The density of toluene (C₇H₈) is 0.867 g/mL, and the density of thiophene (C₄H₄S) is 1.065 g/mL. A solution is made by dissolving 8.10 g of thiophene in 250.0 mL of toluene. (b) Calculate the molality of thiophene in the solution.

Verified step by step guidance

1. Calculate the moles of thiophene using its molar mass. The molar mass of thiophene (C_4H_4S) is calculated by adding the atomic masses of its constituent atoms: 4 carbon atoms, 4 hydrogen atoms, and 1 sulfur atom.
2. Determine the mass of toluene in kilograms. First, calculate the mass of toluene using its density (0.867 g/mL) and the volume of toluene (250.0 mL). Then, convert this mass from grams to kilograms.
3. Use the formula for molality: \( \text{molality} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). Substitute the moles of thiophene and the mass of toluene in kilograms into this formula.
4. Ensure that all units are consistent, particularly that the mass of the solvent is in kilograms and the amount of solute is in moles.
5. Review the calculation setup to ensure that the steps align with the definition of molality, which is the moles of solute per kilogram of solvent.

Key Concepts

Density

Density is defined as mass per unit volume, typically expressed in grams per milliliter (g/mL) for liquids. It is a crucial property that helps determine how substances interact in solutions. In this question, the densities of toluene and thiophene are provided, which are necessary for calculating the volume of the solute and the solvent in the solution.

Molality

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is particularly useful in situations where temperature changes may affect volume, as it relies on mass rather than volume. To calculate molality, one must first convert the mass of the solute into moles and the volume of the solvent into kilograms.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between grams and moles when calculating concentrations like molality. For thiophene, knowing its molar mass allows for the determination of how many moles are present in the given mass, which is a critical step in the molality calculation.