Step 1: Understanding the Question:
The question asks to calculate the osmotic pressure of an electrolyte solution, given its molarity, temperature, van't Hoff factor, and the universal gas constant.
Step 2: Key Formula or Approach:
The formula for osmotic pressure (\(\Pi\)) of an electrolyte solution is given by the van't Hoff equation:
\[
\Pi = i \times C \times R \times T
\]
where:
- \(i\) is the van't Hoff factor
- \(C\) is the molar concentration (Molarity) of the solution
- \(R\) is the universal gas constant
- \(T\) is the absolute temperature in Kelvin
Step 3: Detailed Explanation:
Given values:
- Molarity, \(C\) = 0.2 M (or 0.2 mol/dm\(^3\))
- Temperature, \(T\) = 300 K
- van't Hoff factor, \(i\) = 1.6
- Gas constant, \(R\) = 0.0821 atm dm\(^3\) K\(^{-1}\) mol\(^{-1}\)
Substitute these values into the osmotic pressure formula:
\[
\Pi = (1.6) \times (0.2 \text{ mol/dm}^3) \times (0.0821 \text{ atm dm}^3 \text{ K}^{-1} \text{ mol}^{-1}) \times (300 \text{ K})
\]
Now, perform the calculation:
\[
\Pi = 1.6 \times 0.2 \times 0.0821 \times 300 \text{ atm}
\]
\[
\Pi = 0.32 \times 0.0821 \times 300 \text{ atm}
\]
\[
\Pi = 0.32 \times 24.63 \text{ atm}
\]
\[
\Pi = 7.8816 \text{ atm}
\]
Rounding to two decimal places, the osmotic pressure is 7.88 atm.
Step 4: Final Answer:
The calculated osmotic pressure is 7.88 atm, which matches option (B).