Step 1: Understanding the Question:
We need to find the osmotic pressure of a glucose solution using its molarity and temperature.
Step 2: Key Formula or Approach:
Van't Hoff Equation for osmotic pressure:
\[ \pi = iCRT \]
Where \(C\) is molarity, \(R\) is the gas constant, and \(T\) is absolute temperature.
Step 3: Detailed Explanation:
1. Determine \(i\): Glucose is a non-electrolyte, so it does not dissociate. \(i = 1\).
2. Convert Temperature: \(T = 27 + 273 = 300 \text{ K}\).
3. Constants: \(R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\).
4. Calculation:
\[ \pi = 1 \times 0.1 \times 0.0821 \times 300 \]
\[ \pi = 0.1 \times 24.63 \]
\[ \pi = 2.463 \text{ atm} \]
Step 4: Final Answer:
The osmotic pressure of the solution is approximately 2.46 atm.