Question

The ratio of the value of any colligative property for $K_4[Fe(CN)_6]$ solution to that of sugar solution is (Consider 75% dissociation of $K_4[Fe(CN)_6]$)

Answer 1

4

Answer 2

To determine the ratio of the value of any colligative property for $K_4[Fe(CN)_6]$ solution to that of sugar solution, we need to calculate the van't Hoff factor ($i$) for each solution. Colligative properties are directly proportional to the van't Hoff factor ($i$) for solutions of the same initial concentration.

1. Van't Hoff factor ($i$) for $K_4[Fe(CN)_6]$ solution:

   $K_4[Fe(CN)_6]$ dissociates in water as follows:

   $K_4[Fe(CN)_6](aq) \rightleftharpoons 4K^+(aq) + [Fe(CN)_6]^{4-}(aq)$

   From the dissociation equation, one molecule of $K_4[Fe(CN)_6]$ ideally produces $n = 4$ potassium ions ($K^+$) and $1$ ferrocyanide ion ($[Fe(CN)_6]^{4-}$), so the total number of ions produced per formula unit is $n = 4 + 1 = 5$.

   The degree of dissociation ($\alpha$) is given as 75%, which means $\alpha = 0.75$.

   The van't Hoff factor ($i$) for dissociation is calculated using the formula:

   $i = 1 + (n - 1)\alpha$

   Substitute the values:

   $i_{K_4[Fe(CN)_6]} = 1 + (5 - 1) \times 0.75$

   $i_{K_4[Fe(CN)_6]} = 1 + (4) \times 0.75$

   $i_{K_4[Fe(CN)_6]} = 1 + 3$

   $i_{K_4[Fe(CN)_6]} = 4$

2. Van't Hoff factor ($i$) for sugar solution:

   Sugar (e.g., sucrose) is a non-electrolyte. It does not dissociate or associate in solution. Therefore, for sugar:

   $i_{sugar} = 1$

3. Ratio of colligative properties:

   Assuming the initial concentrations of both solutions are the same, the ratio of their colligative properties will be equal to the ratio of their van't Hoff factors.

   Ratio = $\frac{\text{Colligative property for } K_4[Fe(CN)_6] \text{ solution}}{\text{Colligative property for sugar solution}} = \frac{i_{K_4[Fe(CN)_6]}}{i_{sugar}}$

   Ratio = $\frac{4}{1}$

   Ratio = 4

Colligative properties depend on the number of solute particles. The van't Hoff factor ($i$) accounts for the effective number of particles in solution due to dissociation or association. For $K_4[Fe(CN)_6]$, which dissociates into 5 ions ($4K^+$ and $1[Fe(CN)_6]^{4-}$), its 75% dissociation means that for every 100 molecules, 75 dissociate. This leads to an $i$ value of 4. Sugar, being a non-electrolyte, does not dissociate, so its $i$ value is 1. When comparing colligative properties of solutions with the same initial concentration, the ratio of their colligative properties is simply the ratio of their van't Hoff factors.