Physics
Gas Laws
Gas laws are a set of principles that describe the behavior of gases under various conditions, including pressure, volume, and temperature. These laws, such as Boyle's law, Charles's law, and the ideal gas law, provide mathematical relationships that help predict how gases will behave in different situations. They are fundamental to understanding the properties and behavior of gases in physics.
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12 Key excerpts on "Gas Laws"
eBook - ePubChemistry
With Inorganic Qualitative Analysis
- Therald Moeller(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
3THE GASEOUS STATE
Publisher Summary
This chapter reviews the properties of gases. It discusses some practical aspects of measuring pressure. It presents the kinetic-molecular theory of gases to show how the theory relates to each gas law. The chapter discusses Boyle’s law, Charles’ law, and the combined gas law, all of which deal with pressure, volume, and temperature changes in a fixed quantity of gas. It describes Avogadro’s law, Gay–Lussac’s law, and the ideal gas law. The chapter discusses Dalton’s law of partial pressures, effusion and diffusion, and deviations from the Gas Laws. All gases expand uniformly to occupy whatever space is available, whether large or small. A substance in the gaseous state occupies a much larger volume than the same amount of that substance occupies in the liquid or solid state.In this chapter we first briefly review the properties of gases and discuss some practical aspects of measuring pressure. Next, the kinetic-molecular theory of gases is presented, so that subsequently we can show how the theory relates to each gas law. Boyle’s law, Charles’ law, and the combined gas law, all of which deal with pressure, volume, and temperature changes in a fixed quantity of gas, are given in the following sections. Through Avogadro’s law, Gay-Lussac’s law, and the ideal gas law, the amount of gas involved is introduced into the pressure– volume– temperature relationships. Finally, Dalton’s law of partial pressures, effusion and diffusion, and deviations from the Gas Laws are discussed.The word “gas” was created in 1662 to describe a specific form of matter. Johann van Helmont, a Belgian physician, derived the word from the Greek word “chaos,” which referred to the original matter from which the Earth was formed. (Some have suggested that he chose “chaos” because his equipment kept blowing up when he tried to make gases.)Forty years later, the first of the “Gas Laws” describing the behavior of gases was discovered by Robert Boyle. But after Boyle, more than one hundred years passed before a great period of discovery transformed the young science of chemistry. In the mid-eighteenth century, individual gases were recognized as different from air, which was discovered to contain several different gases.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Explain what this term describes and how it was used in this experiment. F. The kinetic molecular theory describes how a system of gas molecules behaves and is based on a small number of straightforward postulates. Provide arguments derived from the kinetic molecular theory that support Boyle’s law, Charles’ law, Gay-Lussac’s law, Graham’s law, and Dalton’s law. Summary Organized by Learning Objective Describe the physical properties of gases at the microscopic and molecular levels. Gases expand to fill any container, are easily compressed, have low densities, and are affected by temperature and pressure. Explain the measurement of pressure using barometers and manometers. Atmospheric pressure is measured with a barometer, in which a pressure of one standard atmosphere (1 atm) will support a column of mercury 760 mm high. This is a pressure of 760 torr. By definition, 1 atm = 101,325 pascals (Pa) and 1 bar = 100 kPa. Manometers, both open-end and closed-end, are used to measure the pressure of trapped gases. Describe and use the Gas Laws of Dalton, Charles, Gay- Lussac, and the combined gas law. Boyle’s Law (Pressure–Volume Law). Volume varies inversely with pressure. V ∝ 1/P, or P 1 V 1 = P 2 V 2 . Charles’ Law (Temperature–Volume Law). Volume varies directly with the Kelvin temperature. V ∝ T, or V 1 /V 2 = T 1 /T 2 . Gay-Lussac’s Law (Temperature–Pressure Law). Pressure varies directly with Kelvin temperature. P ∝ T, or P 1 /P 2 = T 1 /T 2 . Graham’s Law of Effusion. The rate of effusion of a gas varies inversely with the square root of its density (or the square root of its molecular mass). Combined Gas Law. PV divided by T for a given gas sample is a con- stant. PV/T = C, or P 1 V 1 /T 1 = P 2 V 2 /T 2 . Perform stoichiometric calculations using the Gas Laws and Avogadro’s Law. Stoichiometric calculations are made using the Gas Laws and Avogadro’s Law and the previous stoichiometric methods.
