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Stoichiometric Calculations

100 mg of a p...

Question

100 mg of a protein is dissolved in just enough water to make 10.0 mL of solution. If this solution has an osmotic pressure of 13.3 mm Hg at $25^{0} C$ , what is the molar mass of the protein?
[R=0.0821 L atm ${m o l}^{- 1}$ $K^{- 1}$ and 760 mm Hg=1 atm]

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Solution

Mass of protein $(w_{2}) = 0.1$ $g$
$R = 0.082$ $L a t m / (k m o l)$
$T = 298 K$
$π = 13.33$ mm of Hg $= \frac{13.33}{760} = 0.0175 a t m$

volume of solution $= 0.01 L$
Using,
$M_{2} = \frac{W_{2} R T}{π V}$
We get
$M_{2} = \frac{0.1 \times 0.082 \times 298}{0.0175 \times 0.01}$ $= 13963.42 g / m o l$

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