like water.
• Dispersion forces: Found in all molecules, particularly strong in nonpolar molecules.

For ideal solutions, the intermolecular forces between mixed molecules are similar, which is why their enthalpy of mixing is zero. For example, in mixtures like carbon tetrachloride and silicon tetrachloride, the predominant interactions are dispersion forces, leading to very similar energy arrangements in mixing and in the pure states. Unlike these, a combination like water and butanol involves differences in hydrogen bonding potential and polarity, leading to non-ideal behavior due to variations in intermolecular forces.