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# 100mg of a protein is dissolved in just enough water to make 10.0mL of solution.If this solution has an osmotic pressure of 13.3mm Hg at $25^{\large\circ}C$,what is the molar mass of the protein?(R=0.0821Latm $mol^{-1}K^{-1}$,760mm Hg =1atm)

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

$W=100mg=0.100g$
$V=10.0mL=0.01L$
$\pi=13.33$mm Hg=$\large\frac{13.3}{760}$ atm
$T=25^{\large\circ}C=25+273=298K$
R=0.0821L atm $mol^{-1}K^{-1}$
Molar mass $M=\large\frac{WRT}{\pi V}$
$\Rightarrow \large\frac{0.1\times 0.0821\times 298}{\Large\frac{13.3}{760}\times \normalsize 0.01}$
$\Rightarrow \large\frac{0.1\times 0.0821\times 298\times 760}{13.3\times 0.01}$
$\Rightarrow\large\frac{ 1859\times 4008}{0.133}$
$\Rightarrow 13980.4g mol^{-1}$