Chemistry
Gay-Lussac's Law
Gay-Lussac's Law states that the pressure of a gas is directly proportional to its temperature, provided that the volume and amount of gas remain constant. This means that as the temperature of a gas increases, so does its pressure, and vice versa. The law is a fundamental principle in understanding the behavior of gases and is often used in various applications in chemistry and physics.
Written by Perlego with AI-assistance
Related key terms
1 of 5
11 Key excerpts on "Gay-Lussac's Law"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Charles's law states that volume and temperature are directly proportional to each other as long as pressure is held constant. Boyle's law asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally, Gay-Lussac's Law introduces a direct proportionality between temperature and pressure as long as it is at a constant volume. The inter-dependence of these variables is shown in the combined gas law, which clearly states that: “ The ratio between the pressure-volume product and the temperature of a system remains constant. ” This can be stated mathematically as where: p is the pressure V is the volume T is the temperature measured in kelvins k is a constant (with units of energy divided by temperature). For comparing the same substance under two different sets of conditions, the law can be written as: The addition of Avogadro's law to the combined gas law yields the ideal gas law. Derivation from the Gas Laws Boyle's Law states that the pressure-volume product is constant: Charles's Law shows that the volume is proportional to absolute temperature: ________________________ WORLD TECHNOLOGIES ________________________ Gay-Lussac's Law says that the pressure is proportional to the absolute temperature: where P is the pressure, V the volume and T the absolute temperature and of an ideal gas. By combining (1) and either of (2) or (3) we can gain a new equation with P, V and T. Equation (2) is used in this example, and the arbitrary subscript on the constant is dropped so that k = k 2 . Substituting in Avogadro's Law yields the ideal gas equation. Physical Derivation A derivation of the combined gas law using only elementary algebra can contain surprises. For example, starting from the three empirical laws ............ (1) Gay-Lussac's Law, volume assumed constant ............ (2) Charles's Law, pressure assumed constant ............
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 - 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 - PDF- William R. Robinson, Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
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: 406 Chapter 8 | Gases This OpenStax book is available for free at http://cnx.org/content/col12012/1.7 P ∝ T or P = constant × T or P = k × T where ∝ means “is proportional to,” and k is a proportionality constant that depends on the identity, amount, and volume of the gas. For a confined, constant volume of gas, the ratio P T is therefore constant (i.e., P T = k ). If the gas is initially in “Condition 1” (with P = P 1 and T = T 1 ), and then changes to “Condition 2” (with P = P 2 and T = T 2 ), we have that P 1 T 1 = k and P 2 T 2 = k, which reduces to P 1 T 1 = P 2 T 2 . This equation is useful for pressure-temperature calculations for a confined gas at constant volume. Note that temperatures must be on the kelvin scale for any gas law calculations (0 on the kelvin scale and the lowest possible temperature is called absolute zero).
eBook - ePubCompressors
Selection and Sizing
- Royce N. Brown(Author)
- 2011(Publication Date)
- Gulf Professional Publishing(Publisher)
Many of the common “gases” used in compressors for process plant service are actually vapors. In many cases, the material may change states during a portion of the compression cycle. Water is a good example, since a decrease in temperature at high pressure will cause a portion of the water to condense. This is a common occurrence in the first intercooler of a plant air compressor. Conversely, lowering the pressure in a reservoir of liquid refrigerant at a fixed temperature will cause the vapor quantity to increase.Perfect Gas Equation
Jacques A. C. Charles and Joseph Gay-Lussac, working independently, found that gas pressure varied with the absolute temperature. If the volume was maintained constant, the pressure would vary in proportion to the absolute temperature [4] . Using a proportionality constant R, the relationships can be combined to form the equation of state for a perfect gas, otherwise known as the Perfect Gas Law.(2.1)whereP = absolute pressure v = specific volume R = constant of proportionality T = absolute temperatureIf the specific volume v is multiplied by mass m, the volume becomes a total volume V. Therefore, multiplying both sides of Equation 2.1 by m yields(2.2)In process engineering, moles are used extensively in performing the calculations. A mole is defined as that mass of a substance that is numerically equal to its molecular weight. Avogadro’s Law states that identical volumes of gas at the same temperature and pressure contain equal numbers of molecules for each gas. It can be reasoned that these identical volumes will have a weight proportional to the molecular weight of the gas. If the mass is expressed as
eBook - PDF- Edward W. Finucane(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
P 1 V 1 = P 2 V 2 Where: P 1 = the Pressure of a gas @ Time #1, measured in some suitable pressure units; V 1 = the Volume of that same gas @ Time #1, measured in some suitable volumetric units; P 2 = the Pressure of that same gas @ Time #2, measured in the same pressure units as P 1 above; & V 2 = the Volume of that same gas @ Time #2, measured in the same volumetric units as V 1 above Equation #1-6 : The following relationship, Equation #1-6 , is Charles' Law, which describes how the Vol-ume and the Absolute Temperature of a gas vary under conditions of constant pressure . V 1 T 1 = V 2 T 2 Where: 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 #1-5 , above on this page; T 1 = the Absolute Temperature of a gas @ Time #1, measured in either K or ° R; & T 2 = the Absolute Temperature of the same gas @ Time #2, measured in the same Absolute Temperature units as T 1 DEFINITIONS, CONVERSIONS, AND CALCULATIONS 1-18 Equation #1-7 : The following relationship, Equation #1-7 , is Gay-Lussac's Law, which describes how the Pressure and Temperature of a gas vary under conditions of constant volume . P 1 T 1 = P 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; & 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. 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.
