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 as follows: \[ \text{MX}_3 \rightarrow \text{M}^{3+} + 3\text{X}^- \] For each mole of MX\(_3\), it dissociates to give one mole of M\(^{3+}\) and three moles of X\(^-\). 
Step 2: van't Hoff Factor (i)
The van't Hoff factor \(i\) is given as \(i = 2\). The van't Hoff factor represents the total number of particles in solution per formula unit of solute. In this case, for MX\(_3\), the dissociation would produce 4 particles (1 M\(^{3+}\) and 3 X\(^-\)) per formula unit of MX\(_3\). 
However, since \(i = 2\), this suggests that the dissociation is not complete, and the actual number of particles formed is only double the initial number of formula units. 
Step 3: Using the Formula for Percentage Dissociation
The formula for the percentage dissociation (\(\alpha\)) is given by: \[ i = 1 + \alpha (n - 1) \] Where:
\(i\) is the van't Hoff factor (2 in this case), \(\alpha\) is the degree of dissociation, \(n\) is the number of ions produced per formula unit of solute (which is 4 for MX\(_3\)).
\[ 2 = 1 + \alpha (4 - 1) \] \[ 2 = 1 + 3\alpha \] \[ 3\alpha = 1 \] \[ \alpha = \frac{1}{3} \] 
Step 4: Calculating the Percentage Dissociation
The percentage dissociation is given by:
\[ \text{Percentage dissociation} = \alpha \times 100 = \frac{1}{3} \times 100 = 33.33% \] To the nearest integer, the percentage dissociation is 33%.

Answer 2

Step 1: 
For a salt MX₃, the dissociation can be represented as:
\[ MX_3 \rightleftharpoons M^{3+} + 3X^- \] This gives us a van't Hoff factor \( i = 2 \), which indicates the total number of ions produced in solution when the salt dissociates. The van't Hoff factor \( i \) is the number of particles (ions) in solution relative to the number of formula units of the salt initially present.
 

Step 2:
The relationship between the observed and theoretical values for the van't Hoff factor is:
\[ i = 1 + \alpha(n - 1) \] where: - \( \alpha \) is the degree of dissociation. - \( n \) is the number of ions formed per formula unit (in this case, \( n = 4 \) for MX₃ because one formula unit gives 4 ions: M³⁺ and 3X⁻).
We are given \( i = 2 \) for this salt. Substituting in the values, we get: \[ 2 = 1 + \alpha(4 - 1) \] \[ 2 = 1 + 3\alpha \] \[ \alpha = \frac{1}{3} \]

Step 3:
Now, the percentage dissociation is given by: \[ \text{Percentage dissociation} = \alpha \times 100 = \frac{1}{3} \times 100 = 33\% \]

Final Answer:
The percentage dissociation of the salt is 33%.