Density - Online Tutor, Practice Problems & Exam Prep

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

So density represents the amount of mass per units of volume. And here we have our purple box again. Remember when we have a purple box, that means that is a formula or some type of concept you need to commit to memory. So density is equal to mass over volume.

Depending on the phase of matter, the units forward can be different. So we're going to say for solids and liquids, which are more dense than gases. Solids and liquids have the unit for mass in grams and a unit for volume in milliliters, or they have the unit for mass still in grams or the units for volume in centimeters cubed. Remember when we talked about conversion factors for volume? We said that one milliliter was equal to 1cm3. That's why we're allowed to basically swap out MLS here for centimeters, cubes here.

Now, gases themselves are much less dense than solids and liquids, so their units for density are a little bit different. Their mass is still in grams, but now because they're less dense, we wouldn't use milliliters, we'd use liters. And remember, within our conversion factors, we said that one liter was equal to 1dm3. So we could say the density of gases is grams per liter or grams per decimeters cubed.

So just remember, density itself is just massive over volume. Depending on the phase of matter that we're dealing with, the units can be slightly different. Now that we've looked at the basic setup of density, let's move on to our example and practice questions.

Density Example 1

So here in this example question, it says if the density of an unknown metal is two 1.4g per centimeters cubed, express its density in pounds per feet. Cute. Alright, so here the information they're giving to us is not a given amount, it's actually a conversion factor. It's 21.4g per 1 centimeters cubed, and they're telling us that we need to get to our end amounts, which will be pounds per feet cubed.

We can set this up as a dimensional analysis type of question because all we're doing is setting things up with conversion factors, allowing them to cancel out and wind up with end units or end amounts. All right, So we need to find a way of changing grams to pounds and changing centimeters cubed to feet cubed. So let's do the easier one first. Let's go from grams to pounds. Here we're going to use a new conversion factor. We're already starting out with our first conversion factor. This question actually doesn't have a given amount a unit by itself. That can happen.

Now we know that there is a connection between grams and pounds. When we talked about the different types of conversion factors, we said here that 1 LB was equal to 453.59g. Grams go on the bottom so that they can cancel out like this. So we've done the easy part. We've converted grams to pounds. Now it's up to us to convert centimeters cubed to feet cubed. All right, So what we're going to do first is we're going to say that there is a connection between centimeters and inches. We want to get rid of these centimeters, which are on the bottom. So we actually have to put centimeters here on top.

Centimeters and inches are connected and the relationship is that one inch is equal to 2.54 centimeters. However, this is cubed and these centimeters here are not, so you would cube the whole thing. We'll come back and see what effect that has on our numbers. So basically, centimeters, cubes are cancelled out. Now we have inches cubed. We want to get rid of inches, so we put inches up here. We want feet. Remember, there's a connection between inch and feet, and that's one foot is equal to 12 inches. These inches are cubed, but these are not. So I'd have to cube this whole thing and this would represent my conversion factor.

4 inches cancel out, inches cubes cancel out. So what I'd have at the end is pounds over, feet cubed, which are the units I'm trying to isolate. Let's come down here and see what effect would all of this have. So we'd have 21.4g and then we'd have on the bottom 1 centimeters cubed. We'd have 1 LB for 453.59 grams. When we do 2.54 ³, that's 2.54 * 2.54 * 2.54. That comes out to one 6.387cm ³ / 1 ³ is just one over inches cubed and then 12 ³ is 12 * 12 * 12 which is 1728 inches cubed over one foot cubed.

So conversion factor 123 and four counseling Oval units will give us what we need for it and amount which will be in pounds per feet cubed. If we look it would be two 1.4 times one 6.387 * 1728 divided on the bottom by 453.59. So we get initially is we would get 1335.97. But remember, the number of sig figs in your answer is based on the digits given within the question. Two 1.4 has within it three significant figures, so our answer needs three significant figures. To get that, I'd have to convert it to scientific notation. So I'd go 123 spaces and this will come out to be 1.34 * 10 to the three pounds per feet cubed as our final answer.

O This would be a way of converting the units of density from one set of values to another set of values. And remember it's treat it like a dimensional analysis question. Use conversion factors in order to isolate your end amounts at the end. It just happens to be here that our end amounts are two units, those of pounds and feet cubed.

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

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.