The osmotic pressure of a solution containing 0.2 mol of solute per litre at 273 K is

Options

A. 4.48atm
B. 5.48atm
C. 2.47atm
D. 3.98atm

Answer

To find the osmotic pressure of a solution containing 0.2 mol of solute per liter at 273 K, we can use the formula for osmotic pressure (π):

\[ \pi = CRT \]

Where:
- \(C\) = concentration of the solution in moles per liter (mol/L)
- \(R\) = universal gas constant
- \(T\) = temperature in Kelvin (K)

### Step-by-step Solution:

**Step 1: Identify the values needed for the calculation.**
- Concentration \(C = 0.2 \, \text{mol/L}\)
- Temperature \(T = 273 \, \text{K}\)
- Gas constant \(R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1}\)

**Step 2: Substitute the values into the osmotic pressure formula.**
\[ \pi = C \cdot R \cdot T \]
\[ \pi = 0.2 \, \text{mol/L} \cdot 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \cdot 273 \, \text{K} \]

**Step 3: Perform the multiplication.**
\[ \pi = 0.2 \cdot 0.0821 \cdot 273 \]
Calculating \(0.2 \cdot 0.0821\):
\[ 0.2 \cdot 0.0821 = 0.01642 \]
Now multiply by 273:
\[ 0.01642 \cdot 273 \approx 4.48 \, \text{atm} \]

**Step 4: State the final result.**
The osmotic pressure of the solution is approximately:
\[ \pi \approx 4.48 \, \text{atm} \]

### Final Answer:
The osmotic pressure of the solution is 4.48 atm.

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