Back To Course

Chemistry: High School19 chapters | 179 lessons | 1 flashcard set

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Amy Lange*

Amy has taught university-level earth science courses and has a PhD in Geology.

The density of gas is more complicated than solids because gases are highly affected by temperature and pressure. This lesson will lead you through two equations to calculate the density of a gas.

The density of solid objects are easy to understand because you can physically feel it. If you have a rock and a piece of foam that are exactly the same size, the rock will feel heavier. This heaviness is due to the rock having a higher density than foam.

**Density** is a physical property of matter and is defined as the mass of the object divided by volume. Remember that **mass** is the measure of the amount of matter in an object and is measured in grams. **Volume** is the 3-dimensional space that an object occupies and is measured in cubic meters. If we have two objects of the same volume, the one with greater mass will have a higher density than the one with the lesser mass.

In solids, density remains mostly constant because the subatomic bonds keep the molecules tightly packed. However, in gases, the bonds are much weaker, which makes them responsive to temperature and pressure. Gases will assume the shape of whatever container they are in. Assuming we have a fixed mass of gas, meaning that we haven't added or taken away any of the gas, when we change the volume of the container, we are changing the density of the gas. A smaller container means a smaller volume. According to our equation, density is inversely related to volume. So, a smaller volume will produce a denser gas. This is because you are packing the same amount of molecules into a smaller space.

So, how do we actually measure the density of a gas? An easy way to visualize gas density is to observe its behavior compared to air. Think of helium-filled balloons. These balloons rise because they are less dense than the surrounding air. This density is so much lower that it causes the rubber balloon and string to float in the air. While observing the floating balloon tells us that helium is less dense than air, it doesn't give us a quantitative measure of what the density of helium actually is.

If we know the mass of the gas and the volume, we can easily calculate density. Let's assume we have a gas with a mass of 500 g in a volume of 2m^3. Dividing 500 by 2 will give you a density of 250 g/m^3.

Gases are highly responsive to changes in both temperature and pressure. In fact, car tire manufacturers recommend that you check your tires frequently if you live in climates that experience large temperature variations. Gases expand in high temperatures and condense in low temperatures. Thus, when temperatures drop, you could experience dangerously low tire pressures due to the low volume of air in your car tires. This is the same phenomenon that causes hot air balloons to fly. The gas burner heats the air inside the balloon making it less dense than the surrounding air. The less dense air rises compared to the surrounding air.

We can calculate how the density of air changes with changing temperature using the ideal gas law. The **ideal gas law** is defined as *PV* = *nRT*. *P* is pressure, *V* is volume, *n* is the number of gas moles, *R* is the ideal gas constant and *T* is temperature. The **ideal gas constant** is 0.0821 L * atm/mol * K. Generally, constants are values that have been previously verified by scientists, and we can insert directly into equations.

You'll notice that volume is a variable in the ideal gas law, but neither density nor mass is a variable. To find density, we have to solve the equation for volume, or *V*. *V* = *nRT* / *P*. To incorporate mass, we can use the number of moles, or *n*. The number of moles equals the mass of the gas divided by the molecular mass. **Molecular mass** is the mass calculated by adding atomic masses in the chemical formula. For instance, CO2 is composed of one carbon and two oxygen atoms. The atomic mass of carbon is 12.01 g/mol and oxygen is 15.999 g/mol. So, the molecular mass of CO2 is 12.01 + (15.999 * 2) = 44.01 g/mol.

We can substitute for *n* into the ideal gas law in order to get mass into the equation. Since *n* equals mass divided by molecular mass, this would insert into our equation as *V* = *mRT* / *MM* * *P*. Remember our original equation for density is mass divided by volume. Since we have volume on one side, we divide both sides by *m*: *V* / *m* = *mRT* / *MM* * *P* * *m*.

Since mass is on the top and bottom of the fraction on the right, they cancel each other out. On the left, the equation is the inverse of density. Thus, if we flip the fractions on both sides of the equation, the left will be density.

*V*/*m*=*RT*/*MM***P**m*/*V*=*MM***P*/*RT*- Density =
*MM***P*/*RT*

Using this equation, we are now ready to calculate the density of gas using temperature and pressure. Let's use CO2, as we were discussing earlier.

- The molecular mass of CO2 is 44.01 g/mol.
*R*is 0.0821 L * atm/mol * K.*T*is 273.15 K.*P*is 1 atm.

Note that the temperature in this equation must be in Kelvin. 273.15 K is 0 degrees Celsius and the freezing point of water.

