Question

An aqueous solution has an osmotic pressure of \(4.92\) atm at \(300\) K.
Calculate the molarity of the solution.
(\(R = 0.082\) L atm mol\(^{-1}\) K\(^{-1}\))

• A. \(0.1\) M
• B. \(0.2\) M
• C. \(0.25\) M
• D. \(0.4\) M

Hint:

Use \(\pi = CRT\) and solve for \(C\).

Answer 1

The Correct Option is B

Step 1: Key Formula:
For a dilute solution, \(\pi = CRT\), where \(C\) is the molarity.

Step 2: Calculate:
\[ C = \frac{\pi}{RT} = \frac{4.92}{0.082\times300} = \frac{4.92}{24.6} = 0.2\ \text{M} \]

Step 3: Other options:
\(0.1\) M would give \(\pi = 2.46\) atm and \(0.4\) M would give \(9.84\) atm. \(0.25\) M gives \(6.15\) atm. None matches \(4.92\) atm.

Final Answer:
The molarity is \(0.2\) M, option (B). \[ \boxed{0.2\ \text{M}} \]