# How to find volume of substance from molar concentration

The concentration of a substance dissolved in water $i$ is known in (mol/m3), so is the molar mass in (g/mol) and the density in (g/m3).

I want to find the volume of this substance in m3.

I have two possible ideas for equations to use: $$\mathrm{volume}_i= \frac{\mathrm{mass}_i}{c_i \times M_{W,i}},$$ however, to use this equation I need to know the mass of the substance, which is not obvious.

Also I could use something like this: $$\mathrm{volume}_i = \frac{c_i \times M_{W,i} \times \mathrm{volume}_{?}}{\rho_i },$$ however, I'm not sure what volume$_?$ would be, as I don't know the volume of the solution and I am trying to find the volume of the substance $i$.

Any ideas how to find the mass in the first equation or the volume in the second equation, or other equations to use?

Extra comments: My real aim is to find the volume of the solution so I can use the following formula for volume concentration, where I already know the volume concentration $\phi_i$: $$\phi_i = \frac{\mathrm{volume}_i} {\mathrm{volume}_\mathrm{solution}}$$ or $$\mathrm{volume}_\mathrm{solution} = \frac{\mathrm{volume}_i} {\phi_i}$$

Nothing has been said about the actual volume of the solution, only concentration of the solution has been given.

Assume that $c$ moles of solute is present in 1m$^3$ of solution.

Then mass of solute=c*molar mass

volume of solute * density of solute = c* molar mass

From this equation, volume of solute can be known.

Clearly, if the volume of the solution increases, the volume of the solute will also increase. Since the volume of the solution has not been given, it must give you a hint to take the above assumption.

• See extra comments in original post. Also with my units and your calculation don't I end up with (g)=(g/m^3) if molar mass is in (g/mol). Maybe I am asking the impossible Mar 14, 2017 at 5:17
• You have not been given anything about this volume concentration term(in the question) that you made up on your own. You have been given Molarity(the units given are mol/m$^3$) and you have to use that. Mar 14, 2017 at 5:43
• Also, your volume concentration term in unitless and the concentration term(molarity) given in the question has units mol/m$^3$ Mar 14, 2017 at 5:47