Gas Laws: Pressure, Volume, and Hot Air

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Gas Laws: Pressure, Volume, and Hot Air
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Introduction This lesson will introduce three ways of predicting the behavior of gases: Boyle’s Law, Charles’ Law and Gay-Lussac’s Law. Never heard of them? Don’t worry– that’s the purpose of this lesson! PREVIOUS NEXT

Navigation Throughout this lesson, you will use buttons at the bottom right corner of the page to navigate. Takes you to the next page Takes you to the previous page Takes you to the Main Menu PREVIOUS NEXT

Main Menu Basic Terminology Charles’ Law Boyle’s Law Ideal Gas Law
Lesson 1 Lesson 3 Charles’ Law Lesson 2 Lesson 4 Boyle’s Law Ideal Gas Law Review Review of all four lessons

Lesson 1: Basic Terminology
This lesson reviews terms used to describe the properties and behavior of gases. MAIN MENU NEXT

Opening thoughts… Have you ever: Seen a hot air balloon? MAIN MENU
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Opening thoughts… Have you ever: Seen a hot air balloon?
Had a soda bottle spray all over you? Baked (or eaten) a nice, fluffy cake? These are all examples of gases at work! MAIN MENU PREVIOUS NEXT

Major Components of the Earth’s Atmosphere
Nitrogen 78.08% Oxygen 20.95% Argon 0.934% Nitrogen is the predominant gas in the atmosphere due to its geochemical inertness. Oxygen is almost entirely biological. Argon is the product that forms from the decay of the mantel and crust.

Minor Components of the Earth’s Air
0.036% Ne % He % CH4 0.0002% Kr % CO2 is most abundant of the minor gases. He is a decay product of radioactive elements in the Earth. Ne is probably primordial.

Properties of Gases Gas properties can be modeled using math. Model depends on— V = volume of the gas (L)= vol. of container T = temperature (Kelvin) (K) ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! n = amount (moles) P = pressure (atmospheres)

Properties of Gases You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature Lets review each of these briefly… video MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties:
Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Pressure Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa. If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area).pressure explained Atmospheric pressure video MAIN MENU PREVIOUS NEXT

Pressure Pressure of air is measured with a BAROMETER
Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) P of Hg pushing down related to Hg density column height

Pressure Column height measures Pressure of atmosphere
1 standard atmosphere (atm) = 760 mm Hg = 760 torr = kPa (SI unit is PASCAL) = 101,300 Pascals

Pressure Conversions A. What is 475 mm Hg expressed in atm?
760 mm Hg = 1 atm 475 mm Hg = x x = 475/760 = atm B. The pressure of a tire is measured as 10 kPa. What is this pressure in mm Hg?

Pressure Conversions A. What is 2 atm expressed in torr?

SATP and STP Scientists have agreed to use a set of standard conditions for reporting properties of gases and other substances, SATP. Standard Ambient Temperature and Pressure (SATP) is 25° C and 100 kPa. Previous conditions used were referred to as STP (standard temperature and pressure) STP is 0°C and kPa

You can predict the behavior of gases based on the following properties:
Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Volume Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the Litre, L. Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…) MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties:
Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Amount (moles) 1 mol of any gas occupies 22.4L.
Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas. By definition, one mole of a substance contains approximately x 1023 particles of the substance. You can understand why we use mass and moles! 1 mol of any gas occupies 22.4L. MAIN MENU PREVIOUS NEXT

You can predict the behavior of gases based on the following properties:
Pressure Volume Amount (moles) Temperature MAIN MENU PREVIOUS NEXT

Temperature Temperature is the measurement with which you’re probably most familiar (and the most complex to describe completely). For these lessons, we will be using temperature measurements in Kelvin, K. Temperature is the average kinetic energy of the particles in a substance. The Kelvin scale starts at Absolute 0, which is °C. To convert Celsius to Kelvin, add MAIN MENU PREVIOUS NEXT

Kelvin scale Absolute zero
The Kelvin scale starts at Absolute 0, which is °C. To convert Celsius to Kelvin, add To convert Kelvin to Celsius, subtract

How do they all relate? Some relationships of gases may be easy to predict. Some are more subtle. Now that we understand the factors that affect the behavior of gases, we will study how those factors interact. MAIN MENU PREVIOUS NEXT

