Density: Videos & Practice Problems

Density is defined as the amount of mass per unit volume, expressed mathematically as $D=\frac{m}{V}$. For solids and liquids, mass is measured in grams and volume in milliliters or cubic centimeters, while for gases, mass remains in grams but volume is in liters or cubic decimeters. Understanding density is crucial for distinguishing between different phases of matter and their properties, as it influences behaviors in various chemical reactions and applications.

Density

Density is a fundamental concept in science that quantifies how much mass is contained in a given volume. The formula for density is expressed as:

\( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \)

When discussing the units of density, it's important to note that they vary depending on the phase of matter. For solids and liquids, which are generally denser than gases, the mass is measured in grams (g) and the volume can be expressed in either milliliters (mL) or cubic centimeters (cm³). This equivalence arises from the fact that:

\( 1 \, \text{mL} = 1 \, \text{cm}^3 \)

Thus, for solids and liquids, density can be represented as grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³).

In contrast, gases have a significantly lower density compared to solids and liquids. Therefore, while the mass of gases is still measured in grams, the volume is typically measured in liters (L). The relationship between liters and cubic decimeters is given by:

\( 1 \, \text{L} = 1 \, \text{dm}^3 \)

Consequently, the density of gases is expressed in grams per liter (g/L) or grams per cubic decimeter (g/dm³). Understanding these distinctions in units is crucial for accurately calculating and interpreting density across different states of matter.

Density Example 1

To convert the density of an unknown metal from grams per cubic centimeter to pounds per cubic foot, we can utilize dimensional analysis, which involves using conversion factors to systematically change units while ensuring they cancel appropriately.

Starting with the given density of the metal, which is 21.4 grams per cubic centimeter, we need to convert grams to pounds and cubic centimeters to cubic feet. The first step is to convert grams to pounds using the conversion factor that 1 pound is equal to 453.59 grams. This means we can express grams in the denominator to facilitate cancellation:

Density in pounds per cubic foot = 21.4 g/cm³ × (1 lb / 453.59 g)

Next, we need to convert cubic centimeters to cubic feet. We start by converting centimeters to inches, knowing that 1 inch equals 2.54 centimeters. Since we are dealing with cubic measurements, we must cube this conversion factor:

1 cm³ = (1 in / 2.54 cm)³ = (1 in³ / 16.387 cm³)

Now, we convert inches to feet, using the fact that 1 foot equals 12 inches, and again, we cube this conversion factor:

1 in³ = (1 ft / 12 in)³ = (1 ft³ / 1728 in³)

Combining these conversions, we can express the density in pounds per cubic foot as follows:

Density in pounds per cubic foot = 21.4 g/cm³ × (1 lb / 453.59 g) × (1 in³ / 16.387 cm³) × (1728 in³ / 1 ft³)

Now, substituting the values into the equation, we have:

Density = 21.4 × 1 × 1728 / (453.59 × 16.387)

Calculating this gives:

Density ≈ 1335.97 lb/ft³

Since the original measurement of 21.4 has three significant figures, we need to express our final answer in scientific notation to maintain this precision. Thus, we convert 1335.97 to:

Density ≈ 1.34 × 10³ lb/ft³

This process illustrates how to effectively use dimensional analysis and conversion factors to change units of density from grams per cubic centimeter to pounds per cubic foot, ensuring that all units are appropriately canceled and the final answer is presented with the correct number of significant figures.

When lead levels in blood exceed 0.80 ppm (parts per million) the level is considered dangerous. 0.80 ppm means that 1 million g of blood would contain 0.80 g of Pb. Given that the density of blood is 1.060 kg/cm³, how many grams of Pb would be found in 400.00 mL of blood at 0.620 ppm?

• A. 0.891 g Pb
• B. 0.522 g Pb
• C. 0.263 g Pb
• D. 0.059 g Pb

Answer: (C)

Here’s what students ask on this topic:

What is the formula for calculating density?

The formula for calculating density is given by:

$D=\frac{m}{V}$

where $D$ represents density, $m$ represents mass, and $V$ represents volume. This formula indicates that density is the mass of an object divided by its volume.

What are the units of density for solids and liquids?

For solids and liquids, the units of density are typically expressed as grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³). This is because the mass is measured in grams (g) and the volume is measured in milliliters (mL) or cubic centimeters (cm³).

How does the density of gases differ from that of solids and liquids?

The density of gases is generally much lower than that of solids and liquids. For gases, the mass is still measured in grams (g), but the volume is measured in liters (L) or cubic decimeters (dm³). Therefore, the units of density for gases are grams per liter (g/L) or grams per cubic decimeter (g/dm³).

Why is understanding density important in chemistry?

Understanding density is crucial in chemistry because it helps distinguish between different phases of matter and their properties. Density influences how substances interact in chemical reactions, their behavior in mixtures, and their applications in various fields. For example, knowing the density of a substance can help predict whether it will float or sink when placed in a liquid.

How can you convert between milliliters and cubic centimeters?

Milliliters (mL) and cubic centimeters (cm³) are equivalent units of volume. Therefore, 1 milliliter is equal to 1 cubic centimeter. This means you can directly swap these units without any conversion factor. For example, 50 mL is the same as 50 cm³.