Can you find the mass of solvent with mass of solute, volume of solution, and solution density?

If you have, for example, $\pu{10 g}$ of a solute dissolved into $\pu{100 ml}$ of a solution, and the solution density is $\pu{1.5 g ml^-1}$, can you just multiply $100\ \mathrm{ml} \times 1.5\ \mathrm{\frac{g}{ml}}$, then subtract the $\pu{10 g}$ of solute from the result to get the mass of the solvent in grams? 


Does that work or am I trying to do do this wrong?




That works! In most chemistry (but not nuclear reactions!), mass is always conserved, so 


$$m\_\text{solution} = m\_\text{solvent} + m\_\text{solutes}$$


Mass is also equal to density times volume, so


$$m\_\text{solution} = \rho\_\text{solution} V\_\text{solution} = m\_\text{solvent} + m\_\text{solutes}$$


Solving for $m\_\text{solvent}$:


$$m\_\text{solvent} = \rho\_\text{solution} V\_\text{solution} - m\_\text{solutes}$$


Which is exactly the calculation you did.


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