Determining the molar mass of a substance by the osmotic pressure as a function of a mass concentration

Let's say that I have a solution of some substance in some solvent. The density of the solute is $$\rho_\text{solute}$$ and the density of the solvent is $$\rho_\text{solvent}$$. Suppose that the osmotic pressure of this solution is $$\Pi(\gamma) = k\gamma$$ where $$k$$ is some constant. We know that osmotic pressure is generally given by $$\Pi = icRT.$$ If we express the molar concentration as $$c = \gamma / M$$ and rearrange the equation, we get $$\Pi(\gamma) = \frac{iRT}{M}\gamma.$$ That means that $$k = \frac{iRT}{M}.$$ Now, if I know the constant $$k$$, but not the temperature $$T$$, that means that I can't calculate the molar mass $$M$$? Is there maybe another way to calculate it? Perhaps using the given densities? Thank you in advance.

• Well, the temperature can be determined from the density of the solvent. Or estimated. Sep 7, 2023 at 14:02
• By that, do you mean looking at charts or something else? @Poutnik Sep 7, 2023 at 14:53
• Charts or using empirical formulas. But estimation of T could be good enough. Sep 7, 2023 at 14:55
• If you have been able to calculate the constant $k$ in an osmosis experiment, it means that you know the formula and the molar mass of the solute (and the temperature). Sep 7, 2023 at 16:33
• I was given the value of $k$ and need to find out the molar mass. Sep 7, 2023 at 19:22