0.5 M aquous solution of Glucose is isotonic with:

Options

A. 0.5 M KCl solution
B. 0.5 M `CaCl_(2)` solution
C. 0.5 M Urea solution
D. 1 M solution of sucrose

Answer

To determine which solution is isotonic with a 0.5 M aqueous solution of glucose, we need to understand the concept of osmotic pressure and how it relates to the van 't Hoff factor (i) and concentration (C).

### Step-by-Step Solution:

1. **Understand Isotonic Solutions**:
- Isotonic solutions have the same osmotic pressure. This means that the solutions exert equal pressure when separated by a semipermeable membrane.

2. **Osmotic Pressure Formula**:
- The formula for osmotic pressure (π) is given by:
\[ \pi = iCRT \]
where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = concentration of the solution (in molarity)
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

3. **Determine the Osmotic Pressure of Glucose**:
- For glucose, which does not dissociate in solution, the van 't Hoff factor \( i = 1 \).
- Given that the concentration \( C = 0.5 \, M \):
\[ \pi_{\text{glucose}} = 1 \times 0.5 \times R \times T = 0.5RT \]

4. **Evaluate Other Solutions**:
- We need to find a solution with the same osmotic pressure \( 0.5RT \).

- **Option 1: 0.5 M KCl**:
- KCl dissociates into \( K^+ \) and \( Cl^- \), so \( i = 2 \).
- Therefore, \( \pi_{\text{KCl}} = 2 \times 0.5 \times R \times T = 1RT \) (not isotonic).

- **Option 2: 0.5 M CaCl2**:
- CaCl2 dissociates into \( Ca^{2+} \) and \( 2Cl^- \), so \( i = 3 \).
- Therefore, \( \pi_{\text{CaCl2}} = 3 \times 0.5 \times R \times T = 1.5RT \) (not isotonic).

- **Option 3: 0.5 M Urea**:
- Urea does not dissociate, so \( i = 1 \).
- Therefore, \( \pi_{\text{urea}} = 1 \times 0.5 \times R \times T = 0.5RT \) (isotonic).

- **Option 4: 1 M Sucrose**:
- Sucrose does not dissociate, so \( i = 1 \).
- Therefore, \( \pi_{\text{sucrose}} = 1 \times 1 \times R \times T = 1RT \) (not isotonic).

5. **Conclusion**:
- The only solution that has the same osmotic pressure as the 0.5 M glucose solution is the 0.5 M urea solution.

### Final Answer:
The solution that is isotonic with a 0.5 M aqueous solution of glucose is **0.5 M urea solution**.