Question

Glycerol is a syrupy liquid often used in cosmetics and soaps. A \(3.25 \mathrm{~L}\) sample of pure glycerol has a mass of \(4.10 \times 10^{3} \mathrm{~g}\). What is the density of glycerol in \(\mathrm{g} / \mathrm{cm}^{3}\) ? MISSED THIS? Read Section 1.6; Watch KCV 1.6

Short answer

The density of glycerol is \(1.26 \mathrm{g} / \mathrm{cm}^{3}\).

Step-by-step solution

Convert volume from liters to cubic centimeters

First, convert the volume of glycerol from liters to cubic centimeters using the conversion factor 1 liter = 1000 cubic centimeters. Multiply the volume in liters by 1000 to get the volume in cubic centimeters.

Calculate the density

Density is defined as mass divided by volume. Use the formula \( density = \frac{mass}{volume} \) with the mass given in grams and the volume in cubic centimeters to calculate the density of glycerol.

Express the density in the correct units

Make sure that the density is expressed in grams per cubic centimeter (\(\mathrm{g} / \mathrm{cm}^{3}\)), as requested in the problem statement.

Key concepts

Density of Glycerol

Understanding the density of glycerol is crucial for many applications in science and industry. Density can be thought of as the 'compactness' of a substance - how much mass is contained in a given volume. Specifically, for glycerol, a common liquid in soaps and cosmetics, knowing its density helps with formulation and quality control.

To find the density, we use the simple equation:
density (D) = \( \frac{mass (m)}{volume (V)} \)

In layman's terms, if you take a sample of glycerol and weigh it, and then determine how much space that sample takes up, you can calculate its density by dividing the mass by the volume. This measurement is helpful not only for scientists and manufacturers but also for educators and students who are studying properties of materials.

Mass to Volume Conversion

When calculating density, converting mass to volume or vice-versa is a common practice. In our exercise, mass was given in grams and volume in liters, but to calculate density, we needed to flip the volume to cubic centimeters. Why? Because density is most commonly expressed in grams per cubic centimeter.

One key conversion to remember is that 1 liter equals 1,000 cubic centimeters. Hence, we simply multiply the volume value by 1,000. This kind of conversion is a basic skill in scientific calculations, pivotal for making accurate and meaningful comparisons between different substances.

Common Conversion Factors

• 1 liter = 1,000 cubic centimeters
• 1 kilogram = 1,000 grams
• 1 meter = 100 centimeters

Being comfortable with these conversions allows students and professionals to adeptly navigate between systems of measurement, which is essential for global scientific communication.

Units of Measurement

Units of measurement are the standardized quantities used to express the size, amount, or quantity of something we are measuring. Commonly used systems include the International System of Units (SI), commonly known as the metric system, and the United States customary units.

For scientific work, SI units are widely adopted because they facilitate clearer communication among the global scientific community. In the case of our glycerol density calculation, we've used grams per cubic centimeter (\( \mathrm{g}/\mathrm{cm}^{3} \)) as our unit for density. This ensures that anyone, regardless of their location, can understand the measurement. By mastering unit conversion, students can avoid confusion and errors when comparing or replicating experiments.

Stressing the consistent use of units and careful conversion between them is essential for accuracy and is a foundation for successful scientific study and research.