How do they all relate? Let’s go!
Some relationships of gases may be easy to predict. Some are more subtle. Now that we understand the factors that affect the behavior of gases, we will study how those factors interact. Let’s go! MAIN MENU PREVIOUS

Lesson 2: Boyle’s Law This lesson introduces Boyle’s Law, which describes the relationship between pressure and volume of gases. MAIN MENU NEXT

Boyle’s Law This law is named for Charles Boyle, who studied the relationship between pressure, p, and volume, V, in the mid-1600s. Boyle determined that for the same amount of a gas at constant temperature, p x V = constant This defines an inverse relationship: when one goes up, the other comes down. pressure volume MAIN MENU PREVIOUS NEXT

What does Boyle’s Law mean?
p x V = constant Suppose you have a cylinder with a piston in the top so you can change the volume. The cylinder has a gauge to measure pressure, is contained so the amount of gas is constant, and can be maintained at a constant temperature. A decrease in volume will result in increased pressure. Hard to picture? Let’s fix that! MAIN MENU PREVIOUS NEXT

Boyle’s Law at Work… Doubling the pressure reduces the volume by half. Conversely, when the volume doubles, the pressure decreases by half. MAIN MENU PREVIOUS NEXT

Application of Boyle’s Law
Boyle’s Law can be used to predict the interaction of pressure and volume. If you know the initial pressure and volume, and have a target value for one of those variables, you can predict what the other will be for the same amount of gas under constant temperature. Let’s try it! MAIN MENU PREVIOUS NEXT

Application of Boyle’s Law
p1 x V1 = p2 x V2 p1 = initial pressure V1 = initial volume p2 = final pressure V2 = final volume If you know three of the four, you can calculate the fourth. MAIN MENU PREVIOUS NEXT

Application of Boyle’s Law
p1 x V1 = p2 x V2 p1 = 1 KPa V1 = 4 liters p2 = 2 KPa V2 = ? Solving for V2, the final volume equals 2 liters. So, to increase the pressure of 4 liters of gas from 1 KPa to 2 KPa, the volume must be reduced to 2 liters. MAIN MENU PREVIOUS NEXT

Boyle’s Law: Summary Pressure * Volume = Constant p1 x V1 = p2 x V2
With constant temperature and amount of gas, you can use these relationships to predict changes in pressure and volume. MAIN MENU PREVIOUS NEXT

Charles’ Law This lesson introduces Charles’ Law, which describes the relationship between volume and temperature of gases. MAIN MENU NEXT

Charles’ Law This law is named for Jacques Charles, who studied the relationship volume, V, and temperature, T, around the turn of the 19th century. He determined that for the same amount of a gas at constant pressure, V / T = constant This defines a direct relationship: an increase in one results in an increase in the other. volume temperature MAIN MENU PREVIOUS NEXT

What does Charles’ Law mean?
V / T = constant Suppose you have that same cylinder with a piston in the top allowing volume to change, and a heating/cooling element allowing for changing temperature. The force on the piston head is constant to maintain pressure, and the cylinder is contained so the amount of gas is constant. An increase in temperature results in increased volume. Hard to picture? Let’s fix it (again)! MAIN MENU PREVIOUS NEXT

Charles’ Law at Work… As the temperature increases, the volume increases. Conversely, when the temperature decreases, volume decreases. MAIN MENU PREVIOUS NEXT

Application of Charles’ Law
Charles’ Law can be used to predict the interaction of temperature and volume. If you know the initial temperature and volume, and have a target value for one of those variables, you can predict what the other will be for the same amount of gas under constant pressure. Let’s try it! MAIN MENU PREVIOUS NEXT

Application of Charles’ Law
V1 = initial volume T1 = initial temperature V2 = final volume T2 = final temperature If you know three of the four, you can calculate the fourth. MAIN MENU PREVIOUS NEXT

Application of Charles’ Law
V1 = 2.5 liters T1 = 250 K V2 = 4.5 liters T2 = ? Solving for T2, the final temperature equals 450 K. So, increasing the volume of a gas at constant pressure from 2.5 to 4.5 liters results in a temperature increase of 200 K. MAIN MENU PREVIOUS NEXT

Charles’ Law: Summary Volume / Temperature = Constant
With constant pressure and amount of gas, you can use these relationships to predict changes in temperature and volume. MAIN MENU PREVIOUS NEXT

Gay-Lussac’s Law He measured the temperature of air at different pressures, and observed a pattern of behavior which led to his mathematical law. Old man Lussac determined the relationship between temperature and pressure of a gas. During his experiments volume of the system and amount of gas were held constant.

