I would like to make an NaCl and water solution with a density of 1.2 g/ml. How would you calculate the grams of NaCl required to make a 1000 ml solution?

I have used density of mixture = (mass NaCl + mass H2O)/1000 ml and solved for the mass of NaCl. However, the resulting mass does not give a density of 1.2 g/ml in practice (and in fact does not dissolve) so is there another way of calculating this? (at room temperature (~21 °C))

  • $\begingroup$ The density also depends on the temperature.. $\endgroup$ – ParaH2 Mar 8 '16 at 22:40

To answer in detail Jan, I didn't make stranged calculus, now I answered more than a year ago I can't tell you if my calculus are the same, but here is the logic.

For any solution (aqueous) we have, $$m_{solution}=\rho_{solution}\times V \tag1$$

We also have, $$\rho_{solution}=d\times \rho_{water} \tag2$$

where d is the relative density of the solution and then, merging both $(1)$ and $(2)$, $$m_{solution}=d \times \rho_{water}\times V \tag3$$

The mass of solute in the solution is a percentage of the masse of the whole solution then, because,

$$n_{solute}=\frac{m_{solute}}{M_{solute}} \tag4$$

We have,

$$n_{solute}=\frac{p\times d \times \rho_{water}\times V}{100\times M_{solute}}\tag5$$

Then find my previous result with $C\times V=n_{solute}$.

Now I think everyone is able to goes from molar to mass concentration then I can stop here. If not ask me.


The answer is: as much as water can dissolve.

The density of saturated sodium chloride in water at 21°C is $1.20~\pu{g cm^{-3}}$.

So you may take roughly $1000~\pu{ml}$ water of 21°C and put in sodium chloride such that not all of it can be dissolved (it will take some 400 grams). From the resulting solution‘s supernatant take $1000~\pu{ml}$.

  • $\begingroup$ table of densities at 60 F (15.5 C). brinemaker.com/TechnicalDocument/Sodium-Chloride-Table.pdf $\endgroup$ – MaxW Oct 9 '17 at 4:26
  • $\begingroup$ How do you do if in your laboratory water is at 25°C ? :-) $\endgroup$ – ParaH2 Oct 9 '17 at 15:32
  • 1
    $\begingroup$ At 25°C and normal pressure there exists no such thing as sodium chloride solution with a density of 1.2000 g/ml (as requested). You had to live with a density of about 1.1978 g/ml which is 1.2 g/cm when rounded to two significant figures. ;-) $\endgroup$ – aventurin Oct 9 '17 at 18:14

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