Physics
Gas Pressure and Temperature
Gas pressure is the force exerted by gas particles on the walls of their container. It is directly proportional to the temperature of the gas, as described by the ideal gas law. When the temperature of a gas increases, its particles move faster and collide with the container walls more frequently, leading to an increase in pressure.
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10 Key excerpts on "Gas Pressure and Temperature"
eBook - PDFChemistry
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.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
As the gas is heated, the pressure of the gas in the sphere increases. This relationship between temperature and pressure is observed for any sample of gas confined to a constant volume. An example of experimental pressure-temperature data is shown for a sample of air under these conditions in Figure 9.11. We find that temperature and pressure are linearly related, and if the temperature is on the kelvin scale, then P and T are directly proportional (again, when volume and moles of gas are held constant); if the temperature on the kelvin scale increases by a certain factor, the gas pressure increases by the same factor. FIGURE 9.11 For a constant volume and amount of air, the pressure and temperature are directly proportional, provided the temperature is in kelvin. (Measurements cannot be made at lower temperatures because of the condensation of the gas.) When this line is extrapolated to lower pressures, it reaches a pressure of 0 at –273 °C, which is 0 on the kelvin scale and the lowest possible temperature, called absolute zero. Guillaume Amontons was the first to empirically establish the relationship between the pressure and the temperature of a gas (~1700), and Joseph Louis Gay-Lussac determined the relationship more precisely (~1800). Because of this, the P-T relationship for gases is known as either Amontons’s law or Gay-Lussac’s law. Under either name, it states that the pressure of a given amount of gas is directly proportional to its temperature on the kelvin scale when the volume is held constant. Mathematically, this can be written: where ∝ means “is proportional to,” and k is a proportionality constant that depends on the identity, amount, and volume of the gas. 426 9 • Gases Access for free at openstax.org For a confined, constant volume of gas, the ratio is therefore constant (i.e., ).
eBook - PDF- Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
As the gas is heated, the pressure of the gas in the sphere increases. This relationship between temperature and pressure is observed for any sample of gas confined to a constant volume. An example of experimental pressure-temperature data is shown for a sample of air under these conditions in Figure 8.11. We find that temperature and pressure are linearly related, and if the temperature is on the kelvin scale, then P and T are directly proportional (again, when volume and moles of gas are held constant); if the temperature on the kelvin scale increases by a certain factor, the gas pressure increases by the same factor. FIGURE 8.11 For a constant volume and amount of air, the pressure and temperature are directly proportional, provided the temperature is in kelvin. (Measurements cannot be made at lower temperatures because of the condensation of the gas.) When this line is extrapolated to lower pressures, it reaches a pressure of 0 at –273 °C, which is 0 on the kelvin scale and the lowest possible temperature, called absolute zero. Guillaume Amontons was the first to empirically establish the relationship between the pressure and the temperature of a gas (~1700), and Joseph Louis Gay-Lussac determined the relationship more precisely (~1800). Because of this, the P-T relationship for gases is known as either Amontons’s law or Gay-Lussac’s law. Under either name, it states that the pressure of a given amount of gas is directly proportional to its temperature on the kelvin scale when the volume is held constant. Mathematically, this can be written: where ∝ means “is proportional to,” and k is a proportionality constant that depends on the identity, amount, and volume of the gas. 370 8 • Gases Access for free at openstax.org For a confined, constant volume of gas, the ratio is therefore constant (i.e., ).
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
In contrast, in liquids and solids, atoms and molecules are closer together and are quite sensitive to the forces between them. Figure 13.17 Atoms and molecules in a gas are typically widely separated, as shown. Because the forces between them are quite weak at these distances, the properties of a gas depend more on the number of atoms per unit volume and on temperature than on the type of atom. To get some idea of how pressure, temperature, and volume of a gas are related to one another, consider what happens when you pump air into an initially deflated tire. The tire’s volume first increases in direct proportion to the amount of air injected, without much increase in the tire pressure. Once the tire has expanded to nearly its full size, the walls limit volume expansion. If we continue to pump air into it, the pressure increases. The pressure will further increase when the car is driven and the tires move. Most manufacturers specify optimal tire pressure for cold tires. (See Figure 13.18.) Chapter 13 | Temperature, Kinetic Theory, and the Gas Laws 485 Figure 13.18 (a) When air is pumped into a deflated tire, its volume first increases without much increase in pressure. (b) When the tire is filled to a certain point, the tire walls resist further expansion and the pressure increases with more air. (c) Once the tire is inflated, its pressure increases with temperature. At room temperatures, collisions between atoms and molecules can be ignored. In this case, the gas is called an ideal gas, in which case the relationship between the pressure, volume, and temperature is given by the equation of state called the ideal gas law. Ideal Gas Law The ideal gas law states that (13.18) PV = NkT , where P is the absolute pressure of a gas, V is the volume it occupies, N is the number of atoms and molecules in the gas, and T is its absolute temperature.
