Density - Online Tutor, Practice Problems & Exam Prep

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

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 it 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 for it can be different. We're going to say for solids and liquids, which are denser than gases, solids and liquids have the unit for mass in grams and the 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 1 milliliter was equal to 1 centimeter cubed. That's why we're allowed to basically swap out ml for centimeters cubed. Now, gases themselves are much less dense than solids and liquids, so their units for density are a little 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 1 liter was equal to 1 decimeter cubed. So we could say the density of gases is grams per liter or grams per decimeter cubed. Just remember, density itself is just mass 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 21.4 grams per centimeters cubed, express its density in pounds per feet cubed. Alright. So here, the information they're giving to us is not a given amount. It's actually a conversion factor. It's 21.4 grams per 1 centimeter cubed, and they're telling us that we need to get to our end amounts, which will be 1 pound per foot 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. Alright. 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 pound was equal to 453.59 grams. 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. Alright. So what we're gonna do first is we're gonna 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 1 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 canceled out, now we have inches cubed. We want to get rid of inches, so we put inches up here. We want feet remember there is a connection between inch and feet and that's 1 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. 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 21.4 grams and then we'd have on the bottom 1 centimeter cubed. We'd have 1 pound for 453.59 grams. When we do 2.54 cubed, that's 2.54 times 2.54 times 2.54. That comes out to 16.387 centimeters cubed over 1 cubed is just 1, over inches cubed, and then 12 cubed is 12 times 12 times 12, which is 1728 inches cubed over 1 foot cubed. So conversion factor 1, 2, 3, and 4. Canceling all the units will give us what we need for our end amount, which will be in pounds per feet cubed. If we look, it would be 21.4 times 16.387 times 1728 divided on the bottom by 453.59. So what 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. 21.4 has within it 3 significant figures, so our answer needs 3 significant figures. To get that, I'd have to convert it to scientific notation, so I go 1, 2, 3 spaces, and this will come out to be 1.34 times 10 to the 3 pounds per feet cubed as our final answer. So 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 treated 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 2 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 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.