100 mg of a protein is dissolved in enough water to make 10.0mL of a solution.If this solution has an osmotic pressure of 13.3 mm Hg at $25^{\large\circ}C$.What is the molar mass of protein.

Question

$\begin{array}{1 1}13980.4gmol^{-1}\\12980.4gmol^{-1}\\11980.4gmol^{-1}\\10980.4gmol^{-1}\end{array} $

Answer 1

$V=10.0mL$

$\pi$=13.3mm Hg

$\Rightarrow \large\frac{13.3}{760}$ atm

$T=25^{\large\circ}C=25+273=298K$

R=0.0821L atm mol$^{-1}K^{-1}$

Molar mass $M=\large\frac{WRT}{\pi V}$

$\Rightarrow \large\frac{0.1\times 0.0821\times 298}{\Large\frac{13.3}{760}\normalsize\times 0.01}$

$\Rightarrow \large\frac{0.10\times 0.0821\times 298\times 760}{13.3\times 0.01}$

$\Rightarrow \large\frac{1859.4008}{0.133}$

$\Rightarrow 13980.4 g mol^{-1}$