Density: Videos & Practice Problems

Density is a fundamental concept in chemistry, defined as the mass of a substance divided by its volume, with the formula:

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

For solids and liquids, which are denser than gases, density is typically measured in grams per milliliter (g/mL) or grams per cubic centimeter (g/cm³), since 1 mL is equivalent to 1 cm³. In contrast, gases have lower densities, so their density is often expressed in grams per liter (g/L) or grams per decimeter cubed (g/dm³), as 1 L is equal to 1 dm³. Understanding the units and how to convert between them is essential for accurate measurement and comparison of densities across different states of matter.

Density Concepts

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 is crucial, as 1 mL is equal to 1 cm³, allowing for flexibility in calculations.

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 expressed in liters (L) or cubic decimeters (dm³). Here, it is also important to remember that 1 L is equivalent to 1 dm³.

In summary, density is calculated as mass divided by volume, and the units used can differ based on whether the substance is a solid, liquid, or gas. Understanding these distinctions is essential for accurately measuring and comparing the densities of various materials.

Density Conversion Example

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 21.4 grams per cubic centimeter, we first need to convert grams to pounds. The conversion factor for this is:

1 \text{ pound} = 453.59 \text{ grams}

By placing grams in the denominator, we can cancel out the grams:

\frac{21.4 \text{ grams}}{1 \text{ 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, using the conversion factor:

1 \text{ inch} = 2.54 \text{ cm}

Since we are dealing with cubic measurements, we cube this conversion factor:

\left(\frac{1 \text{ inch}}{2.54 \text{ cm}}\right)^3 = \frac{1 \text{ inch}^3}{(2.54)^3 \text{ cm}^3} = \frac{1 \text{ inch}^3}{16.387 \text{ cm}^3}

Next, we convert inches to feet, using the conversion factor:

1 \text{ foot} = 12 \text{ inches}

Again, we cube this conversion factor:

\left(\frac{1 \text{ foot}}{12 \text{ inches}}\right)^3 = \frac{1 \text{ foot}^3}{(12)^3 \text{ inches}^3} = \frac{1 \text{ foot}^3}{1728 \text{ inches}^3}

Now, we can combine all these conversion factors into one expression:

\frac{21.4 \text{ grams}}{1 \text{ cm}^3} \times \frac{1 \text{ pound}}{453.59 \text{ grams}} \times \frac{1 \text{ inch}^3}{16.387 \text{ cm}^3} \times \frac{1 \text{ foot}^3}{1728 \text{ inches}^3}

After canceling out the units, we are left with pounds per cubic foot. The calculation proceeds as follows:

\frac{21.4 \times 1 \times 1728}{453.59 \times 16.387} \text{ pounds/foot}^3

Calculating this gives:

21.4 \times 1728 \approx 36907.2

453.59 \times 16.387 \approx 7425.4

Thus, the density in pounds per cubic foot is approximately:

\frac{36907.2}{7425.4} \approx 4.97 \text{ pounds/foot}^3

However, we must consider significant figures. The original measurement of 21.4 grams has three significant figures, so our final answer should also reflect this. Therefore, we express the result in scientific notation:

4.97 \approx 4.97 \times 10^0 \text{ pounds/foot}^3

In conclusion, the density of the unknown metal, converted from grams per cubic centimeter to pounds per cubic foot, is approximately 4.97 \text{ pounds/foot}^3.

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 density?

Density is a physical property of a substance that expresses the relationship between its mass and volume. It's essentially a measure of how much stuff is packed into a given space. Mathematically, density (ρ) is defined as mass (m) divided by volume (V), which can be expressed with the formula:

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

The units of density are typically expressed in grams per cubic centimeter (g/cm³) for solids and liquids, and kilograms per cubic meter (kg/m³) for gases, though other units can be used depending on the context.

In practical terms, if you have two objects of the same volume but different densities, the one with the higher density will be heavier. Density is an important concept in various scientific disciplines, including physics, chemistry, and engineering, because it affects how substances interact, such as whether they will float or sink when placed in a fluid.

How do you calculate density?

Density is a measure of how much mass is contained in a given volume. To calculate the density of an object or substance, you'll use the formula:

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

Here's a step-by-step guide to calculate density:

1. Measure the mass (m) of the object or substance using a balance or scale. The unit for mass is typically grams (g) or kilograms (kg).
2. Determine the volume (V) of the object or substance. For regular-shaped objects, you can calculate volume using geometric formulas. For example, the volume of a cube is $V={\mathrm{side}}^3$. For irregular objects, you might use water displacement in a graduated cylinder to find the volume, which is typically measured in cubic centimeters (cm³) or liters (L).
3. Divide the mass by the volume to find the density. Make sure your units are consistent when performing the calculation.

For example, if you have a block of metal with a mass of 300 grams and a volume of 100 cubic centimeters, the density would be:

$\rho =\frac{300}{100 {\mathrm{cm}}^3}=3 g/{\mathrm{cm}}^3$

This result tells you that each cubic centimeter of the metal has a mass of 3 grams.

How do you find volume with density and mass?

To find the volume of an object when you have its density and mass, you can use the formula:

$\mathrm{Volume}=\frac{\mathrm{Mass}}{\mathrm{Density}}$

The density of a substance is its mass per unit volume, which is usually expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). Mass is the amount of matter in the object, typically measured in grams (g) or kilograms (kg).

Here's how you would apply the formula:

1. Make sure that the mass and density are in compatible units (e.g. if mass is in grams, density should be in g/cm³).
2. Divide the mass of the object by its density.
3. The result will give you the volume of the object.

For example, if you have a mass of 200 grams and a density of 50 g/cm³, the volume would be:

$\frac{200}{50\text{g/cm³}}=4\text{cm³}$

Remember that the calculated volume will be in the cubic unit corresponding to the unit of density you've used (cubic centimeters for g/cm³, cubic meters for kg/m³, etc.).

How do you measure density?

Density is a physical property defined as mass per unit volume and is measured in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³). To measure the density of an object, you need to determine its mass and volume, then divide the mass by the volume.

Here's a step-by-step guide:

1. Mass Measurement: Use a balance or scale to measure the mass of the object. Make sure the balance is calibrated and the object is at room temperature.
2. Volume Measurement: There are several methods to determine volume, depending on the object:
   • For regular-shaped objects (like a cube or sphere), use mathematical formulas (length x width x height for a cube, or $\frac{4}{3}\Pi \; x\; radius3for\; a\; sphere).$
   • For irregular-shaped objects, you can use the displacement method. Submerge the object in water in a graduated cylinder and record the volume of water displaced, which is equal to the volume of the object.
3. Calculation: Divide the mass by the volume to get the density (Density = Mass/Volume).

Ensure you use consistent units when performing these measurements and calculations to obtain an accurate density value.