Question

Calculate the temperature of the solution in which a solution containing \(10\) g solute in \(0.4\) dm\({}^{3}\) has an osmotic pressure of \(3.4\) atm.
[Molar mass of solute \(=180\) g mol\({}^{-1}\), \(R=0.082\) atm dm\({}^{3}\) K\({}^{-1}\)mol\({}^{-1}\)]

• A. \(25.5{}^{\circ }\)C.
• B. \(20.2{}^{\circ }\)C.
• C. \(27.5{}^{\circ }\)C.
• D. \(30.7{}^{\circ }\)C.

Hint:

Use the osmotic pressure equation with moles of solute and volume, then convert kelvin to Celsius.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
\(\pi V=nRT\), with \(n=\dfrac{w}{M}\), so \(T=\dfrac{\pi V M}{wR}\).

Step 2: Substitute the Values
\(n=\dfrac{10}{180}=0.0556\) mol
\(\pi=3.4\) atm, \(V=0.4\) dm\(^{3}\), \(R=0.082\)

Step 3: Calculation
\(T=\dfrac{3.4\times0.4}{0.0556\times0.082}\approx298.5\) K
\(t=298.5-273\approx25.5^{\circ}\)C

Step 4: Compare the options
The closest value is option (A).

Final Answer:
The temperature is about 25.5 degrees Celsius. \[ \boxed{\text{(A) }\text{25.5}^{\circ}\text{C}} \]