Osmotic pressure of a solution is `0.0821 atm` at a temperature of 300 K. The concentration in mole/litre will be

Options

A. 0.033
B. 0.066
C. `0.33 xx10^(-2)`
D. 3

Answer

To find the concentration in mole per liter (C) of a solution given its osmotic pressure (π) and temperature (T), we can use the formula for osmotic pressure:

\[ \pi = C \cdot R \cdot T \]

Where:
- π = osmotic pressure (in atm)
- C = molar concentration (in mol/L)
- R = ideal gas constant (0.0821 L·atm/(K·mol))
- T = temperature (in K)

### Step-by-Step Solution:

1. **Identify the given values:**
- Osmotic pressure (π) = 0.0821 atm
- Temperature (T) = 300 K
- Ideal gas constant (R) = 0.0821 L·atm/(K·mol)

2. **Rearrange the formula to solve for C:**
\[ C = \frac{\pi}{R \cdot T} \]

3. **Substitute the known values into the equation:**
\[ C = \frac{0.0821 \text{ atm}}{0.0821 \text{ L·atm/(K·mol)} \cdot 300 \text{ K}} \]

4. **Calculate the denominator:**
\[ R \cdot T = 0.0821 \cdot 300 = 24.63 \text{ L·atm/mol} \]

5. **Now substitute this value back into the equation for C:**
\[ C = \frac{0.0821}{24.63} \]

6. **Perform the division:**
\[ C \approx 0.00334 \text{ mol/L} \]

7. **Convert to scientific notation:**
\[ C \approx 3.34 \times 10^{-3} \text{ mol/L} \]

### Final Answer:
The concentration in mole per liter (C) is approximately \(3.34 \times 10^{-3} \text{ mol/L}\).