eBook - PDFIntroductory Chemistry
An Active Learning Approach
- Mark Cracolice, Edward Peters, Mark Cracolice(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
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. 140 Chapter 4 Introduction to Gases 4.7 The Combined Gas Law: Volume, Temperature, and Pressure Goal 15 For a fixed amount of a confined gas, given the initial volume, pressure, and temperature and the final values of any two variables, calculate the final value of the third variable. 16 State the values associated with standard temperature and pressure (STP) for gases. As you ascend a mountain while you drive up a steep mountain road, you can feel the temperature of the air decrease as you gain altitude. Your ears may also pop as they adjust to the decreasing pressure. This prompts the question: How is the volume of a gas affected by both a change in temperature and a change in pressure? In Section 4.5, you built an understanding of Charles’s Law: The volume and the Kelvin temperature of a fixed amount of a gas at constant pressure are directly proportional, V ~ T. In Section 4.6, you worked on acquiring knowledge about Boyle’s Law: The volume and the pressure of a fixed amount of a gas at constant temperature are inversely proportional, V ~ 1/P.
eBook - PDF- William R. Robinson, Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Chapter 8 | Gases 413 Visit this interactive PhET simulation (http://openstaxcollege.org/l/ 16IdealGasLaw) to investigate the relationships between pressure, volume, temperature, and amount of gas. Use the simulation to examine the effect of changing one parameter on another while holding the other parameters constant (as described in the preceding sections on the various gas laws). The Ideal Gas Law To this point, four separate laws have been discussed that relate pressure, volume, temperature, and the number of moles of the gas: • Boyle’s law: PV = constant at constant T and n • Amontons’s law: P T = constant at constant V and n • Charles’s law: V T = constant at constant P and n • Avogadro’s law: V n = constant at constant P and T Combining these four laws yields the ideal gas law, a relation between the pressure, volume, temperature, and number of moles of a gas: PV = nRT where P is the pressure of a gas, V is its volume, n is the number of moles of the gas, T is its temperature on the kelvin scale, and R is a constant called the ideal gas constant or the universal gas constant. The units used to express pressure, volume, and temperature will determine the proper form of the gas constant as required by dimensional analysis, the most commonly encountered values being 0.08206 L atm mol –1 K –1 and 8.314 kPa L mol –1 K –1 . 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.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
221 Chapter Six GASES 6.1 Temperature 6.2 Temperature as a Property of Matter 6.3 The States of Matter 6.4 Elements or Compounds That Are Gases at Room Temperature 6.5 The Properties of Gases 6.6 Pressure versus Force 6.7 Atmospheric Pressure 6.8 Boyle’s Law 6.9 Amontons’ Law 6.10 Charles’ Law 6.11 Gay-Lussac’s Law 6.12 Avogadro’s Hypothesis 6.13 The Ideal Gas Equation 6.14 Dalton’s Law of Partial Pressures 6.15 Ideal Gas Calculations: Part I 6.16 Ideal Gas Calculations: Part II 6.17 The Kinetic Molecular Theory 6.18 How the Kinetic Molecular Theory Explains the Gas Laws 6.19 Graham’s Laws of Diffusion and Effusion Special Topics 6A.1 Deviations from Ideal Gas Law Behavior: The van der Waals Equation 6A.2 Analysis of the van der Waals Constants The Nobel Prize–winning physicist Richard Feynman once asked, “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sen- tence passed on to the next generations of creatures, what statement would contain the most information in the fewest words?” Feynman then answered the question, “I believe it is the atomic hypothesis that all things are made of atoms––little particles that move about in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.” 1 This is, as Feynman observed, a statement of enormous power. So far we have developed the idea that all things are made of atoms, but we haven’t discussed the other parts of Feynman’s statement––that atoms move about in per- petual motion and that particles attract and repel each other. Atoms and molecules in a gas are never at rest. The N 2 and O 2 molecules in the atmosphere move through space at speeds of almost a thousand miles per hour until they collide with another particle in the gas or with the walls of the container.
