The osmotic pressure of a solution containing 0.4 mol of solute per litre at 323 K is

Explanation

To calculate the osmotic pressure of a solution containing 0.4 mol of solute per liter at 323 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⁻¹·mol⁻¹)
- \(T\) = temperature in Kelvin

### Step 1: Identify the values
- Number of moles of solute, \(n = 0.4 \, \text{mol}\)
- Volume of the solution, \(V = 1 \, \text{L}\) (since it is given as per liter)
- Temperature, \(T = 323 \, \text{K}\)
- Gas constant, \(R = 0.0821 \, \text{atm·L·K⁻¹·mol⁻¹}\)

### Step 2: Substitute the values into the formula
Now, we substitute these values into the osmotic pressure formula:

\[ \pi = \frac{0.4 \, \text{mol}}{1 \, \text{L}} \times 0.0821 \, \text{atm·L·K⁻¹·mol⁻¹} \times 323 \, \text{K} \]

### Step 3: Calculate the osmotic pressure
Now we perform the calculation:

\[ \pi = 0.4 \times 0.0821 \times 323 \]

Calculating this step-by-step:

1. Calculate \(0.4 \times 0.0821 = 0.03284\)
2. Then, multiply by 323:
\[ 0.03284 \times 323 \approx 10.59 \, \text{atm} \]

### Final Answer
Thus, the osmotic pressure of the solution is approximately:

\[ \pi \approx 10.59 \, \text{atm} \]