# Get the molar mass of a polymer in a mixture given its osmotic pressure

Have a dissolution with $12$g of an unknown polymer for each liter of solution at $25^\text{o}$C has an osmotic pressure of $12.1$ torr. What is the molar mass of the polymer?

Apparently the formula for osmotic pressure is

$$M\cdot R\cdot T$$

That's

$$0.0159 = M\cdot 0.0821\cdot 298$$

Therefore the molarity is

$$M = \frac{0.0159}{0.0821\cdot 298} = 0.000649$$

The formula for Molarity is

$$\frac{\text{moles of this polymer}}{\text{liters of dissolution}} = 0.000649$$

They ask me for the molar mass of the polymer, but how do I find it?

You have 0.000649 moles of something that weighs (has a mass of) 12 g. Thus, molar mass is: $${12\;{\rm g}\over 0.000649\;{\rm mol}} = 18490\;{\rm g\over mol}$$