eBook - PDF- John Kenkel(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
9.6 Charles’ Law The fact that gas volumes change when the temperature changes can also be treated mathematically . In this case, it is a direct relationship rather than an inverse one . As temperature increases, the volume increases . And as tempera-ture decreases, the volume decreases . This means that if we were to divide the volume by the temperature we would obtain a constant . V T = Constant (9 .5) Thus, at a particular temperature, T 1 , a given sample of gas would occupy a volume, V 1 , as shown on the left in Figure 9 .8 Dividing this volume by this temperature would then yield a constant . V T 1 1 = Constant (9 .6) If the gas were heated to a new temperature, T 2 , it would expand to a new volume, V 2 , as shown on the right in Figure 9 .8 . Dividing this volume by this temperature would yield the same constant as before . V T 2 2 = Constant (9 .7) Basic Chemistry Concepts and Exercises 228 From this observation, we can obtain the following relationship: V T V T 1 1 2 2 = (9 .8) This is a statement of what has come to be known as Charles’ law . Charles’ law holds true regardless of whether the temperature increases or decreases, meaning we could also have cooled the gas sample pictured in Figure 9 .8 with an ice bath rather than heated it with a hot plate . The smaller volume divided by the smaller temperature would yield the same constant . Once again, the units of volume are irrelevant as long as both V 1 and V 2 have the same units . However, both temperatures must be in Kelvin units . Thus if either temperature is given in Celsius or Fahrenheit units, they must be converted to Kelvin units before dividing . Also, Charles’ law only holds true if the pressure is held constant . Obviously if the pressure were also to change, then the volume would change for a reason other than there being a change in temperature, and Charles’ law would not hold true .
eBook - PDF- David Ball(Author)
- 2014(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. 6 Chapter 1 | Gases and the Zeroth Law of Thermodynamics Unless otherwise noted, all art on this page is © Cengage Learning 2014. where the function is written as F ( p, V ) to emphasize that the variables are pressure and volume, and that the outcome yields the value of the temperature T . Equations like equation 1.1 are called equations of state. One can also define equations of state that yield p or V instead of T . In fact, many equations of state can be algebraically rearranged to yield one of several possible state variables. The earliest equations of state for gases were determined by Boyle, Charles, Amontons, Avogadro, Gay-Lussac, and others. We know these equations as the various gas laws. In the case of Boyle’s gas law, the equation of state involves multiplying the pressure by the volume to get a number whose value depended on the temperature of the gas: p # V 5 F 1 T 2 at fixed n (1.2) whereas Charles’s gas law involves volume and temperature: V T 5 F 1 p 2 at fixed n (1.3) Avogadro’s law relates volume and amount, but at fixed temperature and pressure: V 5 F 1 n 2 at fixed T, p (1.4) In the above three equations, if the temperature, pressure, or amount were kept constant, then the respective functions F ( T ) , F ( p ) , and F ( n ) would be constants. This means that if one of the state variables that can change does, the other must also change in order for the gas law to yield the same constant.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
and pressure? Answer: 0.537 L Chemical Stoichiometry and Gases Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions. We have previously measured quantities of reactants and products using masses for solids and volumes in conjunction with the molarity for solutions; now we can also use gas volumes to indicate quantities. If we know the volume, pressure, and temperature of a gas, we can use the ideal gas equation to calculate how many moles of the gas are present. If we know how many moles of a gas are involved, we can calculate the volume of a gas at any temperature and pressure. Avogadro’s Law Revisited Sometimes we can take advantage of a simplifying feature of the stoichiometry of gases that solids and solutions do not exhibit: All gases that show ideal behavior contain the same number of molecules in the same volume (at the same temperature and pressure). Thus, the ratios of volumes of gases involved in a chemical reaction are given by the coefficients in the equation for the reaction, provided that the gas volumes are measured at the same temperature and pressure. We can extend Avogadro’s law (that the volume of a gas is directly proportional to the number of moles of the gas) to chemical reactions with gases: Gases combine, or react, in definite and simple proportions by volume, provided that all gas volumes are measured at the same temperature and pressure. For example, since nitrogen and hydrogen gases react to produce ammonia gas according to a given volume of nitrogen gas reacts with three times that volume of hydrogen gas to produce two times that volume of ammonia gas, if pressure and temperature remain constant. The explanation for this is illustrated in Figure 9.23. According to Avogadro’s law, equal volumes of gaseous N 2 , H 2 , and NH 3 , at the same temperature and pressure, contain the same number of molecules.
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 - PDF- Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
Answer: 0.583 L Chemical Stoichiometry and Gases Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions. We have previously measured quantities of reactants and products using masses for solids and volumes in conjunction with the molarity for solutions; now we can also use gas volumes to indicate quantities. If we know the volume, pressure, and temperature of a gas, we can use the ideal gas equation to calculate how many moles of the gas are present. If we know how many moles of a gas are involved, we can calculate the volume of a gas at any temperature and pressure. Avogadro’s Law Revisited Sometimes we can take advantage of a simplifying feature of the stoichiometry of gases that solids and solutions do not exhibit: All gases that show ideal behavior contain the same number of molecules in the same volume (at the same temperature and pressure). Thus, the ratios of volumes of gases involved in a chemical reaction are given by the coefficients in the equation for the reaction, provided that the gas volumes are measured at the same temperature and pressure. We can extend Avogadro’s law (that the volume of a gas is directly proportional to the number of moles of the gas) to chemical reactions with gases: Gases combine, or react, in definite and simple proportions by volume, provided that all gas volumes are measured at the same temperature and pressure. For example, since nitrogen and hydrogen gases react to produce ammonia gas according to a given volume of nitrogen gas reacts with three times that volume of hydrogen gas to produce two times that volume of ammonia gas, if pressure and temperature remain constant. The explanation for this is illustrated in Figure 8.23. According to Avogadro’s law, equal volumes of gaseous N 2 , H 2 , and NH 3 , at the same temperature and pressure, contain the same number of molecules.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
