Percent solution?

Question

A bottle of wine contains 12.5% ethanol by volume. the density of ethanol is 0.789 g/cm3. calculate the concentration of ethanol in wine in terms of mass percent and molality

Answer 1

12.5% (v/v) means you have 12.5 ml ethanol in 100 ml wine

Find out how much the 12.5 ml of ethanol weigh with the help of the density
d=mass/V => mass=d*V =0.789*12.5 = 9.86
the % (w/v) is g per 100 ml of wine so it is 9.86% (w/v)

MolaRity (M) is mole ethanol per 1 L wine so we multiply 9.86% (w/v) by 10 to have the g in 1L and divide by the molecular weight to get convert grams into moles: 10*9.86/46 =2.14 M

MolaLity (m) is mole of ethanol per Kg of solvent. Assuming that we have only ethanol and water, that the density of water is 1 g/ml and that the volume of the solution is exactly equal to the sum of the volume of solvent and solute...
we had 12.5 ml ethanol per 100 ml of solution so we have 100-12.5=87.5 ml water. Since dwater=1 g/ml that corresponds to 87.5 g water.
So 9.86 g ethanol per 100ml solution correspond to
0.214 mole ethanol per 87.5 g water
so (0.214/87.5)*1000 mole Ethanol per 1 Kg water = 2.45 m

Finally, we know that
100ml of solution are 12.5ml ethanol and 87.5 ml water or
12.5*0.789= 9.86 g ethanol and 1*87.5=87.5 g water

so 100 ml of solution weigh 9.86+87.5 = 97.36 g

9.86 g ethanol in 97.36 g solution
x .. .. .. .. .. .. .. ..100

x =(9.86/97.36)*100 = 10.13 % (w/w)

So now you have the concentration expressed in all possible ways