To calculate the molality of ethanol in the solution, we use the following formula for molality:

$\text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$

Step 1: Calculate the moles of ethanol

The molar mass (MM) of ethanol is given as 46.07 g/mol.

$\text{moles of ethanol} = \frac{\text{mass of ethanol}}{\text{MM of ethanol}} = \frac{161.5 \, \text{g}}{46.07 \, \text{g/mol}} \approx 3.51 \, \text{mol}$

Step 2: Convert the mass of water to kilograms

The mass of water is 120.0 g. To convert this to kilograms:

$\text{mass of water in kg} = \frac{120.0 \, \text{g}}{1000} = 0.1200 \, \text{kg}$

Step 3: Calculate the molality

Now we can calculate the molality:

$\text{Molality} = \frac{3.51 \, \text{mol}}{0.1200 \, \text{kg}} \approx 29.25 \, \text{mol/kg}$

Final Answer:

The molality of ethanol in the solution is approximately 29.25 mol/kg.

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Would you like more details on any of these steps? Here are some related questions:

1. How does molality differ from molarity in solutions?
2. Why do we use kilograms for the solvent in molality calculations?
3. What is the role of molar mass in determining moles of a substance?
4. How does temperature affect molality and molarity differently?
5. What are some common methods for preparing a solution of known molality?

Tip: Always double-check unit conversions (e.g., grams to kilograms) to ensure accurate calculations.