Volume of Gas

12 Key excerpts on "Volume of Gas"

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  eBook - ePub

  Gas Engineering

  Vol. 2: Composition and Processing of Gas Streams

  • James G. Speight(Author)
  • 2022(Publication Date)
  • De Gruyter

    (Publisher)

  The gas laws are derived from the following assumptions and which relate to the kinetic–molecular theory is based on the following assumptions: (1) a gas consists of tiny particles, either atoms or molecules, moving about at random, (2) the volume of the particles themselves is negligible compared with the total volume of the gas, (3) the gas particles act independently of one another; there are no attractive or repulsive forces between particles, (4) collisions of the gas particles, either with other particles or with the walls of a container, are elastic so that the total kinetic energy of the gas particles is constant at constant temperature, and (5) the average kinetic energy of the gas particles is proportional to the Kelvin temperature (in Kelvin, K) of the sample. Beginning with these assumptions, it is possible not only to understand the behavior of gases but also to derive quantitatively a series of laws leading to the derivation of the ideal gas law.

  Thus, by definition, gases are the state of matter in which the molecules are far apart from each other and are characterized by a lack of definite volume and density. The following laws (listed alphabetical rather than by any preference) are (1) Avogadro’s law, (2) Boyle’s law, (3) Charles law, (4) Gay-Lussac’s law, (5) Graham’s law, and (6) the ideal gas law; these laws provide the relation between mass, pressure, volume, temperature, and density of ideal gas molecules.

  Gases, unlike solids and liquids, show similar physical behavior regardless of the chemical makeup of the gas. Form this behavior, the properties of any gas can be defined by four variables, namely (1) the pressure, P, (2) the temperature, T, (3) the volume, V, and (4) the number of moles, n, and the specific relationships among these four variables form the basis for the gas laws and, consequently, an ideal gas is a gas whose behavior follows the gas laws.

  There are two types of gases: an ideal gas and a nonideal gas. An ideal gas has the following properties: (1) there are no intermolecular forces between the gas particles, (2) the volume occupied by the particles is negligible compared to the volume of the container they occupy, and (3) the only interactions between the particles and with the container walls are perfectly elastic collisions.

  An ideal gas can be characterized by three variables which are (1) the absolute pressure, P, (2) the volume, V, and (3) the absolute temperature, T. Thus:

  P V = n Z R T

  Typically, in this equation, P is the pressure, V is the volume, T is the absolute temperature in Kelvin, Z is the compressibility, n is the number of kilomoles, and R

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  eBook - ePub

  The Britannica Guide to Matter

  • Britannica Educational Publishing, Erik Gregersen(Authors)
  • 2010(Publication Date)
  • Britannica Educational Publishing

    (Publisher)

  T is the absolute thermodynamic temperature. To a rough degree, the expression is accurate within a few percent if the volume is more than 10 times the critical volume; the accuracy improves as the volume increases. The expression eventually fails at both high and low temperatures, owing to ionization at high temperatures and to condensation to a liquid or solid at low temperatures.

  The ideal gas equation of state is an amalgamation of three ideal gas laws that were formulated independently. The first is Boyle’s law, which refers to the elastic properties of the gas; it was described by the Anglo-Irish scientist Robert Boyle in 1662 in his famous “… Experiments … Touching the Spring of the Air.…” It states that the volume of a gas at constant temperature is inversely proportional to the pressure; i.e., if the pressure on a gas is doubled, for example, its volume decreases by one-half. The second, usually called Charles’s law, is concerned with the thermal expansion of the gas. It is named in honour of the French experimental physicist Jacques-Alexandre-César Charles for the work he carried out in about 1787. The law states that the volume of a gas at constant pressure is directly proportional to the absolute temperature; i.e., an increase of temperature of 1 °C (1.8 °F) at room temperature causes the volume to increase by about 1 part in 300, or 0.3 percent.

