A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?

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Calculate the mass of the toluene by subtracting the mass of the solid from the total mass of the solid and toluene: \( m_{\text{toluene}} = 58.58 \text{ g} - 32.65 \text{ g} \).

Use the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the volume of the toluene: \( V_{\text{toluene}} = \frac{m_{\text{toluene}}}{0.864 \text{ g/mL}} \).

Determine the volume of the solid by subtracting the volume of the toluene from the total volume: \( V_{\text{solid}} = 50.00 \text{ mL} - V_{\text{toluene}} \).

Calculate the density of the solid using the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) with the mass of the solid and the volume of the solid: \( \text{Density}_{\text{solid}} = \frac{32.65 \text{ g}}{V_{\text{solid}}} \).

Ensure all units are consistent and check calculations for accuracy.

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Key Concepts

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

Density

Density is defined as mass per unit volume, typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). It is a physical property that helps identify substances and can be calculated using the formula: density = mass/volume. Understanding density is crucial for solving problems involving mixtures and solutions, as it allows for the determination of how substances interact in a given volume.

Mass and Volume Relationships

In chemistry, the relationship between mass and volume is fundamental for calculating densities and understanding how substances behave in mixtures. When a solid is added to a liquid, the total mass is the sum of the individual masses, while the total volume is the sum of the individual volumes. This relationship is essential for determining the density of the solid when it is mixed with a liquid, especially when the solid is insoluble.

Buoyancy and Insolubility

Buoyancy refers to the ability of an object to float in a fluid, which is influenced by the densities of both the object and the fluid. In this scenario, the solid is insoluble in toluene, meaning it does not dissolve and retains its own volume when mixed. This property is important for calculating the density of the solid, as it allows for the use of the total mass and volume of the system to isolate the solid's characteristics.