Molality = (0.96)/(0.04*18/1000)......no of !oles of ethanol'...0.96....ttl weight of water...= 0.04 *18/1000....

The molality of a solution is defined as the number of moles of solute per kilogram of solvent. In this case, we need to calculate the molality of ethanol in water when the mole fraction of ethanol is given as 0.040.

Step 1: Understanding mole fraction
Mole fraction is the ratio of the number of moles of one component to the total number of moles in the solution. It is calculated by dividing the moles of a particular component by the total moles in the solution.

Step 2: Determining moles of ethanol and water
In this case, we have the mole fraction of ethanol as 0.040. This means that for every 100 moles of solution, 4 moles are ethanol and the remaining 96 moles are water. Since the mole fraction is a ratio, we can assume any number of moles for the solution, such as 100 moles.

To calculate the moles of ethanol and water, we multiply the respective mole fractions by the total number of moles assumed for the solution:
- Moles of ethanol = 0.040 * 100 = 4 moles
- Moles of water = 0.960 * 100 = 96 moles

Step 3: Calculating the mass of water
The molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water. To calculate the mass of water, we need to convert the moles of water to grams and then to kilograms.

The molar mass of water (H2O) is approximately 18 g/mol. Therefore, the mass of 96 moles of water is:
- Mass of water = 96 moles * 18 g/mol = 1728 g

To convert grams to kilograms, we divide the mass by 1000:
- Mass of water in kg = 1728 g / 1000 = 1.728 kg

Step 4: Calculating the molality
Now that we have the moles of ethanol (4 moles) and the mass of water (1.728 kg), we can calculate the molality using the formula:

Molality (m) = moles of solute / mass of solvent (in kg)

Plugging in the values:
Molality = 4 moles / 1.728 kg ≈ 2.31 mol/kg

Conclusion:
The molality of ethanol in water, with a mole fraction of ethanol equal to 0.040, is approximately 2.31 mol/kg.