  The third law embodied in equation (15) is based on the 1811 hypothesis of the Italian scientist Amedeo Avogadro—namely, that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. The number of particles (or molecules) is proportional to the number of moles n , the constant of proportionality being Avogadro’s number, N 0 . Thus, at constant temperature and pressure the volume of a gas is proportional to the number of moles. If the total volume V contains n moles of gas, then only v = V/n appears in the equation of state. By measuring the quantity of gas in moles rather than grams, the constant R is made universal; if mass were measured in grams (and hence v in volume per gram), then R

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  It also explains why we have gas laws for gases, and the same laws for all gases, but not compa- rable laws for liquids or solids. The chemical identity of the gas does not matter, because gas molecules do not touch each other except when they collide, and there are extremely weak interactions, if any, between them. We cannot go over the mathematical details, but we can describe some of the ways in which the laws of physics and the model of an ideal gas account for the gas laws and other properties of matter. Definition of Temperature The greatest triumph of the kinetic theory came with its explanation of gas temperature, which we discussed in Section 6.2. What the calculations showed was that the product of gas pressure and volume, PV, is proportional to the average kinetic energy of the gas molecules. PV ∝ average molecular KE But from the experimental study of gases, culminating in the equation of state for an ideal gas, we have another term to which PV is proportional—namely, the Kelvin temperature of the gas. PV ∝ T 12 In perfectly elastic collisions, no energy is lost by friction as the colliding objects deform momentarily. 520 CHAPTER 10 Properties of Gases (We know what the proportionality constant here is—namely, nR—because by the ideal gas law, PV equals nRT.) With PV proportional both to T and to the “average molecular KE,” then it must be true that the temperature of a gas is proportional to the average molecular KE. T ∝ average molecular KE (10.8) PV ∝ T Pressure–Volume Law (Boyle’s Law) Using the model of an ideal gas, physi- cists were able to demonstrate that gas pressure is the net effect of innumerable collisions made by gas particles with the walls of the container. Let’s imagine that one wall of a gas container is a movable piston that we can push in (or pull out) and so change the volume (see Figure 10.13). If we reduce the volume by one-half, we double the number of molecules per unit volume.

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  eBook - PDF

  Introductory Chemistry

  An Active Learning Approach

  • Mark Cracolice, Edward Peters, Mark Cracolice(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  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. 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. 144 Chapter 4 Introduction to Gases Goal 2 Use the postulates of the kinetic molec- ular theory to explain the reasons for the macro- scopic characteristics unique to the gas phase of matter. The reasons for the macroscopic characteristics unique to the gas phase of matter are as follows: 1. A gas consists of molecules and empty space. 2. The volume occupied by the molecules in a gas is negligible when compared with the volume of the space they occupy. 3. The attractive forces among molecules of a gas are negligible. 4. The average kinetic energy of gas molecules is proportional to the temperature, expressed in kelvins. 5. Molecules interact with one another and with the container walls without loss of total kinetic energy. Goal 3 Define pressure and interpret statements in which the term pressure is used. Pressure is defined as force per unit area. Goal 4 Explain the cause of the pressure of a gas. Pressure is the effect of the force of the interactions of the huge number of rapidly moving molecules of a gas as they collide with the surface area of an object in contact with that gas.

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  Chemistry

  The Molecular Nature of Matter

  • James E. Brady, Neil D. Jespersen, Alison Hyslop(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Although real gases do not exactly obey Boyle’s law or any of the other gas laws that we’ll study, it is often useful to imagine a hypothetical gas that would. We call such a hypothetical gas an ideal gas. An ideal gas obeys the gas laws exactly over all temperatures and pressures. A real gas behaves more and more like an ideal gas as its pressure decreases and its temperature increases. Most gases we work with in the lab can be treated as ideal gases unless we’re dealing with extremely precise measurements. Temperature–Volume Law In 1787 a French chemist and mathematician named Jacques Alexander Charles became interested in hot-air ballooning, which at the time was becoming popular in France. His new interest led him to study what happens to the volume of a sample of gas when the temperature is varied, keeping the pressure constant. ■ Jacques Alexandre César Charles (1746–1823), a French scientist, had a keen interest in hot-air balloons. He was the first to inflate a balloon with hydrogen. Figure 10.6 | Compressing a gas increases its pressure. A molecular view of what happens when a gas is squeezed into a smaller volume. By crowding the molecules together, the number of collisions within a given area of the walls increases, which causes the pressure to rise. Figure 10.7 | The variation of volume with pressure at constant temperature for a fixed amount of gas. (a) A typical graph of volume versus pressure, showing that as the pressure increases, the volume decreases. (b) A straight line is obtained when volume is plotted against 1 P , which shows that V µ 1 P . Pressure (P ) Volume (V ) 1/Pressure (1/P ) Volume (V ) (a) (b) 474 Chapter 10 | Properties of Gases When data from experiments such as Charles’ are plotted, a graph like that shown in Figure 10.8 is obtained. Here the volume of the gas is plotted against the temperature in degrees Celsius. The colored points correspond to typical data, and the lines are drawn to most closely fit the data.

