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I conducted an experiment to separate methanol and water. I am trying to determine the mole fraction of the distillate collected but having a little trouble with the calculation.

The flow rate was $\pu{55 ml/min}.$ When I collected my sample, I got a specific density of $0.815$ and a volume of $\pu{334 ml}.$ I tried to work out the mass, but I cannot use specific density as it is a dimensionless ratio.

Would I just assume the specific density is the density and set units to $\pu{g/cm3}$ so I can get the mass of the distillate and the concentration, and then determine the mole fraction from there, or does that not make sense?

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  • $\begingroup$ How exactly you got specific density ? By areometer, or by pyknometry ? Are you sure your result is unitless as the true ratio ? Or, can it be the case the units are implied ? E.g areometers provide density in implied units. Pyknometry should provide results in units, considering temperature and water density. Sure, if you just took the mass ratio, you got massless specific gravity. $\endgroup$
    – Poutnik
    Sep 26, 2019 at 7:13
  • $\begingroup$ The density was measured with a hydrometer. Well the density value is a ratio so it must be unit less. $\endgroup$
    – Emm
    Sep 26, 2019 at 16:05
  • $\begingroup$ Well, the buoyancy is independent on water density. $\endgroup$
    – Poutnik
    Sep 26, 2019 at 16:10

1 Answer 1

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Yes, you can do that.

Specific gravity is considered as unitless ratio of density related to water density.

Density as a specific mass is mass per volume, in $\pu{ g/cm^3}$ or $\pu{ kg/m^3}$

Regardless of country specific quantity naming convention:

Numerically, for 3 valid decimal digits,considering value uncertainty, the unitless quantity and quantity in $\pu{g/cm^3}$ are about interchangeable at $\pu{20 ^{°}C}$, as water density is near $\pu{0.9982 g/cm^3}$

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    $\begingroup$ Density should be mass/volume. Specific gravity is density of substance relative to density of water and thus unitless. Since the density of water is near 1, Density $\approx$ Specific gravity $\endgroup$
    – MaxW
    Sep 25, 2019 at 18:13
  • $\begingroup$ @MaxW I have never heard the term specific gravity, only density ( relative specific mass ) and ( absolute) specific mass. But the truth is, it is translation to English. In English speaking countries, it may be different, so you may be right, also, consulting the Wikipedia. Generally, specific quantities are not unitless. like conductivity being specific conductance as conductance of 1m cube,, or specific heat capacity as heat capacity per mass. $\endgroup$
    – Poutnik
    Sep 26, 2019 at 0:13

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