Answer:
The mass percentage of the solution is 10.46%.
The molality of the solution is 2.5403 mol/kg.
Explanation:
A bottle of wine contains 12.9% ethanol by volume.
This means that in 100 mL of solution 12.9 L of alcohol is present.
Volume of alcohol = v = 12.9 L
Mass of the ethanol = m
Density of the ethanol ,d= [tex]0.789 g/cm^3=0.789 g/mL[/tex]
[tex]1 cm^3=1 mL[/tex]
[tex]m=d\times v=0.798 g/ml\times 12.9 mL = 10.1781 g[/tex]
Mass of water = M
Volume of water ,V= 100 mL - 12.9 mL = 87.1 mL
Density of water = D=1.00 g/mL
[tex]M=D\times V=1.00 g/ml\times 87.1 mL =87.1 g[/tex]
Mass percent
[tex](w/w)\%=\frac{m}{m+M}\times 100[/tex]
[tex]\frac{10.1781 g}{10.1781 g+87.1 g}\times 100=10.46\%[/tex]
Molality :
[tex]m=\frac{m}{\text{molar mass of ethanol}\times M(kg)}[/tex]
M = 87.1 g = 0.0871 kg (1 kg =1000 g)
[tex]=\frac{10.1781 g}{46 g/mol\times 0.0871 kg}[/tex]
[tex]m=2.5403 mol/kg[/tex]