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  eBook - ePub

  Survival Guide to General Chemistry

  • Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  20 Working with Gas Laws

  I	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)

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  Chemistry

  Structure and Dynamics

  • James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  The same amount of O 2 gas at room temperature and atmospheric pressure has a volume of 753 mL––an increase of a factor of about 800. One gram of solid CO 2 at 79C has a volume of 0.641 mL. At room temperature and atmospheric pressure, the same amount of CO 2 gas has a volume of 548 mL––once again, an increase of a factor of about 800. The consequences of the enormous change in volume that occurs when a liquid or solid is transformed into a gas are often used to do work. The steam engine, which brought about the Industrial Revolution, is based on the fact that water boils to form a gas (steam) that has a much larger volume. The gas there- fore escapes from the container in which it has been generated, and the escaping steam can be made to do work. The same principle is at work when dynamite is used to blast rocks. In 1867, the Swedish chemist Alfred Nobel discovered that the highly dangerous liquid explosive known as nitroglycerin could be absorbed onto clay or sawdust to produce a solid that was much more stable and therefore safer to use. When dynamite is detonated, the nitroglycerin decomposes to pro- duce a mixture of CO 2 , H 2 O, N 2 , and O 2 gases. Because 29 mol of gas are produced for every 4 mol of liquid that decomposes, and each mole of gas occupies a volume hundreds of times larger than a mole of liquid, the reaction produces a shock wave that destroys anything in its vicinity. The same phenomenon occurs on a much smaller scale when we “pop” pop- corn. When kernels of popcorn are heated in oil, the liquids inside the kernel turn into gases. The pressure that builds up inside the kernel is enormous and eventu- ally causes the kernel to explode. 6.6 Pressure versus Force The volume of a gas is one of its characteristic properties. Another characteristic property is the pressure the gas exerts on its surroundings.

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  General Chemistry for Engineers

  • 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.

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  Chemistry

  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.

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  Understanding Chemistry through Cars

  • Geoffrey M. Bowers, Ruth A. Bowers(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  9 Chapter one: The properties and behavior of gases • Understand that for a gas at constant temperature, its pressure and volume are inversely proportional • Understand that for a gas at constant pressure, its volume and absolute temperature are proportional • Explain how a shock absorber dissipates energy using gas laws, the concepts of heat and work, and kinetic molecular theory Pistons play critical roles in many automotive systems, from the engine itself to the brakes and suspension. Pistons are also essential to demon-strate critical relationships between other gas properties, namely the links between pressure and volume and temperature and volume. In this section, we introduce Boyle’s and Charles’s laws using concepts from kinetic molec-ular theory and a simple piston. Then we use these concepts to explain how a typical gas-filled shock absorber or strut functions in your car’s suspen-sion, and why you use a liquid in your brake lines rather than a gas. The simple piston is an idealized system where a fixed quantity of gas is trapped within a chamber sealed on one side by a piston in contact with the atmosphere. The chamber functions as a closed system, and thus fixes the number of molecules of gas within the system, defined here as gas trapped within the chamber. The remainder of the apparatus lets temperature, pres-sure, and volume vary. If we hold one of these variables constant (tempera-ture, pressure, or volume), the relationship between the other two variables can be explored via experiment. The key element to each experiment is understanding that the piston itself will not move when the pressure inside the chamber is equivalent to the pressure outside the chamber. This crite-rion of equal pressures establishes the equilibrium position of the piston. If one holds the temperature constant, the pressure in the system can be varied by changing the external force applied to the piston (Figure 1.2).

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  Physics in the Modern World

  • Jerry Marion(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  T held constant, Boyle found that the product of pressure and volume always remains constant. That is,

  FIGURE 10-9 Robert Boyle discovered the relationship that connects the volume and the pressure of a confined gas at constant temperature: PV = constant.

