Answer : The mass percent of ethanol is, 10.38 % and the molality of ethanol is, 2.52 mole/kg
Explanation :
In wine, the solute and solvent are ethanol and water respectively.
Given :
12.8 % ethanol by volume means 12.8 mL ethanol present in 100 mL solution.
Volume of ethanol = 12.8 mL
Volume of solution = 100 mL
Volume of water = 100 - 12.8 = 87.2 mL
Density of ethanol = ![0.789g/cm^3=0.789g/mL](https://tex.z-dn.net/?f=0.789g%2Fcm%5E3%3D0.789g%2FmL)
Density of water = 1 g/mL
Now we have to calculate the mass of ethanol and water.
![\text{Mass of ethanol}=\text{Density of ethanol}\times \text{Volume of ethanol}=0.789g/mL\times 12.8mL=10.1g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20ethanol%7D%3D%5Ctext%7BDensity%20of%20ethanol%7D%5Ctimes%20%5Ctext%7BVolume%20of%20ethanol%7D%3D0.789g%2FmL%5Ctimes%2012.8mL%3D10.1g)
and,
![\text{Mass of water}=\text{Density of water}\times \text{Volume of water}=1g/mL\times 87.2mL=87.2g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20water%7D%3D%5Ctext%7BDensity%20of%20water%7D%5Ctimes%20%5Ctext%7BVolume%20of%20water%7D%3D1g%2FmL%5Ctimes%2087.2mL%3D87.2g)
Now we have to calculate the total mass of 100 mL of wine.
Total mass of 100 mL of wine = 10.1 + 87.2 = 97.3 g
Now we have to calculate the mass percent of ethanol.
![\text{Mass of percent of ethanol}=\frac{\text{Mass of ethanol}}{\text{Total mass of solution}}\times 100](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20percent%20of%20ethanol%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20ethanol%7D%7D%7B%5Ctext%7BTotal%20mass%20of%20solution%7D%7D%5Ctimes%20100)
![\text{Mass of percent of ethanol}=\frac{10.1g}{97.3g}\times 100=10.38\%](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20percent%20of%20ethanol%7D%3D%5Cfrac%7B10.1g%7D%7B97.3g%7D%5Ctimes%20100%3D10.38%5C%25)
The mass percent of ethanol is, 10.38 %
Now we have to calculate the molality.
![Molality=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Mass of solvent}}](https://tex.z-dn.net/?f=Molality%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solute%7D%5Ctimes%201000%7D%7B%5Ctext%7BMolar%20mass%20of%20solute%7D%5Ctimes%20%5Ctext%7BMass%20of%20solvent%7D%7D)
Molar mass of ethanol = 46 g/mole
![Molality=\frac{10.1g\times 1000}{46g/mole\times 87.2g}=2.52mole/kg](https://tex.z-dn.net/?f=Molality%3D%5Cfrac%7B10.1g%5Ctimes%201000%7D%7B46g%2Fmole%5Ctimes%2087.2g%7D%3D2.52mole%2Fkg)
The molality of ethanol is, 2.52 mole/kg