To find the molality of acetonitrile (CH₃CN) in the solution, we use the formula:

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

Step 1: Calculate the moles of acetonitrile (CH₃CN).

The molar mass of acetonitrile is 41.05 g/mol.

$\text{Moles of acetonitrile} = \frac{\text{mass of acetonitrile}}{\text{molar mass of acetonitrile}} = \frac{50.3 \, \text{g}}{41.05 \, \text{g/mol}} \approx 1.224 \, \text{mol}$

Step 2: Convert the mass of benzene (solvent) into kilograms.

The mass of benzene is given as 80.0 g. To convert this to kilograms:

$\text{Mass of benzene in kg} = \frac{80.0 \, \text{g}}{1000} = 0.0800 \, \text{kg}$

Step 3: Calculate the molality.

Now, we can calculate the molality of acetonitrile:

$\text{Molality (m)} = \frac{1.224 \, \text{mol}}{0.0800 \, \text{kg}} \approx 15.3 \, \text{mol/kg}$

Final Answer:

The molality of acetonitrile in the solution is 15.3 mol/kg.

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Would you like further details or have any questions? Here are some related questions for you:

1. How would the molality change if the mass of acetonitrile were increased to 100 g?
2. How would the molality be affected if a different solvent, like water, were used instead of benzene?
3. How can molality be used to determine freezing point depression or boiling point elevation?
4. What is the difference between molality and molarity?
5. How do you calculate the molality in a dilute solution?

Tip: Always remember to convert the mass of the solvent into kilograms when calculating molality!