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 mL, of 6.54 g of acetone?

Short answer

a. Mass of acetone = 22.4184 g. b. Volume of acetone = 8.3222 mL.

Step-by-step solution

Calculate mass of acetone

To find the mass of acetone, use the density formula which is mass = volume x density. Convert 28.56 mL to cm³ since the density is given in g/cm³ (1 mL = 1 cm³).

Perform the calculation for mass

Use the given density of acetone (0.7857 g/cm³) and the volume in cm³ to calculate the mass. Mass = 28.56 cm³ x 0.7857 g/cm³.

Calculate volume of acetone

To find the volume, use the rearranged density formula: volume = mass / density. Use the given mass of 6.54 g.

Perform the calculation for volume

Divide the mass of the acetone by its density to find the volume. Volume = 6.54 g / 0.7857 g/cm³.

Key concepts

Understanding the Density Formula

Density is a fundamental concept in chemistry that describes how much mass is contained in a given volume. The density formula is a simple yet vital equation given as \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \. \] This formula helps to identify the density of a substance by dividing the mass (typically in grams) by the volume (often in cubic centimeters or milliliters).

For instance, in the case of acetone, the density is 0.7857 grams per cubic centimeter. To find out how much acetone's mass is present in 28.56 milliliters, you can rearrange the formula as \[ \text{Mass} = \text{Volume} \times \text{Density} \. \] It's essential to remember that the units of volume and mass should match those used for the density. Once we have the right units, we simply multiply the volume of acetone by its density to get the mass.

Converting Mass and Volume

In chemistry, it's common to convert between different units of mass and volume. Understanding how to switch from milliliters to cubic centimeters, or from grams to kilograms, is crucial.

For volume conversion, it's beneficial to know that 1 milliliter is equivalent to 1 cubic centimeter (1 mL = 1 cm³). This direct relationship makes conversions straightforward when working with liquids like acetone.

Example of Mass Conversion

If you need to convert kilograms to grams, keep in mind that 1 kilogram is equivalent to 1000 grams (1 kg = 1000 g).

Such conversions are essential when calculating density, as using consistent units ensures accuracy in your results. When the units are not matching, for instance, if you're given a volume in milliliters but the density is in grams per cubic centimeter, convert the volume to cubic centimeters before multiplying by the density.

Unit Conversion in Chemistry

In chemistry, the ability to convert between different units is invaluable, as it ensures that equations and formulas make sense and that the outcomes are accurate. The process of converting units is known as dimensional analysis or the factor-label method. This involves using conversion factors to move from one unit to another.

To perform a unit conversion:

• Determine which units you're converting from and to.
• Find a conversion factor that relates the two units.
• Multiply your original measurement by the conversion factor.

If converting multiple units, such as from grams per milliliter to kilograms per liter, you would use multiple conversion factors in succession to reach the final unit.

Understanding unit conversion is essential when dealing with exercises like finding the volume of acetone in milliliters when the mass is given in grams and the density in grams per cubic centimeter. Correct units will yield correct chemistry results.