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?

Short answer

The density of the solid is 1.63 g/mL.

Step-by-step solution

Find mass of toluene

First, we need to find the mass of the toluene by subtracting the mass of the solid from the total mass of the solid and toluene combined. Mass of Toluene = Total mass - Mass of Solid Mass of Toluene = 58.58 g - 32.65 g = 25.93 g

Find the volume of toluene

Next, we will find the volume of toluene using its mass and density. Volume of Toluene = Mass of Toluene / Density of Toluene Volume of Toluene = 25.93 g / 0.864 g/mL = 30.02 mL

Find the volume of solid

Now, we will find the volume of the solid by subtracting the volume of toluene from the total volume of the solid and toluene combined. Volume of Solid = Total Volume - Volume of Toluene Volume of Solid = 50.00 mL - 30.02 mL = 19.98 mL

Calculate the density of the solid

Finally, we will determine the density of the solid using the mass of the solid and its volume. Density of Solid = Mass of Solid / Volume of Solid Density of Solid = 32.65 g / 19.98 mL = 1.63 g/mL Hence, the density of the solid is 1.63 g/mL.

Key concepts

mass and volume

In chemistry, understanding mass and volume is crucial for solving various problems. Mass refers to the amount of matter in an object and is typically measured in grams (g). Volume, on the other hand, is the amount of space that an object occupies, usually measured in milliliters (mL) or liters (L).
Knowing both mass and volume can help us calculate other important properties of materials, such as density. In our example, we have a mass of a solid, 32.65 g, and the total volume of both the solid and the liquid, which is 50.00 mL.

• Mass of the solid: 32.65 g
• Total volume of solid and liquid: 50.00 mL

By computing these two quantities correctly, we can move on to determining the density.

density formula

Density is a fundamental concept in chemistry defined as the mass of a substance per unit volume. The density formula is given by:$$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$$This is a powerful tool because it allows us to compare how much substance is packed in a given space, which is very useful when identifying substances.
In our exercise, we aim to find the density of the solid. To do this, we'll use the mass of the solid and its volume. With a few steps, we can determine the necessary variables to make this calculation:

• Calculate the mass of toluene, a liquid added in which the solid is insoluble.
• Determine the volume of both the solid and toluene based on the given densities.

With this information, we can find the precise density of the solid.

step-by-step solution

Solving the problem involves a clear step-by-step approach. Let's break it down:

**Step 1: Find Mass of Toluene**
Subtracting the mass of the solid from the combined mass of solid and liquid gives the mass of toluene:

• Mass of Toluene = 58.58 g - 32.65 g = 25.93 g

**Step 2: Determine Volume of Toluene**
Use the density of toluene to find its volume by rearranging the density formula:

• Volume of Toluene = $\frac{\text{Mass of Toluene}}{\text{Density of Toluene}}$
• = $\frac{25.93\text{g}}{0.864\text{g/mL}}=30.02\text{mL}$

**Step 3: Calculate Volume of Solid**
Subtract the volume of toluene from the total volume to find the volume of the solid:

• Volume of Solid = 50.00 mL - 30.02 mL = 19.98 mL

**Step 4: Compute Density of Solid**
Finally, using the mass and volume of the solid, find the density:

• Density of Solid = $\frac{32.65\text{g}}{19.98\text{mL}}=1.63\text{g/mL}$

This methodical approach ensures accuracy and understanding.

chemistry problem solving

Approaching chemistry problems can seem daunting, but breaking them down into manageable steps makes the process smoother. Let's keep these key techniques in mind:

• Understand the information given and what is being asked. Re-frame the problem if necessary to see it clearly (e.g., components of the mix).
• Use formulas and equations as tools. The density formula is crucial for finding relationships between mass and volume.
• Keep units consistent to avoid calculation errors. Whether working with grams, milliliters, or other units, make sure they align.

When facing similar exercises, rely on logical progression just as shown in the step-by-step solution. With practice, these chemistry problems will become much easier and insightful.