Problem 37 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) To identify a liquid substance, a student determined its density, Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\). sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL}\) ) or toluene (density \(0.866 \mathrm{~g} / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires \(45.0 \mathrm{~g}\) of ethylene glycol, a liquid whose density is \(1.114 \mathrm{~g} / \mathrm{mL}\). Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the (d) A cubic piece of metal accuracy of measurement needed? measures \(5.00 \mathrm{~cm}\) on each edge. If the metal is nickel, whose density is \(8.90 \mathrm{~g} / \mathrm{cm}^{3}\), what is the mass of the cube?

Step-by-Step Solution

Answer

The calculated density of the unknown substance is \(0.856 \mathrm{~g/ mL}\), which is closer to the density of toluene ($0.866 \mathrm{~g/ mL}$), so the substance is likely toluene. The chemist should use a volume of approximately $40.3 \mathrm{~mL}$ of ethylene glycol to obtain $45.0 \mathrm{~g}$. The accuracy of a graduated cylinder for this measurement depends on its graduations and the chemist's ability to read the meniscus; more accurate measuring devices might be necessary for certain experiments. The mass of the nickel cube is approximately $1119 \mathrm{~g}$.

Step 1: Calculate the density

We need to calculate the density of the given substance by dividing its mass by its volume. The formula for density is: Density \(= \frac{Mass}{Volume}\) Mass \(= 38.5 \mathrm{~g}\) Volume \(= 45 \mathrm{~mL}\) Density \(= \frac{38.5 \mathrm{~g}}{45 \mathrm{~mL}}\)

Step 2: Compare the calculated density to given densities

After calculating the density of the given substance, we will compare it to the densities of isopropyl alcohol and toluene to identify the substance. Isopropyl alcohol density \(= 0.785 \mathrm{~g/ mL}\) Toluene density \(= 0.866 \mathrm{~g/ mL}\) (b) Calculating the Volume of Ethylene Glycol

Step 1: Use the given mass and density of ethylene glycol to calculate the volume

To find the volume of ethylene glycol, we can rearrange the density formula as: Volume \(= \frac{Mass}{Density}\) Mass \(= 45.0 \mathrm{~g}\) Ethylene glycol density \(= 1.114 \mathrm{~g/ mL}\) Volume \(= \frac{45.0 \mathrm{~g}}{1.114 \mathrm{~g/ mL}}\) (c) Graduated Cylinder Accuracy

Step 4: Comment on the likely accuracy of the graduated cylinder for measurement

The accuracy of a graduated cylinder is typically limited by the level of precision it can measure, which depends on the spacing of the graduation marks and the ability to read the meniscus level accurately. A chemist must consider whether the graduated cylinder provides sufficient accuracy for the specific experiment or if other more accurate measuring devices, like volumetric pipettes, should be used instead. (d) Calculating the Mass of the Nickel Cube

Step 1: Calculate the volume of the cube

To find the volume of the cube, we can use the formula: Volume \(= Length × Width × Height\) Since all edges are equal in length: Volume \(= (5.00 \mathrm{~cm})^{3}\)

Step 2: Use the given density and volume to calculate the mass

To find the mass of the nickel cube, we can use the rearranged density formula: Mass \(= Density × Volume\) Density \(= 8.90 \mathrm{~g/cm^{3}}\) Volume \(= (5.00 \mathrm{~cm})^{3}\) Mass \(= 8.90 \mathrm{~g/cm^{3}} × (5.00 \mathrm{~cm})^{3}\)

Key Concepts

Mass and Volume

Mass and volume are key concepts in understanding density. When calculating the density of a substance, it is important to measure both the mass and the volume accurately. Mass refers to the amount of matter in an object, typically measured in grams (g). Volume is the space that the substance occupies, measured in milliliters (mL) for liquids or cubic centimeters (cm³) for solids.

To find the density, you will use the formula:

• Density = \( \frac{Mass}{Volume} \)

For example, if a liquid has a mass of 38.5 g and a volume of 45 mL, the density is calculated as \( \frac{38.5 \, \text{g}}{45 \, \text{mL}} \).

This simple formula helps in identifying substances by comparing their calculated densities to known values.

Isopropyl Alcohol

Isopropyl alcohol is a common solvent and cleaning agent. It has a known density value of 0.785 g/mL. When identifying an unknown liquid, such as the one described in our exercise, you would calculate the density and compare it to the density of isopropyl alcohol. If the calculated density is close to 0.785 g/mL, the liquid could likely be isopropyl alcohol.

Remember:

• Isopropyl alcohol is often used in laboratories and households as a disinfectant.
• It evaporates quickly, which makes it a good cleaning agent.

Knowing the physical properties like density helps in proper identification and usage of the substance.

Toluene

Toluene is an aromatic hydrocarbon widely used as an industrial solvent. It is crucial to know its properties for safe handling and usage. Toluene has a density of 0.866 g/mL, which can be used to distinguish it from other liquids like isopropyl alcohol.

In an experimental setup where you need to identify toluene, you would calculate the density of your liquid sample. If the density matches or is close to 0.866 g/mL, you might be dealing with toluene. Toluene is known for:

• Having a distinctive, sweet smell.
• Being a common solvent in the manufacturing of paints, chemicals, and cleaning agents.

Using density calculations effectively helps differentiate similar substances.

Ethylene Glycol

Ethylene glycol is a key ingredient in antifreeze and coolants, known for its sweet taste and high boiling point. Its density is 1.114 g/mL, making it denser than both isopropyl alcohol and toluene. When needing a specific mass of ethylene glycol for an experiment, you can use its density to find the corresponding volume.

Here's how: To find how much liquid to use for 45.0 g of ethylene glycol, apply the formula:

• Volume = \( \frac{Mass}{Density} \)
• Volume = \( \frac{45.0 \, \text{g}}{1.114 \, \text{g/mL}} \)

This calculation ensures precise measurements for experimental procedures. Knowing the density of ethylene glycol is essential for its proper use in applications.

Nickel

Nickel is a metallic element with a characteristic density of 8.90 g/cm³. It is often used in alloys, plating, and batteries due to its durability and resistance to corrosion.

To find the mass of a nickel cube, you will first need to calculate the cube's volume. A cube measuring 5.00 cm on each edge has a volume given by:

• Volume = Length × Width × Height = \((5.00 \, \text{cm})^3\)

Then, apply the density formula to find the mass:

• Mass = Density × Volume = 8.90 g/cm³ × \((5.00 \, \text{cm})^3\)

Understanding density and volume relationship allows for accurate determination of a metal's mass, crucial for material sciences and engineering.

Graduated Cylinder Accuracy

The accuracy of a graduated cylinder is critical for precise measurements in experiments. Graduated cylinders are commonly used for measuring liquid volumes, but their accuracy depends on the cylinder's size and design.

Several factors affect accuracy:

• The graduation marks on the cylinder.
• The smallest division the cylinder can reliably measure.
• Your ability to read the meniscus level accurately.

For precise work, choose a graduated cylinder appropriate in size so that the liquid level fills a significant portion of the cylinder. If precision is vital, consider using more accurate devices like volumetric flasks or pipettes, which are designed for exact measurement of volumes.