- Frederick Bettelheim, William Brown, Mary Campbell, Shawn Farrell(Authors)
- 2019(Publication Date)
- Cengage Learning EMEA(Publisher)
The Gas Laws we describe below hold not only for pure gases but also for mixtures of gases. A. Boyle’s Law and the Pressure–Volume Relationship Boyle’s law states that for a fixed mass of an ideal gas at a constant temper-ature, the volume of the gas is inversely proportional to the applied pres-sure. If the pressure doubles, for example, the volume decreases by one-half. This law can be stated mathematically in the following equation, where P 1 and V 1 are the initial pressure and volume and P 2 and V 2 are the final pres-sure and volume: PV 5 constant or P 1 V 1 5 P 2 V 2 This relationship between pressure and volume is illustrated in Figure 5.4 . FIGURE 5.2 A mercury barometer. Vacuum Mercury surface Atmospheric pressure Height (mm) 1 atm 5 760 mm Hg 5 760 torr 5 101,325 Pa 5 29.92 in. Hg 5 1.01325 bars h 5 80 mm P 5 80 mm Hg vacuum Gas inlet Gas sample A B FIGURE 5.3 A mercury manometer. FIGURE 5.4 Boyle’s law. Boyle’s law experiment showing the compressibility of gases. P atm = 760 mm Hg P atm = 760 mm Hg Height (mm) 0 10 20 30 40 Volume (cm 3 ) V 1 Volume (cm 3 ) V 2 0 100 200 300 400 0 100 200 300 400 0 10 20 30 40 h = 305 mm Hg When the mercury levels are the same on both sides of the J, the gas pressure equals atmospheric pressure. At this higher pressure, the gas volume is smaller, as predicted by Boyle’s law. When more mercury is added, atmospheric pressure is augmented by the pressure of a mercury column of height h . 142 | Chapter 5 Gases, Liquids, and Solids Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
eBook - PDF- Young, William Vining, Roberta Day, Beatrice Botch(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
AlbertSmirnov/iStockphoto.com Gases Unit Outline 11.1 Properties of Gases 11.2 Historical Gas Laws 11.3 The Combined and Ideal Gas Laws 11.4 Partial Pressure and Gas Law Stoichiometry 11.5 Kinetic Molecular Theory In This Unit… Matter exists in three main physical states under conditions we encoun-ter in everyday life: gaseous, liquid, and solid. Of these, the most fluid and easily changed is the gaseous state. Gases differ significantly from liquids and solids in that both liquids and solids are condensed states with molecules packed close to one another, whereas gases have mol-ecules spaced far apart. This unit examines the bulk properties of gases and the molecular scale interpretation of those properties. 11 AlbertSmirnov/iStockphoto.com Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Unit 11 Gases 308 11.1 Properties of Gases 11.1a Overview of Properties of Gases Gases are one of the three major states of matter. The physical properties of gases can be manipulated and measured more easily than those of solids or liquids. Because of this, the mathematical relationships between different gas properties were among the first quantitative aspects of chemistry to be studied. In general, gases differ from liquids and solids more than they differ from each other. Solid Liquid Gas Density High High Low Compressible No No Yes Fluid No Yes Yes The most striking property of gases is the simple relationship between the pressure, volume, and temperature of a gas and how a change in one of these properties affects the other properties (Interactive Figure 11.1.1). Interactive Figure 11.1.1 Explore the properties of gases. Charles D. Winters As the gaseous water vapor inside this can condenses to a liquid, the pressure inside the can drops and the can is crushed by the greater external pressure. Copyright 2018 Cengage Learning. All Rights Reserved.
