The correct order of increasing boiling of the following aqueous solutions
0.0001 M NaCl (I), 0.0001 M Urea (II), 0.001 M `MgCl_(2)` (III), 0.01 M NaCl (IV) is

Options

A. `I lt II lt III lt IV `
B. `IV lt III lt II lt I`
C. `II lt I lt III lt IV `
D. `III lt II lt IV lt I `

Explanation

To determine the correct order of increasing boiling points of the given aqueous solutions, we need to use the formula for boiling point elevation, which is given by:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Where:
- \(\Delta T_b\) is the elevation in boiling point.
- \(i\) is the van 't Hoff factor (the number of particles the solute breaks into).
- \(K_b\) is the ebullioscopic constant (which is constant for a given solvent, in this case, water).
- \(m\) is the molality of the solution.

Since \(K_b\) is constant for all solutions in this case, we can focus on the product \(i \cdot m\) to compare the boiling points.

### Step 1: Calculate \(i\) for each solute
1. **0.0001 M NaCl (I)**:
- NaCl dissociates into 2 ions (Na\(^+\) and Cl\(^-\)).
- \(i = 2\)

2. **0.0001 M Urea (II)**:
- Urea does not dissociate in solution.
- \(i = 1\)

3. **0.001 M MgCl\(_2\) (III)**:
- MgCl\(_2\) dissociates into 3 ions (Mg\(^{2+}\) and 2 Cl\(^-\)).
- \(i = 3\)

4. **0.01 M NaCl (IV)**:
- NaCl dissociates into 2 ions (Na\(^+\) and Cl\(^-\)).
- \(i = 2\)

### Step 2: Calculate \(i \cdot m\) for each solution
1. **0.0001 M NaCl (I)**:
- \(i \cdot m = 2 \cdot 0.0001 = 0.0002\)

2. **0.0001 M Urea (II)**:
- \(i \cdot m = 1 \cdot 0.0001 = 0.0001\)

3. **0.001 M MgCl\(_2\) (III)**:
- \(i \cdot m = 3 \cdot 0.001 = 0.003\)

4. **0.01 M NaCl (IV)**:
- \(i \cdot m = 2 \cdot 0.01 = 0.02\)

### Step 3: Compare the values of \(i \cdot m\)
Now we can arrange the solutions in order of increasing boiling point based on the calculated \(i \cdot m\) values:

- **0.0001 M Urea (II)**: \(0.0001\)
- **0.0001 M NaCl (I)**: \(0.0002\)
- **0.01 M NaCl (IV)**: \(0.02\)
- **0.001 M MgCl\(_2\) (III)**: \(0.003\)

### Step 4: Final order of increasing boiling point
From the values calculated, we can conclude that the order of increasing boiling point is:

**0.0001 M Urea (II) < 0.0001 M NaCl (I) < 0.001 M MgCl\(_2\) (III) < 0.01 M NaCl (IV)**

### Final Answer:
The correct order of increasing boiling points is: **(II) < (I) < (III) < (IV)**