Which of the following aqueous solutions should have the highest osmotic pressure?

Options

A. 0.011 M `AlCl_(3)` at ` 50^(@)C`
B. 0.03 M NaCl at `25^(@)C`
C. 0.012 M `(NH_(4))_(2)SO_(4)` at `25^(@)C`
D. 0.03 M NaCl at `50^(@)C`

Answer

To determine which of the given aqueous solutions has the highest osmotic pressure, we will use the formula for osmotic pressure (π):

\[ \pi = iCRT \]

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 (0.0821 L·atm/(K·mol))
- \( T \) = temperature (in Kelvin)

### Step-by-Step Solution:

1. **Identify the Solutions and Their Concentrations**:
- 0.011 M AlCl3 at 50°C
- 0.03 M NaCl at 25°C
- 0.012 M (NH4)2SO4 at 25°C
- 0.03 M NaCl at 50°C

2. **Convert Temperatures to Kelvin**:
- 50°C = 50 + 273 = 323 K
- 25°C = 25 + 273 = 298 K

3. **Calculate the Van't Hoff Factor (i)**:
- For AlCl3:
- Dissociates into 1 Al³⁺ and 3 Cl⁻ → \( i = 1 + 3 = 4 \)
- For NaCl:
- Dissociates into 1 Na⁺ and 1 Cl⁻ → \( i = 1 + 1 = 2 \)
- For (NH4)2SO4:
- Dissociates into 2 NH4⁺ and 1 SO4²⁻ → \( i = 2 + 1 = 3 \)
- For NaCl (again):
- Same as above → \( i = 2 \)

4. **Calculate Osmotic Pressure for Each Solution**:
- **For 0.011 M AlCl3 at 323 K**:
\[ \pi = iCRT = 4 \times 0.011 \times R \times 323 \]
- **For 0.03 M NaCl at 298 K**:
\[ \pi = 2 \times 0.03 \times R \times 298 \]
- **For 0.012 M (NH4)2SO4 at 298 K**:
\[ \pi = 3 \times 0.012 \times R \times 298 \]
- **For 0.03 M NaCl at 323 K**:
\[ \pi = 2 \times 0.03 \times R \times 323 \]

5. **Calculate the Values**:
- **For AlCl3**:
\[ \pi = 4 \times 0.011 \times R \times 323 \approx 14.212 R \]
- **For NaCl (25°C)**:
\[ \pi = 2 \times 0.03 \times R \times 298 \approx 17.88 R \]
- **For (NH4)2SO4**:
\[ \pi = 3 \times 0.012 \times R \times 298 \approx 10.728 R \]
- **For NaCl (50°C)**:
\[ \pi = 2 \times 0.03 \times R \times 323 \approx 19.38 R \]

6. **Compare the Osmotic Pressures**:
- AlCl3: \( 14.212 R \)
- NaCl (25°C): \( 17.88 R \)
- (NH4)2SO4: \( 10.728 R \)
- NaCl (50°C): \( 19.38 R \)

7. **Conclusion**:
The solution with the highest osmotic pressure is **0.03 M NaCl at 50°C**, which has an osmotic pressure of \( 19.38 R \).

### Final Answer:
The aqueous solution with the highest osmotic pressure is **0.03 M NaCl at 50°C**.