Question

A bottle of wine contains 12.8% ethanol by volume. The density of ethanol (CH3OH) is 0.789 g/cm. Calculate the concentratic ethanol in wine in terms of mass percent and molality. Mass percent Molality =

Answer 1

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 = $0.789g/cm^3=0.789g/mL$

Density of water = 1 g/mL

Now we have to calculate the mass of ethanol and water.

$\text{Mass of ethanol}=\text{Density of ethanol}\times \text{Volume of ethanol}=0.789g/mL\times 12.8mL=10.1g$

and,

$\text{Mass of water}=\text{Density of water}\times \text{Volume of water}=1g/mL\times 87.2mL=87.2g$

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.

$\text{Mass of percent of ethanol}=\frac{\text{Mass of ethanol}}{\text{Total mass of solution}}\times 100$

$\text{Mass of percent of ethanol}=\frac{10.1g}{97.3g}\times 100=10.38\%$

The mass percent of ethanol is, 10.38 %

Now we have to calculate the molality.

$Molality=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Mass of solvent}}$

Molar mass of ethanol = 46 g/mole

$Molality=\frac{10.1g\times 1000}{46g/mole\times 87.2g}=2.52mole/kg$

The molality of ethanol is, 2.52 mole/kg