eBook - PDFIntroductory Chemistry
An Active Learning Approach
- Mark Cracolice, Edward Peters, Mark Cracolice(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
Thus, we can state that the pressure exerted by a fixed amount of gas at constant volume is directly proportional to Kelvin temperature. This relationship is called Amontons’s Law or Gay-Lussac’s Law. You now have a broad picture of the Gas Laws that describe pressure, volume, and temperature relationships for a fixed amount of gas. The Combined Gas Law is the most generalized equation, and the other Gas Laws can be derived from it by holding the value of one of the variables constant and canceling it algebraically. The Gas Laws for a fixed amount of gas are summarized in Table 4.3. multiply both sides by T divide both sides by V Learn It Now! Remembering one equation and understanding the algebraic cancellation of variables is easier and will be remembered longer than trying to remember multiple equations. Be sure that you can derive Charles’s Law, Boyle’s Law, and Amontons’s Law from the Combined Gas Law before you proceed further with your studies. Table 4.3 Gas Laws for a Fixed Amount of Gas Name Relationship Variables Constants Relationship to the Combined Gas Law Combined Gas Law P 1 V 1 T 1 5 P 2 V 2 T 2 P, V, T Amount Charles’s Law V 1 T 1 5 V 2 T 2 V, T Amount, P P 1 V 1 T 1 5 P 2 V 2 T 2 Boyle’s Law P 1 V 1 5 P 2 V 2 V, P Amount, T P 1 V 1 T 1 5 P 2 V 2 T 2 Amontons’s Law P 1 T 1 5 P 2 T 2 P, T Amount, V P 1 V 1 T 1 5 P 2 V 2 T 2 CHAPTER 4 IN REVIEW: INTRODUCTION TO GASES Goal 1 Describe five macroscopic characteris- tics unique to the gas phase of matter. Five macroscopic characteristics unique to the gas phase of matter are as follows: 1. Gases may be compressed. 2. Gases may be expanded. 3. Gases have low densities. 4. Gases may be mixed in a fixed volume. 5. Gases exert constant pressure on the walls of their container uniformly in all directions. Art Directors & TRIP/Alamy Stock Photo Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
Gases whose properties of P, V, and T are accurately described by the ideal gas law (or the other Gas Laws) are said to exhibit ideal behavior or to approximate the traits of an ideal gas. An ideal gas is a hypothetical construct that may be used along with kinetic molecular theory to effectively explain the Gas Laws as will be described in a later module of this chapter. Although all the calculations presented in this module assume ideal behavior, this assumption is only reasonable for gases under conditions of relatively low pressure and high temperature. In the final module of this chapter, a modified gas law will be introduced that accounts for the non-ideal behavior observed for many gases at relatively high pressures and low temperatures. The ideal gas equation contains five terms, the gas constant R and the variable properties P, V, n, and T. Specifying any four of these terms will permit use of the ideal gas law to calculate the fifth term as demonstrated in the following example exercises. 9.2 • Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law 433 EXAMPLE 9.9 Using the Ideal Gas Law Methane, CH 4 , is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH 4 . What is the volume of this much methane at 25 °C and 745 torr? Solution We must rearrange PV = nRT to solve for V: If we choose to use R = 0.08206 L atm mol –1 K –1 , then the amount must be in moles, temperature must be in kelvin, and pressure must be in atm. Converting into the “right” units: It would require 1020 L (269 gal) of gaseous methane at about 1 atm of pressure to replace 1 gal of gasoline. It requires a large container to hold enough methane at 1 atm to replace several gallons of gasoline. Check Your Learning Calculate the pressure in bar of 2520 moles of hydrogen gas stored at 27 °C in the 180-L storage tank of a modern hydrogen-powered car.
