Problem 114 - A Complete Resource Book in Chemistry for JEE Main

Question

The van't Hoff factor for \(0.1 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) solution is 2.74. The degree of dissociation is (a) \(91.4 \%\) (b) \(87 \%\) (c) \(100 \%\) (d) \(75 \%\)

Step-by-Step Solution

Answer

The degree of dissociation of the solution is 87\%, so the correct answer is (b).

Step 1: Understand the dissociation process

The compound \(Ba(NO_3)_2\) dissociates in water as follows: \(Ba(NO_3)_2 \rightarrow Ba^{2+} + 2NO_3^-\). This means for each molecule of \(Ba(NO_3)_2\), it ideally produces 3 ions in solution.

Step 2: Calculate the ideal van't Hoff factor

Given the dissociation equation, the ideal van't Hoff factor \(i_{ideal}\) should be 3, since \(Ba(NO_3)_2\) dissociates into 3 ions.

Step 3: Use the van't Hoff factor to find the degree of dissociation

Given is \(i = 2.74\), and we use the formula \(\alpha = \frac{i - 1}{n - 1}\), where \(n\) is the number of ions produced ideally. Substituting, \(\alpha = \frac{2.74 - 1}{3 - 1} = \frac{1.74}{2} = 0.87\).

Step 4: Convert degree of dissociation to percentage

To express \(\alpha\) as a percentage, multiply it by 100: \(\alpha = 0.87 \times 100 = 87\%\).

Key Concepts

Degree of Dissociation

When a solute is dissolved in a solvent, it can break down into its constituent ions. This process is known as dissociation. The degree of dissociation, often denoted by \(\alpha\), measures a solute's extent of dissociation. It is expressed as a fraction or percentage.
For instance, if \(Ba(NO_3)_2\) is dissolved in water, and it dissociates completely, the degree of dissociation is 100%. However, if only part of it dissociates, the value is less than 100%. The degree of dissociation is important because it directly affects properties like the solution's osmotic pressure, boiling point, and freezing point.

Ba(NO3)2 Dissociation

Barium nitrate, or \(Ba(NO_3)_2\), dissociates in water to form ions. The equation representing this process is:

• \(Ba(NO_3)_2 \rightarrow Ba^{2+} + 2NO_3^-\)

This shows that one unit of \(Ba(NO_3)_2\) should ideally dissociate into three ions: one barium ion \(Ba^{2+}\) and two nitrate ions \(NO_3^-\). This theoretical breakdown assumes complete dissociation, which may not occur in practical scenarios due to various factors such as concentration, temperature, and the solute's nature.
The actual number of ions formed can be slightly less, affecting the measured properties of the solution.

Ions in Solution

When \(Ba(NO_3)_2\) dissolves in water, it releases ions into the solution. These ions are charged atoms or molecules that can conduct electricity. The presence of ions is crucial because they influence the solution's physical and chemical properties.
In the case of \(Ba(NO_3)_2\):

• \(Ba^{2+}\): A barium ion with a positive charge.
• \(NO_3^-\): Nitrate ions with a negative charge.

The number of ions directly impacts the van't Hoff factor, which is a measure of the number of particles a compound forms in solution. This factor helps us understand the extent of dissociation and thus the compound's behavior in different scenarios like colligative properties.

Dissociation in Water

In an aqueous solution, dissociation describes how compounds split into ions when dissolved in water. Water acts as a solvent and its polar nature allows ionic compounds like \(Ba(NO_3)_2\) to dissociate readily.
The process is crucial for making solutions conductive, as only ions can carry electric charge through the liquid. The degree to which a compound dissociates depends on factors like:

• Concentration of the solution
• Temperature
• The innate chemical nature of the solute and solvent

Understanding dissociation helps in calculating an aqueous solution's van't Hoff factor and degree of dissociation, which in turn explain various properties and potential uses of the solution in different scientific and industrial applications.