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. (a) Calculate the mole fraction of thiophene in the solution.

Verified step by step guidance

1. Step 1: Calculate the number of moles of each component. The number of moles is given by the formula: n = mass / molar mass. The molar mass of thiophene (C4H4S) is approximately 84.14 g/mol and the molar mass of toluene (C7H8) is approximately 92.14 g/mol.
2. Step 2: Use the given mass of thiophene (8.10 g) and the molar mass from step 1 to calculate the number of moles of thiophene.
3. Step 3: Use the given volume of toluene (250.0 mL), the density of toluene (0.867 g/mL), and the molar mass from step 1 to calculate the number of moles of toluene.
4. Step 4: The mole fraction of a component in a solution is given by the formula: X = n_component / n_total. Calculate the total number of moles (n_total) by adding the number of moles of thiophene and toluene.
5. Step 5: Substitute the number of moles of thiophene and the total number of moles into the formula from step 4 to calculate the mole fraction of thiophene in the solution.

Key Concepts

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the mixture. This concept is crucial for understanding the composition of solutions and is often used in calculations involving colligative properties.

Density and Volume Relationship

Density is defined as mass per unit volume and is a key property of substances. In this context, knowing the density of toluene allows us to convert the volume of toluene (250.0 mL) into mass, which is necessary for calculating the total number of moles in the solution. Understanding this relationship is essential for solving problems involving solutions and mixtures.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the mole fraction of thiophene, we need to determine the number of moles of thiophene and toluene. This requires knowing the molar masses of both compounds, which can be calculated from their chemical formulas by summing the atomic masses of their constituent elements.