eBook - PDF- Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
Gases whose properties of P, V, and T are accurately described by the ideal gas law (or the other Gas Laws) are said to exhibit ideal behavior or to approximate the traits of an ideal gas. An ideal gas is a hypothetical construct that may be used along with kinetic molecular theory to effectively explain the Gas Laws as will be described in a later module of this chapter. Although all the calculations presented in this module assume ideal behavior, this assumption is only reasonable for gases under conditions of relatively low pressure and high temperature. In the final module of this chapter, a modified gas law will be introduced that accounts for the non-ideal behavior observed for many gases at relatively high pressures and low temperatures. The ideal gas equation contains five terms, the gas constant R and the variable properties P, V, n, and T. Specifying any four of these terms will permit use of the ideal gas law to calculate the fifth term as demonstrated in the following example exercises. 8.2 • Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law 377 EXAMPLE 8.9 Using the Ideal Gas Law Methane, CH 4 , is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH 4 . What is the volume of this much methane at 25 °C and 745 torr? Solution We must rearrange PV = nRT to solve for V: If we choose to use R = 0.08206 L atm mol –1 K –1 , then the amount must be in moles, temperature must be in kelvin, and pressure must be in atm. Converting into the “right” units: It would require 1020 L (269 gal) of gaseous methane at about 1 atm of pressure to replace 1 gal of gasoline. It requires a large container to hold enough methane at 1 atm to replace several gallons of gasoline. Check Your Learning Calculate the pressure in bar of 2520 moles of hydrogen gas stored at 27 °C in the 180-L storage tank of a modern hydrogen-powered car.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
In the next chapter we’ll continue the study of factors that control the physical state of a substance, particularly attractive forces and their origins. ■ J. D. van der Waals (1837–1923), a Dutch scientist, won the 1910 Nobel Prize in physics. van der Waals equation of state for real gases 506 Chapter 10 | Properties of Gases | Summary Organized by Learning Objective Describe the properties of gases at the microscopic and molecular levels Gases expand to fill any container, are easily compressed, have low densities, and are affected by temperature and pressure. Explain the measurement of pressure using barometers and manometers Atmospheric pressure is measured with a barometer, in which a pressure of one standard atmosphere (1 atm) will support a column of mercury 760 mm high. This is a pressure of 760 torr. By definition, 1 atm = 101,325 pascals (Pa) and 1 bar = 100 kPa. Manometers, both open-end and closed-end, are used to measure the pressure of trapped gases. Describe and use the Gas Laws of Dalton, Charles, Gay-Lussac, and the combined gas law Boyle’s Law (Pressure–Volume Law). Volume varies inversely with pressure. V µ 1 P , or P 1 V 1 = P 2 V 2 . Charles’ Law (Temperature–Volume Law). Volume varies directly with the Kelvin temperature. V µ T, or V 1 V 2 = T 1 T 2 . Gay-Lussac’s Law (Temperature–Pressure Law). Pressure var- ies directly with Kelvin temperature. P µ T, or P 1 P 2 = T 1 T 2 . Graham’s Law of Effusion. The rate of effusion of a gas varies inversely with the square root of its density (or the square root of its molecular mass). Combined Gas Law. PV divided by T for a given gas sample is a constant. PV T = C , or P 1 V 1 T 1 = P 2 V 2 T 2 . Perform stoichiometric calculations using the Gas Laws and Avogadro’s principle Stoichiometric calculations are made using the Gas Laws and Avogadro’s principle and the previous stoichiometric methods.
eBook - ePub- Jeffrey Gaffney, Nancy Marley(Authors)
- 2017(Publication Date)
- Elsevier(Publisher)
the ratio between the pressure-volume product and the absolute temperature of a fixed mass of gas measured in Kelvin remains constant.Dalton’s law of partial pressures the total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.Gay-Lussac’s law at constant volume, the pressure of a fixed mass of any gas is directly proportional to the absolute temperature in degrees Kelvin.Ideal gas a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically.Ideal gas constant (R )a universal physical constant used in the equation for the ideal gas law.Ideal gas law the product of the pressure and the volume of an ideal gas is equal to the product of the absolute temperature of the gas, the amount of the gas, and the universal gas constant.Kinetic energy energy that a body possesses by virtue of being in motion.Kinetic-molecular theory of gases the view that the temperature and pressure of a gas is related to the motion of the gas molecules.Law of combining volumes at a given temperature and pressure, the volumes of the gaseous species reacting are proportional to the number of moles.Molar volume the volume occupied by 1 mol of an ideal gas at standard temperature and pressure. It is equal to 22.41 L.
