The density of ethanol is 0.789 g/cm^3 at 20°C. What volume of ethanol has a mass of 15.5 grams?

1 Answer
anor277
Jun 11, 2017

Well, by definition, #"density"="mass"/"volume"#

Explanation:

And given the quotient, if I have #"density"# and #"mass"#, I can work out the #"volume"# fairly easily:

#"volume"="mass"/rho=(15.5*cancelg)/(0.789*cancelg*cm^-3)~=20*cm^3#

Note that this is dimensionally consistent. We wanted an answer with units of volume, i.e. #mL-=cm^3#; we got an answer with units of #1/(cm^-3)=1/(1/(cm^3))=cm^3#, i.e. units of volume as required.......

Note that in terms of units...#1*cm^3-=(1xx10^-2*m)^3=1xx10^-6*m^3#...that is #"one millionth of a cubic metre"#, just as #1*L-=1*dm^3-=(1xx10^-1*m)^3#, that is #"one thousandth of a cubic metre"#. Capisce?

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