  P V = constant        

  (

  when   T   is contant

  )

                     

  (10-8)

  (10-8)

  This relationship is called Boyle’s law .

  For a series of three different conditions such as those shown in Fig. 10-9 , we have

  P 1

  V 1

  =

  P 2

  V 2

  =

  P 3

  V 3

         

  (

  when   T   is constant

  )

           

  (10-8a)

  (10-8a)

  In order to halve the volume of a gas, the pressure must be doubled , and so forth.

  For a particular sample of gas, the “constant” in PV = constant is the same for all pressure−volume combinations. But for a different quantity of gas, the “constant” will have a different value.

  The Law of Charles and Gay-Lussac

  An extension of Boyle’s law was made in 1802 by the French physicists Jacques Charles (1746-1823) and Joseph Louis Gay-Lussac (1778-1850), who, independently of one another, discovered the way in which the volume of a gas varies with temperature for constant pressure.

  In order to see the way in which the volume and temperature of a gas are related, let us examine a specific case. Suppose that we confine a certain quantity of gas in a cylinder. We adjust the conditions until the temperature is 0 °C and the volume of the gas 273 cm3 (see Fig. 10-10 ). For all of the remaining operations, we maintain the same pressure . If we lower the temperature to − 1 °C, we find that the volume of the gas decreases to 272 cm3 . At a temperature of −2 °C, the volume is 271 cm3 . That is, for each degree that the temperature is lowered, the volume decreases by 1 cm3 or of the original volume. When T = 173 °C is reached, we find V = 100 cm3 . If the gas continues to behave in this way, we would expect that a temperature of − 273 °C would result in zero volume. We cannot actually reach this extreme condition because (a) any real gas would liquefy at a temperature above − 273 °C and (b) the temperature − 273 °C can never be attained in any real system. In spite of these practical difficulties, the temperature T = − 273 °C has an important significance because it represents the lowest temperature that is conceivable (even if it cannot actually be attained

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  A Mole of Chemistry

  An Historical and Conceptual Approach to Fundamental Ideas in Chemistry

  • Caroline Desgranges, Jerome Delhommelle(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  1 ! He finds the same formula for different gases such as oxygen, nitrogen and hydrogen. He names this relation Charles’ law in Charles’ honor. He also notes that, if he draws a graph for the volume against the temperature, a Volume of Gas of zero (V = 0) is reached for a temperature of –266.66°C! For Gay-Lussac, this shows that Charles’s law must be taken with caution and does not apply at low temperatures. Nevertheless, Lord Kelvin will give another meaning to this number representing the “infinite cold” or absolute zero, leading to an entirely new science, now known as thermodynamics!

  Gay-Lussac also uses the data for the different heights of mercury from his experiments. He deduces that the pressure of the gas increases when temperature increases. Repeating the same process as before, i.e. looking at two experiments for two different temperatures, he finds that P1 T2  = P2 T1 ! This law is called Gay-Lussac’s law. Gathering Boyle’s, Charles’ and Gay-Lussac’s laws, we obtain the famous combined gas law that gives the relationship between temperature, pressure and volume for any gas. Using mathematical equations, this translates into PV = constant (Boyle’s law), V/T = constant (Charles’ law) and P/T = constant (Gay-Lussac’s law). It thus follows that (PV)/T = constant… Q.E.D.! This is a very powerful formula that can be used to solve practical problems. For instance, consider a gas at temperature T1 , with volume V1 and pressure P1 . If we increase the temperature to twice the initial value (T2  = 2T1 ) and keep the same volume (V2  = V1 ), we can calculate the pressure P2  = (P1 V1 T2 )/(V2 T1 ). We thus find that, since V2  = V1 and T2  = 2T1 , P2  = 2P1 ! In other words, when a gas is enclosed in a vessel of fixed volume and we warm it up to twice the initial temperature, we find that the pressure at this new temperature is twice the value it had at the beginning of the experiment! We can also solve much more complex problems, for which two variables change, for instance, P and V, or P and T, or T and V. We just need to use the fact that (P1 V1 )/T1  = (P2 V2 )/T2

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