Think of a tire... Car before a trip Pressure Gauge Let’s get on

Think of a tire... Car after a long trip Pressure Gauge WHEW!

How does Pressure and Temperature of gases relate graphically?
P/T = k Volume, # of particles remain constant Temp

P1 P2 = T1 T2 Gay-Lussac’s Mathematical Law:
What if we had a change in conditions? since P/T = k P P2 T T2 =

Eg: A gas has a pressure of 3. 0 atm at 127º C
Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C? determine which variables you have: T1 = 127°C = 400K P1 = 3.0 atm T2 = 227°C = 500K P2 = ? determine which law is being represented: T and P = Gay-Lussac’s Law

3.0 atm P2 = 400K 500K P2 = 3.8atm (500K)(3.0atm) = P2 (400K)
4) Plug in the variables: 3.0 atm P2 400K K = 5) Cross multiply and divide (500K)(3.0atm) = P2 (400K) P2 = 3.8atm

Gas laws video Gas laws demos

Boyle’s P V T, n Charles’ V T P, n Gay-Lussac’s P T V, n
Summary LAW RELAT-IONSHIP CON-STANT Boyle’s P V P1V1 = P2V2 T, n Charles’ V T V1/T1 = V2/T2 P, n Gay-Lussac’s P T P1/T1 = P2/T2 V, n

Avogadro’s Hypothesis and Kinetic Molecular Theory
The gases in this experiment are all measured at the same T and V. P proportional to n

Equal volumes of gases at the same T and P have the same number of molecules. V and n are directly related. twice as many molecules

Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas V n

Combined Gas Law The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P1 V P2 V2 = T T2 No, it’s not related to R2D2

Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1 V1 P2 Boyle’s Law Charles’ Law Gay-Lussac’s Law V2 T1 T2

Combined Gas Law Problem
A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? Set up Data Table P1 = atm V1 = 180 mL T1 = 302 K P2 = atm V2= 90 mL T2 = ??

Calculation P1 = 0.800 atm V1 = 180 mL T1 = 302 K
P1 V P2 V2 = P1 V1 T2 = P2 V2 T1 T T2 T2 = P2 V2 T1 P1 V1 T2 = 3.20 atm x mL x 302 K atm x mL T2 = 604 K = °C = K

Learning Check A gas has a volume of 675 mL at 35°C and atm pressure. What is the temperature in °C when the gas has a volume of L and a pressure of 802 mm Hg?

One More Practice Problem
A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

Try This One A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

Homework! Pg 549 # 1,2 Pg 552 # 1,2 Pg 553 # 1-6 Pg 559 # 1-3

Lesson 3 Complete! This concludes Lesson 3 on Charles’ Law!
Click the Main Menu button below, then select Lesson 4 to put all the pieces together with the Ideal Gas Law. MAIN MENU PREVIOUS

Lesson 4: Ideal Gas Law This lesson combines all the properties of gases into a single equation. MAIN MENU NEXT

Ideal Gases An “ideal” gas exhibits certain theoretical properties. Specifically, an ideal gas … Obeys all of the gas laws under all conditions. Does not condense into a liquid when cooled. Shows perfectly straight lines when its V and T & P and T relationships are plotted on a graph. In reality, there are no gases that fit this definition perfectly. We assume that gases are ideal to simplify our calculations. We have done calculations using several gas laws (Boyle’s Law, Charles’s Law, Combined Gas Law). There is one more to know…video

Ideal Gas Law Combining Boyle’s and Charles’ laws allows for developing a single equation: PV = nRT P = pressure V = volume n = number of moles R = universal gas constant (we’ll get to that in a minute…) T = temperature MAIN MENU PREVIOUS NEXT

Ideal Gas Law PV = nRT This is one of the few equations in chemistry that you should commit to memory! By remembering this single equation, you can predict how any two variables will behave when the others are held constant. MAIN MENU PREVIOUS NEXT

UNIVERSAL GAS CONSTANT
A. Ideal Gas Law PV=nRT UNIVERSAL GAS CONSTANT R= Latm/molK R=8.314 LkPa/molK You don’t need to memorize these values!

