Problem 70 - Chemistry: The Central Science

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 \(50.00\) 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 in the mixture

Use the given total mass of the solid and toluene together, as well as the mass of the solid, to find the mass of the toluene. Mass of Toluene = Mass of solid + Toluene mixture — Mass of solid Mass of Toluene = 58.58 g - 32.65 g = 25.93 g

Step 2: Calculate the volume of toluene in the mixture

Using the mass of Toluene we found in Step 1 and the given density of toluene, we can now determine the volume of the toluene in the mixture: Volume of Toluene = \( \frac{Mass_{toluene}}{Density_{toluene}} \) Volume of Toluene = \( \frac{25.93 \mathrm{~g}}{0.864 \mathrm{~g} / \mathrm{mL}} \) = 30.02 mL

Step 3: Determine the volume of the solid

Now we can find the volume of the solid in the mixture. Using the given total volume of the mixture and the volume of toluene we calculated in Step 2: Volume of solid = Total volume of mixture - Volume of Toluene Volume of solid = 50.00 mL - 30.02 mL = 19.98 mL

Step 4: Calculate density of the solid

Using the mass of the solid and the volume we calculated in Step 3, we can now determine the density of the solid: Density of solid = \( \frac{Mass_{solid}}{Volume_{solid}} \) Density of solid = \( \frac{32.65 \mathrm{~g}}{19.98 \mathrm{~mL}} \) = 1.63 g/mL The density of the solid is 1.63 g/mL.

Key Concepts

Mass and Volume Relationship

To understand the relationship between mass and volume, think of mass as the amount of 'stuff' or matter in an object, while volume measures how much space that object occupies. These two properties are fundamental in determining an object's density.
When placed in a container, a solid will displace a certain amount of fluid (if insoluble, like in our exercise), helping us measure its volume indirectly.

• Mass is often measured in grams (g) due to its small-scale, practical usage in chemistry.
• Volume is usually measured in milliliters (mL) in the context of liquids and small solid objects.

In our exercise, the solid's volume is deduced by subtracting the toluene's volume from the total liquid-solid mixture's volume. It's a neat way chemistry teaches us to utilize physical relationships to extract needed information. Mass and volume interplay critically in various scientific and everyday scenarios.

Density Calculation

Calculating density is straightforward if you know an object's mass and volume. Density is a property that describes an object's compactness. Mathematically, it is expressed as:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]For the solid in question, we've determined the mass using a scale, and the volume through displacement in a solvent (toluene) in which it is insoluble. This method is practical in laboratory settings where direct volume measurement might be challenging.

• Density is expressed in units of mass per unit volume, such as grams per milliliter \( \text{g/mL} \).
• Knowing density helps identify a material, assess its purity, or infer other properties.

Once you've isolated the mass and volume: plug them into the formula above. For instance, if the mass of the solid is 32.65 g, and its volume is 19.98 mL, its density becomes \(1.63 \text{ g/mL}\). This numerical insight reveals much about the physical characteristics of the solid.

Insolubility in Solvents

Insolubility is an important factor when mixing different substances. If a solid is insoluble in a liquid, it won't dissolve, meaning you can use the liquid to find its volume by displacement, as in the solid-toluene mixture.

• Insoluble compounds remain distinct and separate from the liquid.
• This property is helpful in labs where separation or isolation of components is needed.

Practically, if you put an insoluble solid like the one discussed in water or any solvent, it remains separate, allowing you to observe and measure effects like volume displacement. Insolubility aids in various scientific techniques from simple volumetric analysis, seen here, to more complex separation processes in industrial chemistry.