1. Understand Molality

Molality (m) is a way to express concentration. It's defined as the number of moles of solute dissolved per kilogram of solvent.

2. Set Up the Equation

We know:

* Molality (m) = 0.13 mol/kg

* Mass of solvent (naphthalene) = 100.0 g = 0.100 kg (remember to convert grams to kilograms)

Let:

* x = mass of sulfur (solute) in grams

3. Calculate the Moles of Sulfur

We need to find the number of moles of sulfur (x) that will give us the desired molality. Using the molality definition:

0.13 mol/kg = x moles / 0.100 kg

Solving for x:

x moles = 0.13 mol/kg * 0.100 kg = 0.013 moles

4. Convert Moles to Grams

To find the mass of sulfur (x) in grams, we'll use the molar mass of sulfur (32.07 g/mol):

x grams = 0.013 moles * 32.07 g/mol = 0.417 grams

Answer: You need to dissolve 0.417 grams of sulfur in 100.0 g of naphthalene to make a 0.13 m solution.