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Gas Laws: Pressure, Volume, and Hot Air NEXT

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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! NEXTPREVIOUS

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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 NEXTPREVIOUS

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

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

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Opening thoughts… Have you ever: Seen a hot air balloon? NEXTPREVIOUS 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! NEXTPREVIOUS MAIN MENU

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Major Components of the Earth’s Atmosphere 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. Nitrogen78.08% Oxygen20.95% Argon0.934%

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Minor Components of the Earth’s Air CO 2 is most abundant of the minor gases. He is a decay product of radioactive elements in the Earth. Ne is probably primordial. CO % Ne % He % CH % Kr %

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

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

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

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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 explainedpressure explained Atmospheric pressure video NEXTPREVIOUS MAIN MENU

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14 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 Hg density column height column height

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

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16 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?

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

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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 SATP and STP

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

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Volume Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m 3. 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…) NEXTPREVIOUS MAIN MENU

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

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Amount (moles) 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 particles of the substance. You can understand why we use mass and moles! 1 mol of any gas occupies 22.4L. NEXTPREVIOUS MAIN MENU

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

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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. NEXTPREVIOUS MAIN MENU The Kelvin scale starts at Absolute 0, which is °C. To convert Celsius to Kelvin, add

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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

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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. NEXTPREVIOUS MAIN MENU

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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. PREVIOUS MAIN MENU Let’s go!

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

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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. NEXTPREVIOUS MAIN MENU pressure volume

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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! NEXTPREVIOUS MAIN MENU

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

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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! NEXTPREVIOUS MAIN MENU

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Application of Boyle’s Law p 1 x V 1 = p 2 x V 2 p 1 = initial pressure V 1 = initial volume p 2 = final pressure V 2 = final volume If you know three of the four, you can calculate the fourth. NEXTPREVIOUS MAIN MENU

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Application of Boyle’s Law p 1 x V 1 = p 2 x V 2 p 1 = 1 KPa V 1 = 4 liters p 2 = 2 KPa V 2 = ? Solving for V 2, 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. NEXTPREVIOUS MAIN MENU

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Boyle’s Law: Summary Pressure * Volume = Constant p 1 x V 1 = p 2 x V 2 With constant temperature and amount of gas, you can use these relationships to predict changes in pressure and volume. NEXTPREVIOUS MAIN MENU

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

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Charles’ Law This law is named for Jacques Charles, who studied the relationship volume, V, and temperature, T, around the turn of the 19 th 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. NEXTPREVIOUS MAIN MENU volume temperature

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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)! NEXTPREVIOUS MAIN MENU

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

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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! NEXTPREVIOUS MAIN MENU

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Application of Charles’ Law V 1 = initial volume T 1 = initial temperature V 2 = final volume T 2 = final temperature If you know three of the four, you can calculate the fourth. NEXTPREVIOUS MAIN MENU

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Application of Charles’ Law NEXTPREVIOUS MAIN MENU V 1 = 2.5 liters T 1 = 250 K V 2 = 4.5 liters T 2 = ? Solving for T 2, 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.

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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. NEXTPREVIOUS MAIN MENU

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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. 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.

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Pressure Gauge Pressure Gauge Car before a trip Think of a tire... Let’s get on the road Dude!

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

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

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Gay-Lussac’s Mathematical Law: Gay-Lussac’s Mathematical Law: What if we had a change in conditions? since P/T = k P 1 P 2 T 1 T 2 =

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T and P = Gay-Lussac’s Law T 1 = 127°C = 400K P 1 = 3.0 atm T 2 = 227°C = 500K P 2 = ? T 1 = 127°C = 400K P 1 = 3.0 atm T 2 = 227°C = 500K P 2 = ? 1)determine which variables you have: 2)determine which law is being represented: Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C?

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4) Plug in the variables: (500K)(3.0atm) = P 2 (400K) P 2 = 3.8atm 3.0 atm P 2 400K 500K = = 5) Cross multiply and divide

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Gas laws video Gas laws demos

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LAW RELAT- IONSHIP LAW CON- STANT Boyle’s P VP VP VP V P 1 V 1 = P 2 V 2 T, n Charles’ V TV TV TV T V 1 /T 1 = V 2 /T 2 P, n Gay- Lussac’s P TP TP TP T P 1 /T 1 = P 2 /T 2 V, n

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

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Avogadro’s Hypothesis 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

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V n A. Avogadro’s Principle Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas

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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! P 1 V 1 P 2 V 2 = T 1 T 2 No, it’s not related to R2D2

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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! = P1P1 V1V1 T1T1 P2P2 V2V2 T2T2 Boyle’s Law Charles’ Law Gay-Lussac’s Law

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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 P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ??

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Calculation P 1 = atm V 1 = 180 mL T 1 = 302 K P 2 = 3.20 atm V 2 = 90 mL T 2 = ?? P 1 V 1 P 2 V 2 = P 1 V 1 T 2 = P 2 V 2 T 1 T 1 T 2 T 2 = P 2 V 2 T 1 P 1 V 1 T 2 = 3.20 atm x 90.0 mL x 302 K atm x mL T 2 = 604 K = 331 °C = 604 K

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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?

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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?

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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?

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Pg 549 # 1,2 Pg 552 # 1,2 Pg 553 # 1-6 Pg 559 # 1-3 Pg 562 # 2-11

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

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

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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…videovideo

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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 NEXTPREVIOUS MAIN MENU

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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. NEXTPREVIOUS MAIN MENU

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

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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. NEXTPREVIOUS MAIN MENU

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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.Animated Gas Lab 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 LabAnimated Gas Lab NEXTPREVIOUS MAIN MENU

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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. NEXTPREVIOUS MAIN MENU

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GIVEN: P = ? atm n = mol T = 16°C = 289 K V = 3.25 L R = L 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 b Calculate the pressure in atmospheres of mol of He at 16°C & occupying 3.25 L.

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GIVEN: V = ? n = 85 g T = 25°C = 298 K P = kPa R = L kPa/mol K C. Ideal Gas Law Problems b Find the volume of 85 g of O 2 at 25°C and kPa. = 2.7 mol WORK: 85 g 1 mol = 2.7 mol g PV = nRT (104.5)V=(2.7) (8.314) (298) kPa mol L kPa/mol K K V = 64 L

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

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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. NEXT MAIN MENU

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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.a.Inversely proportional: if one goes up, the other comes down. b.b.Directly proportional: if one goes up, the other goes up. c.c.Not related MAIN MENU

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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 NEXT MAIN MENU

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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! TRY AGAIN MAIN MENU

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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? TRY AGAIN MAIN MENU

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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.a.Inversely proportional: if one goes up, the other comes down. b.b.Directly proportional: if one goes up, the other goes up. c.c.Not related MAIN MENU

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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! TRY AGAIN MAIN MENU

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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. Increasing temperature increases volume. Decreasing temperature decreases volume. NEXT MAIN MENU volume temperature

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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? TRY AGAIN MAIN MENU

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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.a.Increase the force pressing on the outside of the tire. b.b.Increase the temperature of the gas (air) in the tire. c.c.Increase the amount (number of moles) of gas in the tire. MAIN MENU

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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. MAIN MENU TRY AGAIN 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!

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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. MAIN MENU TRY AGAIN 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?

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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. MAIN MENU 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! NEXT

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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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