Answer the following: of aqueous solution of protein contains of protein, the osmotic pressure of…

Given: $\pi = 3\cdot05 \times 10^{-3}\text{ atm}$, $T = 298\text{ K}$, $V = 300\text{ ml} = 0\cdot3\text{ L}$, $w = 1\cdot85\text{ g}$, $R = 0\cdot0821\text{ L atm K}^{-1}\text{ mol}^{-1}$. $\pi = \frac{w R T}{M V} \Rightarrow M = \frac{w R T}{\pi V} = \frac{1\cdot85 \times 0\cdot0821 \times 298}{3\cdot05 \times 10^{-3} \times 0\cdot3} = \frac{45\cdot26}{9\cdot15 \times 10^{-4}} = 49464\text{ g mol}^{-1}$ Final answer: 49464 g mol-1

Given: $w = 2\cdot5\text{ g}$, $W = 120\text{ g} = 0\cdot12\text{ kg}$, $\Delta T_f = 0\cdot85\text{ K}$, $K_f = 5\cdot12\text{ K kg mol}^{-1}$, $M_{\text{theoretical}} = 94\text{ g mol}^{-1}$. $M_{\text{obs}} = \frac{K_f \times w}{\Delta T_f \times W} = \frac{5\cdot12 \times 2\cdot5}{0\cdot85 \times 0\cdot12} = \frac{12\cdot8}{0\cdot102} = 125\cdot49\text{ g mol}^{-1}$ van 't Hoff factor $i = \frac{M_{\text{th}}}{M_{\text{obs}}} = \frac{94}{125\cdot49} = 0\cdot749$ For dimerization ($2\text{C}_6\text{H}_5\text{OH} \rightleftharpoons (\text{C}_6\text{H}_5\text{OH})_2$), $i = 1 - \frac{\alpha}{2} \Rightarrow \alpha = 2(1 - i) = 2(1 - 0\cdot749) = 0\cdot502 = 50\cdot2\%$ Final answer: 50.2%

For $\text{KCl}$, dissociation occurs ($\text{KCl} \rightarrow \text{K}^+ + \text{Cl}^-$, $i \approx 2$), so observed molecular weight is half of theoretical molecular weight ($\sim 37\cdot25\text{ g mol}^{-1}$). For sucrose, no dissociation or association occurs ($i = 1$), so observed molecular weight is equal to theoretical molecular weight ($342\text{ g mol}^{-1}$).