Which has the maximum osmotic pressure at temperature `T`?

Options

A. `100 mL` of `1 M` urea solution.
B. `300 mL` of `1 M` glucose solution.
C. Mixture of `100 mL` of `1 M` urea solution and `300 mL` of `1 M` glucose solution.
D. All are isotonic.

Explanation

To determine which solution has the maximum osmotic pressure at temperature \( T \), we will use the formula for osmotic pressure, which is given by:

\[ \pi = iCRT \]

Where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles the solute breaks into)
- \( C \) = molarity of the solution (moles of solute per liter of solution)
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step-by-Step Solution:

1. **Identify the Solutes**: The question mentions urea and glucose, both of which are non-electrolytes. This means they do not dissociate into ions in solution.

2. **Determine the van 't Hoff Factor**: For non-electrolytes like urea and glucose:
- \( i = 1 \) for both urea and glucose.

3. **Calculate the Molarity**:
- For urea: Given that the concentration is 1 molar, \( C = 1 \, \text{mol/L} \).
- For glucose: Similarly, if the concentration is also 1 molar, \( C = 1 \, \text{mol/L} \).

4. **Calculate the Osmotic Pressure for Each Solution**:
- For urea:
\[ \pi_{\text{urea}} = i \cdot C \cdot R \cdot T = 1 \cdot 1 \cdot R \cdot T = RT \]
- For glucose:
\[ \pi_{\text{glucose}} = i \cdot C \cdot R \cdot T = 1 \cdot 1 \cdot R \cdot T = RT \]

5. **Consider the Mixture**: If we have a mixture of urea and glucose:
- Assuming we mix 100 mL of 1 M urea with 300 mL of 1 M glucose, we need to find the new concentration:
- Total volume = 100 mL + 300 mL = 400 mL = 0.4 L.
- Moles of urea = \( 1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.1 \, \text{mol} \).
- Moles of glucose = \( 1 \, \text{mol/L} \times 0.3 \, \text{L} = 0.3 \, \text{mol} \).
- Total moles = \( 0.1 + 0.3 = 0.4 \, \text{mol} \).
- Concentration of the mixture:
\[ C_{\text{mixture}} = \frac{0.4 \, \text{mol}}{0.4 \, \text{L}} = 1 \, \text{mol/L} \]

6. **Calculate the Osmotic Pressure of the Mixture**:
- For the mixture:
\[ \pi_{\text{mixture}} = i \cdot C_{\text{mixture}} \cdot R \cdot T = 1 \cdot 1 \cdot R \cdot T = RT \]

7. **Conclusion**:
- All solutions (urea, glucose, and the mixture) have the same osmotic pressure of \( RT \). Therefore, they are isotonic.

### Final Answer:
All solutions (urea, glucose, and the mixture) have the same osmotic pressure at temperature \( T \).