Problem 70 - Chemistry A Molecular Approach

Question

Acetone (nail polish remover) has a density of \(0.7857 \mathrm{~g} / \mathrm{cm}^{3} .\) a. What is the mass in g of \(28.56 \mathrm{~mL}\) of acetone? b. What is the volume in \(\mathrm{mL}\) of \(6.54 \mathrm{~g}\) of acetone?

Step-by-Step Solution

Answer

a. The mass of 28.56 mL of acetone is 22.434232 g. b. The volume of 6.54 g of acetone is 8.320122 mL.

Step 1: Calculate the mass of acetone

To calculate the mass of acetone, use the formula: mass (g) = density (g/cm³) × volume (mL). Note that 1 mL is equivalent to 1 cm³. So, multiply the density of acetone by the volume in mL: mass = 0.7857 g/cm³ × 28.56 mL.

Step 2: Perform the multiplication to find the mass

Multiplying the given density by the given volume gives the mass of acetone: mass = 0.7857 g/cm³ × 28.56 cm³ = 22.434232 g.

Step 3: Calculate the volume of acetone

To find the volume, use the formula rearranged from Step 1: volume (mL) = mass (g) / density (g/cm³). Now divide the mass of acetone by its density: volume = 6.54 g / 0.7857 g/cm³.

Step 4: Perform the division to find the volume

Dividing the mass by the density gives the volume of acetone: volume = 6.54 g / 0.7857 g/cm³ = 8.320122 mL.

Key Concepts

Mass-Volume Relationship

Understanding the mass-volume relationship is critical when you're dealing with the quantity of a substance. This relationship is a direct result of a substance's density, which is defined as its mass per unit volume. In scientific terms, density is often expressed in grams per cubic centimeter (\( g/cm^3 \) or \( g/mL \) for liquids).

To find the mass when you have the volume (like in our acetone example), you simply multiply the volume by the density. Conversely, if you're given the mass and need to find the volume, you divide the mass by the density. A critical step in solving such problems is making sure your units are consistent. Since 1 milliliter (\( mL \)) is equal to 1 cubic centimeter (\( cm^3 \)), there's no need to convert units in this particular instance.

Unit Conversion

Being nimble with unit conversion is an essential skill in chemistry and all other sciences. When solving problems, units might not always match up as conveniently as they did with the acetone example. You should be comfortable converting units such as milliliters to liters or grams to kilograms. To convert units, you can use a conversion factor, which is a fraction that represents the equivalence between two different units.

For example, to convert 28.56 mL to liters, you would use the conversion factor of 1 liter = 1000 mL. This is crucial for reaching an answer with the correct unit, which impacts the interpretation of your result and ensures accuracy in scientific communication.

Chemical Properties of Substances

Each chemical substance has a unique set of properties that dictates how it behaves in different situations. Density is one such property, encapsulating the compactness of a substance's mass in a given volume. It's a fundamental trait that you can use to identify substances or predict how they interact with others.

For instance, knowing the density of acetone can help you predict whether it will float on water (it does because its density is less than that of water). Such properties are intrinsic to the substance and do not change unless the substance itself undergoes a chemical transformation. Understanding the chemical properties of substances, including their densities, is vital in a wide array of scientific and practical applications, from designing an experiment to filling a swimming pool with the right amount of water treatment chemicals.