The Calculation of Molality in a 49% Ethanol Solution

How do you calculate the concentration of ethanol in molality in a 49% ethanol solution?

Given that a particular liquor is 49.0% ethanol (CH3CH2OH) by volume, with a density of ethanol at 0.789 g/mL and the density of water at 0.998 g/mL, how do you calculate the molality of ethanol in the solution?

Molality Calculation in a 49% Ethanol Solution

The molality of ethanol in the solution is 0.0165 mol/kg.

To calculate the molality of a 49% by volume ethanol solution, we start by determining the mass of ethanol and water in 100 mL of the solution using their densities. For ethanol, with a density of 0.789 g/mL, the mass of 49 mL ethanol is calculated as:

Mass of ethanol = Density of ethanol × Volume of ethanol = 0.789 g/mL × 49 mL = 38.661 g

Assuming the density of water is 0.998 g/mL, the mass of 51 mL water is calculated as:

Mass of water = Density of water × Volume of water = 0.998 g/mL × 51 mL = 50.898 g

The next step involves converting the mass of ethanol to moles using the molar mass of ethanol (46.07 g/mol):

Moles of ethanol = Mass of ethanol / Molar mass of ethanol = 38.661 g / 46.07 g/mol = 0.839 moles

To find the molality, we divide the moles of ethanol by the mass of water in kilograms:

Molality of ethanol = Moles of ethanol / Kilograms of water = 0.839 moles / 0.050898 kg = 16.49 mol/kg

Thus, the molality of ethanol in the solution is 0.0165 mol/kg, indicating the concentration of ethanol in the 49% solution.