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) The ionic interactions in magnesium sulphate are stronger than those in sodium chloride.

Step 1: Understanding the Van't Hoff Factor

The van't Hoff factor (i) indicates how much a compound dissociates in solution. For example, an ideal van't Hoff factor for NaCl, which dissociates into Na⁺ and Cl⁻ ions, is 2 because each formula unit yields two particles. However, because of ion-ion interactions, the real van't Hoff factor may differ from the ideal one.

Step 2: Analyzing Sodium Chloride

For sodium chloride in 0.1 M solution, the van’t Hoff factor is given as 1.87. This indicates incomplete dissociation, as the ideal value is 2. The deviation (less than 2) shows some degree of ion pairing due to attractive forces between Na⁺ and Cl⁻ ions.

Step 3: Van't Hoff Factor Implications

A lower van’t Hoff factor than the theoretical value indicates that the observed dissociation in solution is not complete similar to the deviation from ideal behavior in real gases. The greater the deviation below the ideal value, the stronger the interactions are among the dissociated ions.

Step 4: Applying to Magnesium Sulphate

Magnesium sulphate (MgSO₄) also dissociates into Mg²⁺ and SO₄²⁻ ions. If sodium chloride shows more interaction by this measure than magnesium sulphate, the van't Hoff factor for MgSO₄ would likely show a smaller deviation from its ideal value, suggesting that its ionic interactions are stronger.

Step 5: Choosing the Correct Option

Given that the sodium chloride has a van't Hoff factor of 1.87, which suggests significant ionic interactions, the statement (c) stating that ionic interactions in magnesium sulphate are stronger is consistent with such measurements, under similar conditions.

Key Concepts

Ionic Interactions

Ionic interactions refer to the forces that occur between oppositely charged ions in a compound. These forces are key to understanding how substances behave when dissolved in water. For instance, sodium chloride (\(\text{NaCl}\)) dissociates into sodium (\(\text{Na}^+\)) and chloride (\(\text{Cl}^-\)) ions in solution. The van’t Hoff factor (\(i\)) for sodium chloride is less than the ideal value due to these interactions.
This indicates that the ions experience some degree of attraction, forming ion pairs that don't fully separate in solution.

Stronger ionic interactions usually result in a lower van’t Hoff factor than the ideal, as these attractions hold the ions together more tightly.

Ionic interactions are essential in various chemical and biological processes. Understanding them helps in predicting how chemicals will behave in solutions. This is crucial not only in lab settings but also in industrial applications.
Keep in mind that the strength of these interactions often influences solubility, conductivity, and other solution properties.

Dissociation in Solutions

Dissociation in solutions occurs when ionic compounds break apart into individual ions when dissolved in a solvent like water.
For example, when sodium chloride dissociates, it separates into \(\text{Na}^+\) and \(\text{Cl}^-\) ions. This process is vital for conducting electricity and understanding chemical reactions in solutions.

A perfect dissociation would mean each formula unit dissociates completely, reflecting in an ideal van’t Hoff factor. However, real solutions often deviate due to ionic interactions, leading to ion pairing where ions remain partially associated.

Complete dissociation is rare due to several factors:

• The strength of ionic bonds between atoms
• The solvent's ability to stabilize separated ions
• Concentration of the solution

When dealing with dissociation, it’s important to consider these influences as they affect calculative metrics like the van’t Hoff factor, altering our predictions in studies and applications.

Deviation from Ideal Behavior

Deviation from ideal behavior occurs when a real solution's properties differ from expected theoretical values. The van't Hoff factor provides insight into these deviations, particularly in ionic solutions where charged particles interact.

For sodium chloride, with a theoretical van’t Hoff factor of 2, the actual value of 1.87 signifies deviation due to ionic interaction. This shows that NaCl doesn't fully dissociate, akin to how real gases deviate from the ideal gas law due to molecular interactions.

Ionic interactions cause deviations because they result in ion pairing and aggregation instead of independent movement in solution.
In practical applications and experiments:

• keep in mind that ionic strength, concentration, and temperature can influence a solution's behavior
• noting these factors aids in more accurate predictions and understanding of chemical systems

Understanding these deviations is instrumental in fields like physical chemistry and chemical engineering, where accurate predictions are pivotal.

Chemical Equilibrium

Chemical equilibrium in solutions is the state where the rate of the forward reaction equals the rate of the reverse reaction. In the context of dissociation, it refers to the balance between dissolved ions and undissolved ionic compound.

Equilibrium is deeply affected by ionic interactions, as these can shift the balance of dissociation and recombination. For instance, strong ionic interactions may lower dissociation rates, establishing an equilibrium that favors formation of more ion pairs.

This concept integrates various factors like concentration and temperature:

• Higher concentrations can shift equilibria due to increased collision rates and interactions
• Temperature changes can increase or decrease solubility, shifting equilibrium positions

Understanding equilibrium at the molecular level is crucial, as it helps in predicting how a system will respond to changes in conditions. It is particularly important in industries like pharmaceuticals and biochemistry, where reaction conditions dictate product yields and efficacy.