The osmotic pressure of a solution containing 0.4 mol of solute per litre at 273 K is

Answer

To find the osmotic pressure of a solution containing 0.4 mol of solute per liter at 273 K, we can use the formula for osmotic pressure:

\[ \Pi = \frac{n}{V}RT \]

Where:
- \(\Pi\) = osmotic pressure
- \(n\) = number of moles of solute
- \(V\) = volume of the solution in liters
- \(R\) = universal gas constant (0.0821 atm·L/(K·mol))
- \(T\) = temperature in Kelvin

### Step-by-step Solution:

1. **Identify the given values**:
- Number of moles of solute, \(n = 0.4 \, \text{mol}\)
- Volume of the solution, \(V = 1 \, \text{L}\) (since it is given per liter)
- Temperature, \(T = 273 \, \text{K}\)
- Gas constant, \(R = 0.0821 \, \text{atm·L/(K·mol)}\)

2. **Substitute the values into the osmotic pressure formula**:
\[ \Pi = \frac{n}{V}RT = \frac{0.4 \, \text{mol}}{1 \, \text{L}} \times 0.0821 \, \text{atm·L/(K·mol)} \times 273 \, \text{K} \]

3. **Calculate the osmotic pressure**:
- First, calculate \(\frac{0.4 \, \text{mol}}{1 \, \text{L}} = 0.4 \, \text{mol/L}\)
- Now, calculate:
\[ \Pi = 0.4 \times 0.0821 \times 273 \]
- Performing the multiplication:
\[ \Pi = 0.4 \times 22.4143 \approx 8.96572 \, \text{atm} \]

4. **Round the final answer**:
- The osmotic pressure is approximately \(8.96 \, \text{atm}\).

### Final Answer:
The osmotic pressure of the solution is approximately \(8.96 \, \text{atm}\).

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