Gas Constant, R The Ideal Gas Law as presented includes use of the Universal Gas Constant. The value of the constant depends on the units used to define the other variables. For the purposes of this lesson, we will use the equation only to predict gas behavior qualitatively. Specific calculations and units will be part of our classroom work. MAIN MENU PREVIOUS NEXT

Putting p*V=n*R*T to Work
After using Boyle’s and Charles’ law for predicting gas behavior, use of the Ideal Gas Law should be relatively straightforward. Use NASA’s Animated Gas Lab to explore the interaction of these variables on gas behavior. Follow the directions on the page for changing values for the variables. When you’re finished, click the Back button on your browser to return to this lesson. Link to site: Animated Gas Lab MAIN MENU PREVIOUS NEXT

Ideal Gas Law: Summary PV = nRT
Learn it! Use it! This single equation can be used to predict how any two variables will behave when the others are held constant. MAIN MENU PREVIOUS NEXT

C. Ideal Gas Law Problems
Calculate the pressure in atmospheres of mol of He at 16°C & occupying L. GIVEN: P = ? atm n = mol T = 16°C = 289 K V = 3.25 L R = 8.314LkPa/molK WORK: PV = nRT P(3.25)=(0.412)(8.314)(289) L mol LkPa/molK K P =

C. Ideal Gas Law Problems
Find the volume of 85 g of O2 at 25°C and kPa. WORK: 85 g 1 mol = 2.7 mol 32.00 g GIVEN: V = ? n = 85 g T = 25°C = 298 K P = kPa R = LkPa/molK = 2.7 mol PV = nRT (104.5)V=(2.7) (8.314) (298) kPa mol LkPa/molK K V = 64 L

Lesson 4 Complete! This concludes Lesson 4 on the Ideal Gas Law!
Click the Main Menu button below, then select Review to try some questions based on these lessons. MAIN MENU PREVIOUS

Review This review contains multiple choice questions on the material covered by Lessons 1 – 4. Select an answer by clicking the corresponding letter. If you choose an incorrect answer, you will be given feedback and a chance to try again. If you want to return to a lesson to review the material, click on the Main Menu button, then select the lesson. When you’re ready to complete the review again, go back to the Main Menu and click the Review button. MAIN MENU NEXT

Question 1 Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related MAIN MENU

Question 1 is Correct! Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. Decreasing volume increases pressure. Increasing volume decreases pressure. pressure volume MAIN MENU NEXT

Try Question 1 again… Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected b. While pressure and volume are related, it is not a direct proportion. Try again! MAIN MENU TRY AGAIN

Try Question 1 again… Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected c. Pressure and volume are related. Is the relationship inverse or direct? MAIN MENU TRY AGAIN

Question 2 Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related MAIN MENU

Try Question 2 again… Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected a. While volume and temperature are related, it is not an inverse proportion. Try again! MAIN MENU TRY AGAIN

Question 2 is Correct! Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are: b. Directly proportional: if one goes up, the other goes up. volume temperature Increasing temperature increases volume. Decreasing temperature decreases volume. MAIN MENU NEXT

Try Question 2 again… Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are: a. Inversely proportional: if one goes up, the other comes down. b. Directly proportional: if one goes up, the other goes up. c. Not related You selected c. Pressure and volume are related. Is the relationship inverse or direct? MAIN MENU TRY AGAIN

Question 3 Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. MAIN MENU

Try Question 3 again… Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. While increasing the load in the car might increase the force on the tires, it would prove to be a difficult way to adjust tire pressure. Try again! MAIN MENU TRY AGAIN

Try Question 3 again… Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. Increasing the temperature of the air in the tire would definitely increase pressure. That is why manufacturers recommend checking air pressures when the tires are cold (before driving). But how would you increase temperature without damaging the tire? Is there a more practical solution? MAIN MENU TRY AGAIN

Question 3 is Correct! Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire? a. Increase the force pressing on the outside of the tire. b. Increase the temperature of the gas (air) in the tire. c. Increase the amount (number of moles) of gas in the tire. When you inflate a tire with a pump, you are adding air, or increasing the amount of air in the tire. This will often result in a slight increase in temperature because a tire is not a controlled environment. Such deviations and quirks will be discussed in class! MAIN MENU NEXT

Mission complete! You have completed the lessons and review. Congratulations! You should now have a better understanding of the properties of gases, how they interrelate, and how to use them to predict gas behavior. Please click on the button below to reset the lesson for the next student. Thanks! Return to Title Slide

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