Question

Given below are two statements:} A semipermeable membrane separates two chambers:

Statement I:} \(H_2O\) molecules move from chamber 1 to chamber 2. Statement II:} The osmotic pressure of a solution prepared by dissolving \(50\,\text{mg}\) of potassium sulphate \((\text{molar mass}=174\,\text{g mol}^{-1})\) in \(2\,\text{L}\) of water (at \(27^\circ\text{C}\)) is \(0.0107\,\text{bar}\). \((R=0.083\,\text{dm}^3\text{bar K}^{-1}\text{mol}^{-1})\) Choose the correct answer.

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is C

Concept: Osmosis occurs from lower solute concentration to higher solute concentration. \[ \pi = iCRT \] where \(i\) is van’t Hoff factor. Step 1: {Check Statement I} Molar mass of glucose \(=180\). Chamber 1: \[ \text{moles}=\frac{18}{180}=0.1 \] Volume \(=0.1\,\text{L}\) \[ C_1=1\,\text{M} \] Chamber 2: \[ \text{moles}=\frac{30}{180}=0.167 \] Volume \(=0.25\,\text{L}\) \[ C_2=0.668\,\text{M} \] Thus \[ C_1>C_2 \] Water moves from lower concentration to higher concentration, i.e. \[ \text{Chamber 2} \rightarrow \text{Chamber 1} \] Hence statement I is false. Step 2: {Check Statement II} Mass \(=50\,\text{mg}=0.05\,\text{g}\) \[ \text{moles}=\frac{0.05}{174}=2.87\times10^{-4} \] Volume \(=2\,\text{L}\) \[ C=1.435\times10^{-4}\,\text{M} \] For \(K_2SO_4\): \[ i=3 \] Temperature \(=27^\circ C = 300\,K\) \[ \pi=iCRT \] \[ \pi=3\times(1.435\times10^{-4})\times0.083\times300 \] \[ \pi\approx0.0107\,\text{bar} \] Thus Statement II is true. Hence the correct option: \[ \text{Statement I is false but Statement II is true} \]