Calculation of Molality of Acetone in Solution

Given:
Mole fraction of acetone in ethyl alcohol = 0.3

Molality is defined as the number of moles of solute per kilogram of solvent. To calculate the molality of acetone in the solution, we need to determine the number of moles of acetone and the mass of the solvent (ethyl alcohol).

Step 1: Calculation of Moles of Acetone

Mole fraction (X) is defined as the ratio of the moles of the component to the total moles of all components in the solution. Mathematically, mole fraction (X) can be expressed as:

X = (moles of component) / (total moles of all components in solution)

In this case, the mole fraction of acetone (X) is given as 0.3. We can rearrange the equation to solve for the moles of acetone:

moles of acetone = X * total moles of all components in solution

Since ethyl alcohol is the solvent and acetone is the solute, the total moles of all components in the solution can be represented as:

total moles of all components in solution = moles of acetone + moles of ethyl alcohol

Step 2: Calculation of Moles of Ethyl Alcohol

From the given information, we know the mole fraction of acetone (X) is 0.3. Therefore, the mole fraction of ethyl alcohol can be calculated as:

mole fraction of ethyl alcohol = 1 - mole fraction of acetone
= 1 - 0.3
= 0.7

Using the same equation as in Step 1, we can calculate the moles of ethyl alcohol:

moles of ethyl alcohol = mole fraction of ethyl alcohol * total moles of all components in solution

Step 3: Calculation of Mass of Ethyl Alcohol

To calculate the mass of ethyl alcohol, we need to know its molar mass (M). The molar mass of ethyl alcohol (C2H5OH) is approximately 46.07 g/mol.

mass of ethyl alcohol = moles of ethyl alcohol * molar mass of ethyl alcohol

Step 4: Calculation of Molality

Molality (m) is defined as the ratio of the moles of solute to the mass of the solvent in kilograms. Mathematically, molality can be expressed as:

molality = (moles of solute) / (mass of solvent in kg)

In this case, the moles of solute is the moles of acetone calculated in Step 1, and the mass of solvent is the mass of ethyl alcohol calculated in Step 3.

molality of acetone in solution = moles of acetone / (mass of ethyl alcohol in kg)

Summary:
To calculate the molality of acetone in the solution, we followed the following steps:
1. Calculate the moles of acetone using the mole fraction of acetone and the total moles of all components in the solution.
2. Calculate the moles of ethyl alcohol using the mole fraction of ethyl alcohol and the total moles of all components in the solution