Arrange the following aqueous solution in the order of their increasing boiling points
(i) `10^-4 M NaCl` (ii) `10^-3 M Urea` (iii) `10^-3 M MgCl_2` (iv) `10^-3 M NaCl`

Options

A. `I lt ii lt iv lt iii`
B. `ii lt I = iii lt iv`
C. `I lt ii lt iii lt iv`
D. `iv lt iii lt I =ii`

Answer

To arrange the given aqueous solutions in the order of their increasing boiling points, we need to consider the colligative properties of solutions, specifically the boiling point elevation, which depends on the number of solute particles in solution. This is determined by the van 't Hoff factor (i) and the molarity (M) of the solutions.

### Step 1: Identify the van 't Hoff factor (i) for each solute.
- **(i) 10^-4 M NaCl**:
- NaCl dissociates into 2 ions: Na⁺ and Cl⁻.
- Therefore, i = 2.

- **(ii) 10^-3 M Urea**:
- Urea is a non-electrolyte and does not dissociate.
- Therefore, i = 1.

- **(iii) 10^-3 M MgCl₂**:
- MgCl₂ dissociates into 3 ions: Mg²⁺ and 2 Cl⁻.
- Therefore, i = 3.

- **(iv) 10^-3 M NaCl**:
- Similar to the first solution, NaCl dissociates into 2 ions: Na⁺ and Cl⁻.
- Therefore, i = 2.

### Step 2: Calculate the effective concentration of particles (i * M) for each solution.
- **(i) 10^-4 M NaCl**:
- Effective concentration = i * M = 2 * 10^-4 = 2 * 10^-4.

- **(ii) 10^-3 M Urea**:
- Effective concentration = i * M = 1 * 10^-3 = 10^-3.

- **(iii) 10^-3 M MgCl₂**:
- Effective concentration = i * M = 3 * 10^-3 = 3 * 10^-3.

- **(iv) 10^-3 M NaCl**:
- Effective concentration = i * M = 2 * 10^-3 = 2 * 10^-3.

### Step 3: Compare the effective concentrations.
- 10^-4 M NaCl: 2 * 10^-4
- 10^-3 M Urea: 10^-3
- 10^-3 M MgCl₂: 3 * 10^-3
- 10^-3 M NaCl: 2 * 10^-3

### Step 4: Arrange the solutions in order of increasing effective concentration.
1. 10^-4 M NaCl (2 * 10^-4)
2. 10^-3 M Urea (10^-3)
3. 10^-3 M NaCl (2 * 10^-3)
4. 10^-3 M MgCl₂ (3 * 10^-3)

### Step 5: Determine the order of increasing boiling points.
Since the boiling point elevation is directly proportional to the effective concentration of solute particles, the order of increasing boiling points will be the same as the order of increasing effective concentration.

Thus, the order of increasing boiling points is:
1. 10^-4 M NaCl
2. 10^-3 M Urea
3. 10^-3 M NaCl
4. 10^-3 M MgCl₂

### Final Answer:
**Increasing boiling points order**: (i) `10^-4 M NaCl` < (ii) `10^-3 M Urea` < (iv) `10^-3 M NaCl` < (iii) `10^-3 M MgCl₂`

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