# How to calculate the molar mass of a protein from its osmotic pressure?

I am unsure how to go about solving this question. I know how to get the osmotic pressure, but where do I go from there?

I can't use the gas law since the protein is not a gas.

$$\pu{2.38 g}$$ of a protein is dissolved in $$\pu{100 mL}$$ of water at $$\pu{25^\circ C}$$. The solution rises to a height of $$\pu{8.5 cm}$$ in an osmometer (a device for measuring osmotic pressure). What is the molar mass, in grams per mole, of the protein?

Data: assuming the water ls pure, then the osmotic pressure $$\pi = \rho gh$$, where $$h$$ is the height of the water, $$\rho$$ is the density of water ($$\pu{1 g/cm^3}$$),and $$g$$ is the acceleration due to gravity ($$\pu{9.81 m/s^2})$$.

UPDATE: I've spoken with a masters student (my TA) about this and it turns out that the way to solve this is to use an osmotic pressure equation which is identical to the ideal gas law, but only because it is an approximation. If this question is unlocked I would be happy to share my answer.

• I'd like to answer this question myself now. I didn't want to give my original workings when I asked this question because I did not want to lead people into the same method that I used. The reason this confused me so much was because the osmotic pressure equation used is identical to the ideal gas law--which I had a long discussion with a masters student and have obtained a basic grasp of the concept (though the relation to the ideal gas law is still odd); anyway, if someone unlocks this I would be happy to provide an answer myself. – Klik Dec 26 '14 at 18:05

Use osmotic pressure $Π=iMRT$
It seems to me that you should use Morse equation $\mathrm{\Pi=iMRT}$ - from your data you should get $\mathrm{M}$ - molarity and then molar mass of the protein. You can skip $\mathrm{i}$ - it's not a problem if it's a dimer or oligomer.