The osmotic pressure of a solution containing `0.1 mol` of solute per litre at `273 K` is

Options

A. `0.1/1 xx 0.08205 xx 273 atm`
B. `0.1 xx 2 xx 0.08205 xx 273 atm`
C. `1/0.1 xx 0.08205 xx 273 atm`
D. `0.1/1 xx 273/0.08205` atm

Explanation

To find the osmotic pressure of a solution containing 0.1 mol of solute per litre at 273 K, we can use the formula for osmotic pressure:

\[ \pi = CRT \]

Where:
- \(\pi\) = osmotic pressure
- \(C\) = concentration of the solution (in mol/L)
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)

### Step 1: Identify the values
From the question, we have:
- Number of moles of solute = 0.1 mol
- Volume of solution = 1 L (since it is given as per litre)
- Temperature = 273 K

### Step 2: Calculate the concentration (C)
The concentration \(C\) can be calculated as:
\[ C = \frac{\text{number of moles}}{\text{volume in liters}} = \frac{0.1 \text{ mol}}{1 \text{ L}} = 0.1 \text{ mol/L} \]

### Step 3: Substitute the values into the osmotic pressure formula
Now we can substitute the values into the osmotic pressure formula:
\[ \pi = C \cdot R \cdot T \]
\[ \pi = (0.1 \text{ mol/L}) \cdot (0.0821 \text{ L·atm/(K·mol)}) \cdot (273 \text{ K}) \]

### Step 4: Perform the calculation
Now we calculate:
\[ \pi = 0.1 \cdot 0.0821 \cdot 273 \]
\[ \pi = 0.1 \cdot 22.4143 \approx 2.24143 \text{ atm} \]

### Step 5: Round the answer
Rounding to three significant figures, we get:
\[ \pi \approx 2.24 \text{ atm} \]

### Final Answer
The osmotic pressure of the solution is approximately **2.24 atm**.

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