Density: Videos & Practice Problems

Density is defined as the amount of mass per unit of 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 grasping concepts in chemistry, such as the behavior of substances in different states of matter and their interactions in chemical reactions.

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, you can interchange mL and cm³ when calculating density for solids and liquids. In contrast, gases have a significantly lower density, leading to different units for their density measurements. For gases, mass is still measured in grams, but volume is typically expressed in liters (L) or cubic decimeters (dm³). The conversion factor here is:

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

Therefore, the density of gases can be represented as grams per liter (g/L) or grams per cubic decimeter (g/dm³). In summary, while the core formula for density remains consistent across different states of matter, the units used for mass and volume will vary, reflecting the unique properties of solids, liquids, and gases.

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:

\[\text{Density} = 21.4 \, \text{grams/cm}^3 \times \frac{1 \, \text{pound}}{453.59 \, \text{grams}}\]

Next, we 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:

\[\text{Conversion from cm to in}^3 = \left(\frac{1 \, \text{inch}}{2.54 \, \text{cm}}\right)^3 = \frac{1}{16.387} \, \text{in}^3/\text{cm}^3\]

Now, we convert inches to feet, where 1 foot equals 12 inches. Again, we cube this conversion factor:

\[\text{Conversion from in}^3 \text{ to ft}^3 = \left(\frac{1 \, \text{foot}}{12 \, \text{inches}}\right)^3 = \frac{1}{1728} \, \text{ft}^3/\text{in}^3\]

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

\[\text{Density} = 21.4 \, \text{grams/cm}^3 \times \frac{1 \, \text{pound}}{453.59 \, \text{grams}} \times \frac{1}{16.387 \, \text{in}^3/\text{cm}^3} \times \frac{1}{1728 \, \text{ft}^3/\text{in}^3}\]

Calculating this gives:

\[\text{Density} = \frac{21.4 \times 1 \times 1728}{453.59 \times 16.387} \, \text{pounds/ft}^3\]

After performing the calculations, we find the result to be approximately 1335.97 pounds per cubic foot. However, we must consider significant figures based on the original measurement, which has three significant figures. Thus, we express the final answer in scientific notation:

\[\text{Final Density} = 1.34 \times 10^3 \, \text{pounds/ft}^3\]

This process illustrates how to effectively use dimensional analysis and conversion factors to change units of density from one system to another, ensuring accuracy and adherence to significant figures throughout the calculation.

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. For solids and liquids, mass is typically measured in grams (g) and volume in milliliters (mL) or cubic centimeters (cm³). For gases, mass is still measured in grams, but volume is measured in liters (L) or cubic decimeters (dm³).

How do the units for density differ between solids, liquids, and gases?

For solids and liquids, density is usually expressed in grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³). This is because solids and liquids are more dense than gases. For gases, density is expressed in grams per liter (g/L) or grams per cubic decimeter (g/dm³). This difference in units is due to the lower density of gases compared to solids and liquids.

Why is understanding density important in chemistry?

Understanding density is crucial in chemistry because it helps explain the behavior of substances in different states of matter and their interactions in chemical reactions. Density affects how substances mix, react, and separate. For example, knowing the density of a liquid can help predict whether it will float or sink when mixed with another liquid. Additionally, density is used in calculations involving mass and volume, which are fundamental in stoichiometry and other chemical analyses.

What are the common units used for measuring volume in density calculations?

The common units used for measuring volume in density calculations depend on the state of matter. For solids and liquids, volume is typically measured in milliliters (mL) or cubic centimeters (cm³). For gases, volume is measured in liters (L) or cubic decimeters (dm³). These units are chosen based on the density of the substance being measured, with gases being less dense and thus requiring larger volume units.

How do you convert between milliliters and cubic centimeters in density calculations?

Converting between milliliters (mL) and cubic centimeters (cm³) in density calculations is straightforward because 1 milliliter is equal to 1 cubic centimeter. This means that:

$1\mathrm{mL}=1\mathrm{cm}^3$

This equivalence allows you to interchange these units without any additional conversion factors, making it easier to perform density calculations for solids and liquids.