Arrange the following aqueous solutions in the order of their increasing boiling points
(i)`10^(-4)` M NaCl , (ii)`10^(-4)` M Urea , (iii)`10^(-3)` M `MgCl_2` , (iv)`10^(-2)` M NaCl

Options

A. (i) lt (ii) lt (iv) lt (iii)
B. (ii) lt (i) = (iii) lt (iv)
C. (ii) lt (i) lt (iii) lt (iv)
D. (iv) lt (iii) lt (i) = (ii)

Explanation

To arrange the given aqueous solutions in the order of their increasing boiling points, we will use the concept of colligative properties, specifically the elevation of boiling point, which is influenced by the number of solute particles in a solution.

### Step-by-Step Solution:

1. **Identify the Solutions and Their Concentrations:**
- (i) `10^(-4)` M NaCl
- (ii) `10^(-4)` M Urea
- (iii) `10^(-3)` M `MgCl_2`
- (iv) `10^(-2)` M NaCl

2. **Determine the Van't Hoff Factor (i) for Each Solute:**
- For NaCl: It dissociates into 2 ions (Na⁺ and Cl⁻), so **i = 2**.
- For Urea: It does not dissociate, so **i = 1**.
- For MgCl₂: It dissociates into 3 ions (Mg²⁺ and 2 Cl⁻), so **i = 3**.
- For NaCl (in solution iv): Again, it dissociates into 2 ions, so **i = 2**.

3. **Calculate the Effective Concentration (i × M) for Each Solution:**
- For (i) `10^(-4)` M NaCl:
\[ i \times M = 2 \times 10^{-4} = 2 \times 10^{-4} \]
- For (ii) `10^(-4)` M Urea:
\[ i \times M = 1 \times 10^{-4} = 10^{-4} \]
- For (iii) `10^(-3)` M `MgCl_2`:
\[ i \times M = 3 \times 10^{-3} = 3 \times 10^{-3} \]
- For (iv) `10^(-2)` M NaCl:
\[ i \times M = 2 \times 10^{-2} = 2 \times 10^{-2} \]

4. **List the Values of i × M:**
- (i) `10^(-4)` M NaCl: \(2 \times 10^{-4}\)
- (ii) `10^(-4)` M Urea: \(10^{-4}\)
- (iii) `10^(-3)` M `MgCl_2`: \(3 \times 10^{-3}\)
- (iv) `10^(-2)` M NaCl: \(2 \times 10^{-2}\)

5. **Order the Solutions Based on Increasing i × M Values:**
- (ii) `10^(-4)` M Urea: \(10^{-4}\) (lowest)
- (i) `10^(-4)` M NaCl: \(2 \times 10^{-4}\)
- (iii) `10^(-3)` M `MgCl_2`: \(3 \times 10^{-3}\)
- (iv) `10^(-2)` M NaCl: \(2 \times 10^{-2}\) (highest)

6. **Conclusion:**
The order of the solutions in terms of increasing boiling points is:
\[ \text{(ii) Urea} < \text{(i) NaCl} < \text{(iii) MgCl}_2 < \text{(iv) NaCl} \]

### Final Answer:
The order of increasing boiling points is:
**(ii) Urea < (i) NaCl < (iii) MgCl₂ < (iv) NaCl**