Problem 132 - A Complete Resource Book in Chemistry for JEE Main

Question

The van't Hoff factor (i), is a measure of association or dissociation. The van't Hoff factor for \(0.1 \mathrm{M}\) aqueous sodium chloride is \(1.87 .\) In magnesium sulphate the ionic interactions (a) Are weaker than that observed in sodium chloride. (b) Are same as that observed in sodium chloride (c) Are stronger than that observed in sodium chloride. (d) Are not responsible for the (i) value.

Step-by-Step Solution

Answer

(c) Are stronger than that observed in sodium chloride.

Step 1: Understand the van't Hoff factor

The van't Hoff factor, denoted by \(i\), represents the number of particles a substance dissociates into in solution. For non-electrolytes, \(i = 1\), while for electrolytes, \(i\) can be greater than 1 due to ion dissociation.

Step 2: Analyze sodium chloride dissociation

Sodium chloride (NaCl) dissociates completely in water into two ions: Na\(^+\) and Cl\(^-\). Ideally, \(i\) for NaCl should be 2, but it can be less due to ion pairing or incomplete dissociation. In this exercise, \(i = 1.87\).

Step 3: Comparing magnesium sulfate

Magnesium sulfate (MgSO\(_4\)) dissociates into Mg\(^{2+}\) and SO\(_4^{2-}\). The van't Hoff factor for MgSO\(_4\) is typically less than 2 due to stronger ionic interactions causing incomplete ion separation.

Step 4: Conclusion from comparison

The van't Hoff factor for MgSO\(_4\) being typically less than NaCl's \(i = 1.87\) suggests MgSO\(_4\) ions associate more strongly, reducing the effective number of particles in solution.

Key Concepts

Ionic Interactions

Ionic interactions play a crucial role in determining the behavior of substances when dissolved in solution. These forces occur between ions of opposite charges. For example, in sodium chloride (NaCl), the positive sodium ions (Na\(^+\)) attract the negative chloride ions (Cl\(^-\)), forming a strong ionic bond.

However, when dissolved in water, these ions separate due to the surrounding water molecules. The van't Hoff factor (\(i\)) helps in understanding these interactions by showing how many particles a solute will form after its dissociation. A perfect dissociation means each formula unit produces as many ions as present in the formula.

• In NaCl, the expected theoretical \(i\) is 2, meaning two ions are formed, but real interactions slightly lower this figure due to phenomena like ion pairing.
• Conversely, compounds like magnesium sulfate (\(\mathrm{MgSO}_4\)) might have stronger ionic interactions, meaning they dissociate less, explaining why the \(i\) for \(\mathrm{MgSO}_4\) might be less than 2.

Understanding these interactions allows for better predictions of a solute's behavior, helping anticipate its effect on properties such as osmotic pressure and boiling point elevation in solutions.

Dissociation in Solution

Dissociation refers to the separation of a compound into its individual ions in a solvent, like water. In the context of ionic compounds, this process depends heavily on both the nature of the ionic bonds and the surrounding solvent's ability to stabilize the ions.

A classic example involves sodium chloride (NaCl), which dissociates completely in water into sodium (Na\(^+\)) and chloride (Cl\(^-\)) ions. This separation is facilitated by water molecules surrounding and stabilizing each ion, termed as solvation.

• Complete dissociation results in a higher number of particles in the solution, raising the colligative properties like boiling point or osmotic pressure.
• On the other hand, magnesium sulfate (\(\mathrm{MgSO}_4\)) might not fully dissociate. Stronger ionic forces between its ions can limit separation, resulting in lower dissociation and deviation from expected theoretical values of\(i = 2\).

Therefore, understanding the dissociation process helps in calculating the van't Hoff factor, offering insight into how entirely a solute breaks down in a particular solvent. This information is essential for accurately predicting solution behaviors.

Electrolytes

Electrolytes are substances that, when dissolved in a solvent such as water, produce a conductive solution due to the presence of free-moving ions. They are categorized based on their ability to dissociate into ions.

• Strong electrolytes completely dissociate into ions, offering highly conductive solutions. Examples include sodium chloride (NaCl) and potassium nitrate (KNO\(_3\)).
• Weak electrolytes partially dissociate, resulting in solutions with fewer ions and reduced conductivity.

The concept of electrolytes is deeply connected to the van't Hoff factor. For strong electrolytes, like NaCl, \(i\) is expected to be close to the number of ions the compound dissociates into. However, in practice, values slightly less than expected can be observed due to ion interactions like pairing.

Magnesium sulfate (\(\mathrm{MgSO}_4\)), often displaying a lower \(i\) than expected, illustrates how strong ionic interactions can lead to incomplete dissociation, classifying it, at times, as a less than perfectly strong electrolyte.

Understanding electrolytes and their behavior assists in predicting how solutions will respond to changes, whether that be in electrical conductivity or other physical properties.