The ratio of value of colligative property for equimolar `Hg_(2)Cl_(2)` solution to that for sugar solution is nearly

Options

A. 4
B. 1
C. 8
D. 3

Answer

To solve the problem of finding the ratio of the value of colligative property for equimolar `Hg2Cl2` solution to that for sugar solution, we will follow these steps:

### Step 1: Understand the nature of the solutes
- `Hg2Cl2` (mercury(I) chloride) is an electrolyte that dissociates into ions in solution.
- Sugar (C6H12O6) is a non-electrolyte and does not dissociate in solution.

### Step 2: Determine the dissociation of `Hg2Cl2`
- `Hg2Cl2` dissociates as follows:
\[ \text{Hg}_2\text{Cl}_2 \rightarrow \text{Hg}_2^{2+} + 2\text{Cl}^- \]
- From this dissociation, we see that 1 mole of `Hg2Cl2` produces 3 moles of ions (1 mole of `Hg2^{2+}` and 2 moles of `Cl^-`).

### Step 3: Calculate the Van't Hoff factor (i)
- The Van't Hoff factor (i) is defined as the number of particles the solute produces in solution.
- For `Hg2Cl2`, since it produces 3 ions:
\[ i = 3 \]

### Step 4: Colligative properties for both solutions
- The colligative property for a solution is proportional to the number of particles in solution.
- For sugar solution (non-electrolyte):
- Theoretical colligative property = 1 (since it does not dissociate).
- For `Hg2Cl2` solution:
- The observed colligative property is given by:
\[ \text{Observed Colligative Property} = i \times \text{Theoretical Colligative Property} \]
- Thus, for `Hg2Cl2`:
\[ \text{Observed Colligative Property} = 3 \times \text{Theoretical Colligative Property} \]

### Step 5: Establish the ratio of colligative properties
- The ratio of the value of colligative property for `Hg2Cl2` solution to that for sugar solution is:
\[ \text{Ratio} = \frac{\text{Observed Colligative Property for } Hg2Cl2}{\text{Theoretical Colligative Property for sugar}} \]
- Substituting the values:
\[ \text{Ratio} = \frac{3 \times \text{Theoretical Colligative Property}}{\text{Theoretical Colligative Property}} = 3 \]

### Conclusion
- Therefore, the ratio of the value of colligative property for equimolar `Hg2Cl2` solution to that for sugar solution is **3**.

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