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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?

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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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