Question

(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a 45-mLsample 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 \(0.866 / \mathrm{mL})\). 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) A cubic piece of metal 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?

Short answer

(a) The calculated density of the substance is approximately \(0.856 \mathrm{g/mL}\), which indicates that the substance is likely to be toluene. (b) The chemist should use approximately \(40.39 \mathrm{mL}\) of ethylene glycol to obtain \(45.0 \mathrm{g}\) of the substance. (c) The mass of the cubic piece of nickel is approximately \(1112.5 \mathrm{g}\).

Step-by-step solution

Calculate the density of the substance

To find the density of the substance, we can use the formula for density: \(Density = \frac{Mass}{Volume}\) We are given the mass of the sample (\(38.5 \mathrm{~g}\)) and the volume of the sample (45 mL). Plug these values into the formula: \(Density = \frac{38.5 \mathrm{g}}{45 \mathrm{mL}} \approx 0.856 \mathrm{g/mL}\)

Identify the substance

We are given the densities of two possible substances: isopropyl alcohol (0.785 g/mL) and toluene (0.866 g/mL). Since the calculated density (0.856 g/mL) is closer to the density of toluene, the substance is most likely toluene. #Part (b)#

Calculate the volume of ethylene glycol

To find the volume of ethylene glycol needed, we can rearrange the formula for density: \(Volume = \frac{Mass}{Density}\) We are given the mass of ethylene glycol required (45.0 g) and the density of ethylene glycol (1.114 g/mL). Plug these values into the formula: \(Volume = \frac{45.0 \mathrm{g}}{1.114 \mathrm{g/mL}} \approx 40.39 \mathrm{mL}\) So, the chemist should use approximately \(40.39 \mathrm{mL}\) of ethylene glycol. #Part (c)#

Calculate the volume of the cube

The volume of a cube can be calculated by raising the length of one edge to the power of 3: \(Volume = edge^3\) Given the length of each edge is \(5.00 \mathrm{cm}\), the volume of the cube is: \(Volume = (5.00 \mathrm{cm})^3 = 125 \mathrm{cm}^3\)

Calculate the mass of the metal cube

Using the formula for density and the given density of nickel (8.90 g/cm³), we can calculate the mass of the cube: \(Mass = Density \times Volume\) \(Mass = (8.90 \mathrm{g/cm}^3)(125 \mathrm{cm}^3) = 1112.5 \mathrm{g}\) Hence, the mass of the cubic piece of nickel is approximately \(1112.5 \mathrm{g}\).

Key concepts

Units of Density

Understanding density requires familiarity with its units, which express how much mass an object has within a given volume. Density is typically measured in grams per cubic centimeter (g/cm³) for solids, grams per milliliter (g/mL) for liquids, or kilograms per cubic meter (kg/m³) for gases.

When conducting density calculations, it's crucial to ensure that the units of mass and volume are compatible. If they're not, you may need to convert them to match, such as converting milliliters to cubic centimeters (since 1 mL is equivalent to 1 cm³). This helps to maintain the accuracy of your calculations and the integrity of your results.

Volume and Mass Measurements

Accurate measurements of volume and mass are pivotal in calculating density. For liquids, volume can be measured with laboratory equipment like graduated cylinders or pipettes, which provide specific measurements. Meanwhile, mass is typically measured using a balance or scale. Precision in these measurements allows for a more exact calculation of density.

To avoid common errors, ensure that all equipment is calibrated correctly and that any measurements are taken at eye level to prevent parallax errors. It's also important to account for the temperature, as volume can be affected by temperature changes. Always record the conditions under which your measurements were taken for future reference or comparison.

Substance Identification

Density calculations are instrumental in identifying substances, as each material has a unique density. For example, in solving the textbook exercise, the calculated density helped to identify the unknown liquid by comparing it to known densities of isopropyl alcohol and toluene.

Consider the Following When Identifying Substances:

• The closest matching density to your calculated value usually indicates the substance's identity.
• Consider potential errors in measurement that might affect the accuracy of identification.
• Use a density reference chart for common substances as a guide during identification.

Always cross-check your calculated density with reputable sources to confirm the identification of the substance.

Chemical Properties

Density is more than just a number; it's a fundamental chemical property that can reveal a substance's composition and structure. For instance, density affects how substances interact with each other – think of oil floating on water due to its lower density.

Understanding Chemical Properties:

• Density is temperature-dependent – it generally decreases as temperature increases.
• The arrangement of particles within a substance greatly impacts its density.
• Differences in density can influence how substances are used in various applications.

By understanding the density and other chemical properties of substances, scientists and engineers can predict behaviors and interactions in different environments, leading to more effective and efficient applications in science and industry.