- Density =
*MM***P*/*RT* - Density = (44.01 g/mol * 1 atm) / ((0.0821 L * atm/mol * K) * 273.15 K)
- Density = (44.01 g * atm/mol) / (22.4 L * atm/mol)
- Density = 1.96 g/L

The density of the gas is 1.96 g/L. You can tell by this equation if you vary the gas or pressure, you will also change the density of the gas.

In this lesson, we learned that the **density of the gas** is equal to the mass divided by volume of a gas. Because gases are greatly affected by changing temperature and pressure, we can also use the **ideal gas law** to solve for density. The ideal gas law states that **PV = nRT**. This equation explains why car tires become under-inflated during winter. When the temperature (*T*) drops, the volume (*V*) of the air must drop as well.

While the ideal gas law is extremely useful in describing the behavior of gases in changing conditions, it does not have density as a variable. In order to insert density into the equation, we must use the relationship that the number of moles (*n*) is equal to the mass divided by molecular mass. This substitution will allow us to calculate the density of a gas with respect to temperature and pressure.

Watch and review this lesson's content to make sure that you can:

- Recollect the definitions of density and volume
- State the equation for calculating the density of a gas and the ideal gas law
- Interpret the purpose of the ideal gas law and understand when to use it
- Go through the process of calculating the density of a gas

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
4 in chapter 11 of the course:

Back To Course

Chemistry: High School19 chapters | 179 lessons | 1 flashcard set

- The Kinetic Molecular Theory: Properties of Gases 6:49
- Pressure: Definition, Units, and Conversions 6:21
- Temperature Units: Converting Between Kelvins and Celsius 5:39
- How to Find the Density of a Gas 7:40
- The Boltzmann Distribution: Temperature and Kinetic Energy of Gases 6:51
- Diffusion and Effusion: Graham's Law 6:57
- Molar Volume: Using Avogadro's Law to Calculate the Quantity or Volume of a Gas 9:09
- Boyle's Law: Gas Pressure and Volume Relationship 6:48
- Charles' Law: Gas Volume and Temperature Relationship 8:13
- Gay-Lussac's Law: Gas Pressure and Temperature Relationship 6:42
- The Ideal Gas Law and the Gas Constant 8:03
- Using the Ideal Gas Law: Calculate Pressure, Volume, Temperature, or Quantity of a Gas 3:42
- Real Gases: Deviation From the Ideal Gas Laws 7:39
- Real Gases: Using the Van der Waals Equation 6:48
- Go to Gases in Chemistry

- FTCE ESOL K-12 (047): Practice & Study Guide
- GACE Media Specialist Test II: Practice & Study Guide
- GACE Media Specialist Test I: Practice & Study Guide
- GACE Political Science Test II: Practice & Study Guide
- NES Essential Components of Elementary Reading Instruction: Test Practice & Study Guide
- 20th Century Spanish Literature
- Sun, Moon & Stars Lesson Plans
- Direct Action & Desegregation from 1960-1963
- Civil Rights Movement from the Civil War to the 1920s
- Civil Rights in the New Deal & World War II Era
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- The Chorus in Antigone
- Where is Mount Everest Located? - Lesson for Kids
- Sperm Cell Facts: Lesson for Kids
- The Motivational Cycle: Definition, Stages & Examples
- Bolivian President Evo Morales: Biography & Quotes
- Labor Unions for Physicians: Benefits & Factors
- Positive Attitude & Call Center Performance
- Chicken Facts: Lesson for Kids
- Quiz & Worksheet - Converting English Measurement Units
- Quiz & Worksheet - What Is Felony Murder?
- Quiz & Worksheet - Characteristics of Agile Companies
- Quiz & Worksheet - A Bend in the River
- Quiz & Worksheet - Sentence Fluency
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- Business Writing: Help & Review
- Computing: Skills Development & Training
- Organizational Behavior Textbook
- Instructional Strategies for Teachers: Help & Review
- GACE Economics: Practice & Study Guide
- Discrete Probability Distributions: Help and Review
- Properties of Matter: Tutoring Solution
- Quiz & Worksheet - Principles of Learning in Patient Education
- Quiz & Worksheet - Competition Within Free Markets
- Quiz & Worksheet - Duke Ellington
- Quiz & Worksheet - Using Tables to Summarize Categorical Data
- Quiz & Worksheet - Multiplying Fractions and Mixed Numbers

- Understanding the Structure of the PSAT Math Section
- Blister Beetles: Life Cycle & Identification
- Debate Lesson Plan
- How to Pass the GED Math Test
- LSAT Test Dates
- Probability Lesson Plan
- How to Pass the PSAT
- Script Writing Prompts
- GMAT Registration Dates
- The New SAT Score Conversion
- Context Clues Lesson Plan
- What Are SAT Test Dates and Locations?

Browse by subject