Problem 82 - Chemistry The Central Science In Si Units

Question

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 \(50.00 \mathrm{~mL}\). The solid and toluene together weigh \(58.58 \mathrm{~g}\). The density of toluene at the temperature of the experiment is \(0.864 \mathrm{~g} / \mathrm{mL}\). What is the density of the solid?

Step-by-Step Solution

Answer

The density of the solid is 1.63 g/mL.

Step 1: Determine the Mass of Toluene

The mass of the toluene can be found by subtracting the mass of the solid from the total mass of the solid and toluene together. Given: - Mass of solid = 32.65 g - Total mass (solid + toluene) = 58.58 g Thus, the mass of toluene is: \[\text{Mass of toluene} = 58.58\,\text{g} - 32.65\,\text{g} = 25.93\,\text{g}.\]

Step 2: Calculate the Volume of Toluene

Use the mass and density of toluene to find its volume. Density formula is: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] Rearrange to find volume: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \] Given density of toluene is 0.864 g/mL: \[ \text{Volume of toluene} = \frac{25.93\,\text{g}}{0.864\,\text{g/mL}} = 30.01\,\text{mL}.\]

Step 3: Calculate the Volume of the Solid

The total volume of the solid and toluene together is given as 50.00 mL, and the volume of the toluene has been calculated as 30.01 mL. Thus, the volume of the solid is: \[ \text{Volume of solid} = 50.00\,\text{mL} - 30.01\,\text{mL} = 19.99\,\text{mL}.\]

Step 4: Calculate the Density of the Solid

The density of the solid can be calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] We have the mass of the solid as 32.65 g and its volume as 19.99 mL. Thus, the density of the solid is: \[ \text{Density of solid} = \frac{32.65\,\text{g}}{19.99\,\text{mL}} = 1.63\,\text{g/mL}.\]

Key Concepts

Mass and Volume Relationship

The relationship between mass and volume is fundamental in understanding density, which is defined as mass per unit volume. It helps us evaluate how much mass an object has in a given space, which is crucial for identifying substances and their properties. In our exercise, we're tasked with finding the density of a solid. To do this, we first need to find both the mass and volume. The volume of the solid can be calculated by considering the total volume of both solid and liquid, then subtracting the liquid's volume, which is derived from its mass and density. The mass and volume relationship can be illustrated through density itself:

• Density Formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

The beauty of the density formula is how it relates two measurable physical quantities, making the concept rather tangible. By determining these values, you can solve many types of problems, like identifying a material or predicting if it will float in a certain liquid.

Solubility

Solubility is a key property that determines whether a substance will dissolve in a particular solvent. It is influenced by the nature of the solvent and solute, temperature, and pressure. In the context of our problem, solubility plays a crucial role. The solid in the exercise is identified as insoluble in toluene. This means it does not dissolve when mixed together and allows for the calculation of its physical properties separately from the toluene. Understanding solubility involves:

• Different types of solutions, such as saturated, unsaturated, and supersaturated.
• The impact of intermolecular forces in determining solubility.

Knowing whether a solid is soluble in a solvent can significantly alter the calculation of density and other physical properties, as dissolution can change both the mass and apparent volume of the substance. Given these factors, ensuring a correct perception of solubility can lead to more accurate scientific inquiries and everyday problem-solving.

Physical Properties of Substances

Understanding the physical properties of substances is pivotal in chemistry and everyday life. These properties, like color, density, boiling point, and melting point, help identify substances and predict how they will behave under different conditions. In the given exercise, density is the primary physical property calculated. Density is intrinsic and unique to each substance, which makes it extremely valuable in identifying materials. Physical properties can include:

• Density: A measure of mass per unit volume, crucial in identifying and comparing substances.
• Solubility: Defines how a substance interacts with solvents, which can affect whether substances can be mixed.
• Boiling/Melting Points: Temperature points where substances change states, essential in processes like distillation.

Understanding these properties leads to better material selection in processes like manufacturing, chemical reactions, and even cooking! Knowing how substances behave helps us create better tools and products and leads to deeper insights into the world around us.