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}* \text{Volume of ethanol}=0.789g/mL* 12.8mL=10.1g`

and,

`\text{Mass of water}=\text{Density of water}* \text{Volume of water}=1g/mL* 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}}* 100`

`\text{Mass of percent of ethanol}=(10.1g)/(97.3g)* 100=10.38\%`

The mass percent of ethanol is, 10.38 %

Now we have to calculate the molality.

`Molality=\frac{\text{Mass of solute}* 1000}{\text{Molar mass of solute}* \text{Mass of solvent}}`

Molar mass of ethanol = 46 g/mole

`Molality=(10.1g* 1000)/(46g/mole* 87.2g)=2.52mole/kg`

The molality of ethanol is, 2.52 mole/kg