There is a solution of a protein $S$ with a concentration of $1553\frac{g}{100\;mL.} $ This solution is placed on one side of a semipermeable membrane, the other compartment being filled with pure water. One observes at $25^ oC$ a $157\;mm$ depression on the water side.
Determine the molar mass of the protein.
International System of Units (SI):
$\Pi$ $=$ $\rho\;g\;h$ $=$ $10^3\cdot 9.8\cdot 0.157 Pa$ $=$ $\frac{10^3\cdot 9.8\cdot 0.157\cdot 10^{-5}}{1.013}$ $ =$ $0.0152\; atm$
Van t'Hoff:
$\Pi$ $=[S]RT$ $=$ $[S]0.082\cdot 298 \; atm$
$[S]$ $=$ $\frac{0.0152}{0.082\cdot 298}$ $=$ $ 6.22\cdot 10^{-4}\frac{mol}{L}$
In $100\;mL$:
$n_S=[S]\cdot 10^{-1}$ $=$ $6.22\cdot 10^{-5}mol$
$M_S=\frac{m_S}{n_S}$ $=$ $\frac{1.553\;g}{6.22\cdot 10^{-5}}$ $=$ $2.50\cdot 10^4 \frac{g}{mol}$
