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Finding molarity, mole fraction & molality from density

practice problem is: Solution containing equal mass of glycerol (C3H8O5) and water has a density of 1.10g/mL.  Calculate molarity, mole fraction & molality.

I know the formulas for molarity, mole fraction & molality but I have no clue how to use the density to even begin sovling this problem.  I was thinking D=m/v needed to be used in some part but I'm not sure.  Glycerol would be 92.094g right? Is this problem saying water will be the same weight also? Any hints/points of direction would be greatly appreciated.

In every mL of solution there will be 0.55g each of glycerol and water as the density is 1.10g/mL and this volume of water will weigh 1.10g
So 1 ml of this solution will contain 0.55/92.094 moles of glycerol

So molarity of glycerol will be (0.55/92.094) x 1000 moles/L

Mole fraction of glycerol will be (I think)

Moles of glycerol/(moles of water + moles of glycerol)

(0.55/92.094)/(0.55/mass of 1 mole of H2O + (0.55/92.094))

I have not included the mass of 1 mole of H2O as I do not know what values of atomic mass you are to use, but it will be approximately 18g)

Molality is moles of solute/kg solution

We know there are 0.55/92.094 moles of glycerol in 1.10 g of solution ( or 1.10 x 10-3 kg)

So 1 kg will contain ((0.55/92.094)/1.10 x 10-3) x 1




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