eBook - PDFThe Atmospheric Environment
Effects of Human Activity
- Michael B. Mcelroy(Author)
- 2021(Publication Date)
- Princeton University Press(Publisher)
A dif- ferential pressure of this magnitude corresponds to a force of 10 5 dyn cm −2 , comparable to the force delivered by a pow- erful bomb. 2.9 The Perfect Gas Law The pressure, density, and temperature of a gas are not inde- pendent quantities. They are related according to an equa- tion known as the equation of state. For a gas of relatively low density, a condition satisfied by the atmosphere, the equation of state assumes the simple form p = nkT , (2.16a) where n defines the number density of molecules, the num- ber of molecules per unit volume (in the cgs system, n is ex- pressed in molecules per cm 3 , abbreviated as cm –3 ). Expressed in the form of (2.16a), the equation of state is known as the perfect gas law. Chemists favor a different expression of the perfect gas law. They prefer to measure pressure in units of atmospheres (atm), density in units of moles (mol) per liter (1) (a mole is equivalent to 6.02 × 10 23 molecules, where 6.02 × 10 23 is known as Avogadro’s number, discussed further in Section 3.3). It is no longer appropriate in this case to use k as the constant in the equation relating p, n, and T. The alternate, chemists’ expression for the perfect gas law is P = NRT , (2.16b) where P is given in atm, N in mol l −1 , and T in K. R, known as the universal gas constant, has the numerical value 0.08206, with units of atm l mol −1 K −1 . h P a P a P a P a Atmospheric pressure Atmospheric pressure Figure 2.4 Schematic view of a mercury barometer. Remember that gh = P a . The height (h) of the mercury in the column is proportional to the pressure P a with which air presses down on the mercury outside of the column. We can rationalize the form of the perfect gas law by considering the momentum content of a gas confined in a container with elastic walls. Molecules are buzzing in all di- rections. From time to time they strike the walls.
eBook - PDF- Edward W. Finucane(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
Equation #1-8 : The following formula, Equation # 1-8 , is the General Gas Law, which is the more general-ized relationship involving changes in any of the basic measurable characteristics of any gas. This relationship permits the determination of the value of any of the three basic char-acteristics of the gaseous material being evaluated — namely: its Pressure, its Temperature, and/or its Volume — any one of which might have changed as a result of changes in either one or both of the other two characteristics. P 1 V 1 T 1 = P 2 V 2 T 2 Where: P 1 & P 2 are the Pressures of the gas of interest at each of its two states, with this term as was defined for Equation #1-5 on the previous page, namely, Page 1-17; V 1 & V 2 are the Volumes of the gas of interest at each of its two states, with this term as was defined for Equation #s 1-5 & 1-6 on the previous page, namely, Page 1-17; & T 1 & T 2 are the Absolute Temperatures of the gas of interest at each of its two states, with this term as was defined for Equation #1-6 , on the previous page, namely Page 1-17, and Equation # 1-7 above on this page. BASIC PARAMETERS AND LAWS 1-19 Equation #1-9 : The following relationship, Equation # 1-9 , is the Ideal Gas Law [it is also frequently called the Perfect Gas Law]. This law is one of the most commonly used Equations of State. Like the immediately preceding formula, this one provides the necessary relationship for de-termining the value of any of the measurable characteristics of a gas — namely, again: its Pressure, its Temperature, and/or its Volume; however, it does not require that one know these characteristics at some alternative state or condition. Unlike Equation # 1-8 , on the previous page, namely, Page 1-18, it does require that the quantity of the gas involved in the determination be known (i.e., the Number of Moles involved, or the weight and identity of the gas involved, etc.).
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.
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