How many grams of sulfur (S) must be dissolved in 100.0 g of naphthalene (C10H8) to make a 0.12 m solution?

Verified step by step guidance

Step 1: Understand the definition of molality (m), which is the number of moles of solute per kilogram of solvent. In this problem, the solute is sulfur (S) and the solvent is naphthalene (C10H8).

Step 2: Calculate the moles of sulfur needed using the formula for molality: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). Rearrange the formula to find moles of solute: \( \text{moles of solute} = m \times \text{kilograms of solvent} \).

Step 3: Convert the mass of the solvent from grams to kilograms. Since the mass of naphthalene is given as 100.0 g, convert it to kilograms by dividing by 1000.

Step 4: Use the molality value (0.12 m) and the converted mass of the solvent in kilograms to calculate the moles of sulfur needed.

Step 5: Convert the moles of sulfur to grams using the molar mass of sulfur. The molar mass of sulfur (S) is approximately 32.07 g/mol. Multiply the moles of sulfur by its molar mass to find the mass in grams.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity and Molality

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution, while molality (m) is defined as the number of moles of solute per kilogram of solvent. In this question, we are dealing with molality, which is particularly useful when the temperature may affect the volume of the solution.

Calculating Moles

To determine how many grams of sulfur are needed, we first need to calculate the number of moles required for the desired molality. The formula for molality is m = moles of solute / mass of solvent (in kg). Rearranging this formula allows us to find the moles of solute needed based on the given mass of naphthalene.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). For sulfur, the molar mass is approximately 32.07 g/mol. Knowing the molar mass is essential for converting between grams and moles, which is necessary to find out how many grams of sulfur are required to achieve the specified molality.

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