Question

The percentage dissociation of a salt (MX$_3$) solution at a given temperature (van't Hoff factor $i = 2$) is .................. % (Nearest integer)

Hint:

The van't Hoff factor \(i\) is a key parameter in determining the degree of dissociation. When \(i\) is less than the theoretical number of particles formed from dissociation, the salt has not fully dissociated.

Answer 1

Correct Answer: 33

Step 1: Understanding the Dissociation of Salt MX\(_3\)
The salt MX\(_3\) dissociates in water according to the equation: \[ \text{MX}_3 \rightarrow \text{M}^{3+} + 3\text{X}^- \]. Each mole of MX\(_3\) yields one mole of M\(^{3+}\) and three moles of X\(^-\).
Step 2: van't Hoff Factor (i)
The provided van't Hoff factor is \(i = 2\). This factor represents the total moles of particles in solution per mole of solute. For MX\(_3\), complete dissociation would result in 4 particles (1 M\(^{3+}\) and 3 X\(^-\)) per formula unit. A van't Hoff factor of 2 indicates incomplete dissociation, where the total particles formed are double the initial formula units. 
Step 3: Using the Formula for Percentage Dissociation
The percentage dissociation (\(\alpha\)) is calculated using the formula: \[ i = 1 + \alpha (n - 1) \]. In this formula, \(i\) is the van't Hoff factor (2), \(\alpha\) is the degree of dissociation, and \(n\) is the number of ions formed per formula unit of solute (which is 4 for MX\(_3\)). Substituting the values: \[ 2 = 1 + \alpha (4 - 1) \] \[ 2 = 1 + 3\alpha \] \[ 3\alpha = 1 \] \[ \alpha = \frac{1}{3} \] 
Step 4: Calculating the Percentage Dissociation
The percentage dissociation is computed as: \[ \text{Percentage dissociation} = \alpha \times 100 = \frac{1}{3} \times 100 = 33.33\% \]. Rounded to the nearest integer, the percentage dissociation is 33%.