Step 1: Understanding the Question:
The question asks to calculate the osmotic pressure of a solution with a given molar concentration and temperature. The solution is assumed to be ideal and non-electrolytic.
Step 2: Key Formula or Approach:
The osmotic pressure (\(\pi\)) of a dilute solution is given by the van 't Hoff equation:
\[ \pi = CRT \]
where:
- \(C\) is the molar concentration of the solution (in mol/L).
- \(R\) is the ideal gas constant.
- \(T\) is the absolute temperature (in Kelvin).
Step 3: Detailed Explanation:
1. Identify the given values:
- Molar concentration, \(C = 0.1 \text{ M}\).
- Temperature = \(27^\circ C\).
2. Convert Temperature to Kelvin:
The temperature must be in Kelvin for use in the ideal gas law equations.
\[ T(K) = T(^\circ C) + 273.15 \]
\[ T = 27 + 273.15 = 300.15 \text{ K} \]
(Using 300 K is usually sufficient for multiple-choice questions).
3. Choose the correct value for R:
Since the options for pressure are in atmospheres (atm), we should use the value of R that includes these units.
\[ R = 0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \]
4. Calculate the Osmotic Pressure:
Substitute the values into the formula \(\pi = CRT\):
\[ \pi = (0.1 \text{ mol/L}) \times (0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}) \times (300 \text{ K}) \]
\[ \pi = 0.1 \times 0.0821 \times 300 \text{ atm} \]
\[ \pi = 0.1 \times 24.63 \text{ atm} \]
\[ \pi = 2.463 \text{ atm} \]
Step 4: Final Answer:
The osmotic pressure of the solution is approximately \(2.46 \text{ atm}\).