eBook - ePub- Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
20 Working with Gas LawsI KINETIC THEORY OF GASES Phases of a compound or element (solid, liquid, gas) are determined by the balance between the strength of intermolecular forces and the average kinetic energy of the molecules. The gas phase is characterized by very weak attractive forces during which the average kinetic energy of motion dominates the physical properties of gases. For a restricted set of conditions, analysis of a gas is characterized by assuming that attractive forces between individual gas molecules are zero and that the volume occupied by the physical size of the molecules is essentially zero as compared to the volume of empty space between the molecules. Under these conditions, the gas, termed an ideal gas, is analyzed through the average statistical behavior of rapidly moving independent particles.Gases have very low density as there is a relatively large amount of empty space between individual molecules. Gases can have variable volumes; they can expand (molecules become farther apart) or be compressed (molecules are squeezed closer together). The pressure of a gas is produced by the kinetic energy of molecular collisions on the walls of the container. Gases can diffuse into each other; the rapidly moving molecules of two distinct gases can occupy the empty spaces between each other and form a gas solution (mixing at the molecular level).The kinetic energy of a gas molecule (or atom) in units of Joules is found from kE = ½ mv2 where m = the molecular (or atomic) mass in kilograms and v = velocity of the molecule in meters per second. The average kinetic energy of any sample of a specific molecular gas is determined by the molecular mass and the average or mean velocity: kE(average) = ½ m(v(average) )2 ; v(average) ≅ v(mean)
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
2. What are Boyle’s law, Charles’s law, and Avogadro’s law? What plots do you make to show a linear relationship for each law? 3. Show how Boyle’s law, Charles’s law, and Avogadro’s law are special cases of the ideal gas law. Using the ideal gas law, determine the relationship between P and n (at constant V and T ) and between P and T (at constant V and n). 4. Rationalize the following observations. a. Aerosol cans will explode if heated. b. You can drink through a soda straw. c. A thin-walled can will collapse when the air inside is removed by a vacuum pump. d. Manufacturers produce different types of tennis balls for high and low elevations. 5. Consider the following balanced equation in which gas X forms gas X 2 : 2Xsgd ¡ X 2 sgd Equal moles of X are placed in two separate containers. One container is rigid so the volume cannot change; the other container is flexible so the volume changes to keep the internal pressure equal to the external pressure. The above reaction is run in each container. What happens to the pressure and density of the gas inside each container as reactants are converted to products? 6. Use the postulates of the kinetic molecular theory (KMT) to explain why Boyle’s law, Charles’s law, Avogadro’s law, and Dalton’s law of partial pressures hold true for ideal gases. Use the KMT to explain the P versus n (at constant V and T ) relationship and the P versus T (at constant V and n) relationship. 7. Consider the following velocity distribution curves A and B. Velocity (m/s) A B Relative number of molecules a. If the plots represent the velocity distribution of 1.0 L of He(g) at STP versus 1.0 L of Cl 2 (g) at STP, which plot corresponds to each gas? Explain your reasoning.
eBook - PDF- John Kenkel(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
We will not be concerned with the mechanism by which these gauges measure pressure . However, we will be concerned with the fact that such pressure can be measured, and we will use this measured pressure in calculations . 9.5 Boyle’s Law One of the properties of gases mentioned in Section 9 .2 was compressibility . We said that if we push down on the piston pictured in Figure 9 .1 with some force, the gas can be made to occupy a smaller volume . At any given point in this process, the force pushing down is equal to the force of the gas push-ing up . In other words, the force of pushing down is equal to the pressure exerted by the gas . When the volume of the gas gets smaller by the act of compression, the force needed to push the piston down (the pressure of the gas) increases . The smaller the volume, the higher the pressure . This inverse relationship can be described mathematically . Multiplying the value of the pressure (expressed in torr, atmospheres, or any pressure unit) by the value of the volume (expressed in liters, milliliters, or any volume unit) at any point along the way in the process of pushing down the piston always gives the same number . If we symbolize the pressure as P and the volume as V, we therefore have the following relationship: PV = Constant (9 .1) If we only push the piston down slightly, such that P = P 1 and V = V 1 as in Figure 9 .7, then we get the result shown .in Equation 9 .2 . P 1 V 1 = Constant (9 .2) 225 Gases and the Gas Laws If we push the piston down further, such that P = P 2 and V = V 2 , then we get the following: P 2 V 2 = Constant (9 .3) The constants indicated in Equations 9 .2 and 9 .3 are the same number if the pressures and volumes were measured in the same units each time . Thus we have the new relationship given in Equation 9 .4 . P 1 V 1 = P 2 V 2 (9 .4) This is a statement of what has come to be known as Boyle’s law .
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