Chemistry
Gas Constant
The gas constant, denoted by the symbol R, is a fundamental physical constant in chemistry. It relates the energy of a system to the temperature and pressure of the gas. Its value depends on the units used for pressure, volume, and the amount of substance, and it is often used in the ideal gas law equation.
Written by Perlego with AI-assistance
Related key terms
1 of 5
9 Key excerpts on "Gas Constant"
eBook - PDF- David Ball(Author)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
(For changes in temperature, the units can be kelvins or degrees Celsius, because the change in temperature will be the same. However, the absolute value of the temperature will be different.) Having established the proper temperature scale for thermodynamics, we can return to the constant R. This value, the ideal gas law constant, is probably the most important physical constant for macroscopic systems. Its specific numerical value depends on the units used to express the pressure and volume. Table 1.2 lists various values of R. The ideal gas law is the best-known equation of state for a gas-eous system. Gas systems whose state variables p, V, n, and T vary according to the ideal gas law satisfy one criterion of an ideal gas (the other criterion is presented in Chapter 2). Nonideal (or real ) gases, which do not follow the ideal gas law exactly, can approximate ideal gases if they are kept at high temperature and low pressure. It is useful to define a set of reference state variables for gases, because they can have a wide range of values that can in turn affect other state variables. The most common set of reference state variables for pressure and temperature is p 5 1.0 bar and T 5 273.15 K 5 273.15°C. These conditions are called standard temperature and pressure,* abbreviated STP. Much of the thermodynamic data reported for gases are given for conditions of STP. SI also defines standard ambient temperature and pressure, SATP, as 298.15 K for temperature and 1 bar for pressure (1 bar 5 0.987 atm). *1 atm is commonly used as standard pressure, although technically it is incorrect. Because 1 bar 5 0.987 atm, the error introduced is slight. FIGURE 1.4 William Thomson, later Baron Kelvin (1824–1907), a Scottish physicist. Thomson established the neces-sity of a minimum absolute temperature, and proposed a temperature scale based on that absolute zero. He also performed valuable work on the first transatlantic cable.
No longer available |Learn more- Irving Granet, Maurice Bluestein(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
Denoting the Gas Constant per unit mass by the symbol R , we have pV = pmv = mRT (6.8) It will be recalled from Chapter 1 that we identified the velocity term in the equation derived on the basis of elementary kinetic theory as being proportional to the temperature of the gas (the random motion of the gas molecules). Using this, we can also obtain the equation of state of a gas as Equation 6.8. In English engineering units, p is the pressure in pounds force per square foot absolute, V is the total volume of the gas in cubic feet, T is the absolute temperature in degrees Rankine, m is the mass of gas in pounds mass, and R is a constant of proportionality in ft. lb f /lb m ·°R. If m is eliminated in Equation 6.8, it becomes pv = RT (6.9) in which p, R, and T correspond to the terms in Equation 6.8, and v represents the specific volume. In SI units, p is in kilopascals, T is in degrees Kelvin, m is in kilograms when R is in kJ/kg·K, and v is in cubic meters per kilogram. R for actual gases is not a constant and varies from gas to gas. However, it has been found experimentally that most gases at very low pressure or with high degrees of super-heat exhibit nearly constant values of R. As further indicated in Table 6.1, the product of molecular weight (MW) and R for most gases is nearly constant and, in usual English engineering units, equals 1545.3 ft. lb f /lb m mol·°R. For any other combination of pressure, volume, and temperature units, it is a relatively straightforward calculation to derive R. Some values of this constant in other systems are listed in Table 6.2. For the purposes of this book, a value of MW × R of 1545 ft. lb f /lb m mol·°R is used. In SI units, the value of this product is 8.314 kJ/kg mol·K. These values are often called the universal Gas Constant in their respective unit systems with the notation R o . TABLE 6.1 Gas Constant Data Gas Gas MW Product MW × R (rounded) Air 28.97 1545 ft.
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
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- Don Shillady(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
Thus, we have F ¼ 180 100 C þ 32 ¼ 9 5 C þ 32 It is easy to show that the two temperature scales give the same value at 40 by substituting one for the other either way. In Fahrenheit we see that absolute zero is F ¼ 9 5 ( 273 : 15 ) þ 32 ¼ 459 : 67 F : The Fahrenheit scale is still used in engineering but in chemistry and physics the centigrade scale is used along with the absolute temperature K . Now let us combine Boyle ’ s law with Charles ’ law to improve the overall phenomenological description (for a fi xed mass of gas). Consider a two-step process that fi rst changes the pressure of the gas followed by a change in the temperature. P 1 T 1 V 1 ! P 2 T 1 V x ! P 2 T 2 V 2 Then by Boyle ’ s law at constant temperature V x ¼ P 1 P 2 V 1 and then use Charles ’ law at constant pressure as V 2 ¼ V x T 2 T 1 ¼ P 1 P 2 V 1 T 2 T 1 ) V 2 V 1 ¼ P 1 P 2 T 2 T 1 : This leads to a very useful equation for a fi xed mass of gas as P 1 V 1 T 1 ¼ P 2 V 2 T 2 This equation implies the existence of another constant C 3 . PV T ¼ C 3 ¼ nR Now we are close to a general phenomenological equation that takes into account P , V , T , and the moles ( n ) of the gas, which fi xes the mass of the gas sample. Usually this equation is given (in high school chemistry!) as PV ¼ nRT So what is R ? And now we come to a key development in 1876. Ideal and Real Gas Behavior 7 Avogadro ’ s hypothesis : Equal volumes of different gases at the same temperature and pressure have the same number of molecules. Amedeo Avogadro (1776 – 1856) was an Italian physicist who published a basic argument in 1811 that related atomic and molecular weights to de fi nite proportions in compounds but that era was a period of intellectual groping by chemists regarding the meaning of the concepts of atoms and molecules.
- Armand Berman(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
1.13 The Equation of State 7 For the accurate value of N A within 7 significant digits after the decimal point, see Appendix, Table A.6. 1.11 The Mass per Molecule m = M/N A (e.g.,g) (1.10) 1.12 The Molar Volume If T = 273.16 K and p = 1.013250 X 10 5 Pa, the molar volume is V M = 22.4 (liters mol 1 ) (1.11) For the accurate value of the molar volume, see Appendix, Table A.6. 1.13 The Equation of State 1.13.1 Single Species of Gas pV = n M RT (1.12) = (W t /M)RT (1.12a) where R is the mohr Gas Constant per mole basis (also known as the universal Gas Constant). The values of the molar Gas Constant R in some system of units are listed in Table 1.3. 1.13.2 Mixture of Gases If V m is the volume of the mixture and p = p x + p 2 + ' * ' + />,· = , (Dalton's law; Eq. 1.6), then pV m = (2n M i )RT (1.12b) Equation 1.12b holds true if all the mixture components have the same pressure. Thus V m = V, + V 2 + · · · + , = /. (1.12c) For the component i in the mixture py m = n Mi RT (1.12d) 8 1 Ideal Gases Thus Pi = ( M / V J R T (1.12e) = X;RT (1.120 where x t is the concentration in moles per unit volume. 1.14 Boltzmann* s Constant k=R/N A = 1.3806 X 10 16 (ergsK 1 ) (1.13) = 1.3806 X 10 23 (JK 1 ) (1.13a) For the conversion of ergs to joules, see Appendix, Table A. 16. For the value of k accurate within 6 significant digits after the decimal point, see Appendix, Table A.6. Boltzmann's constant k is calculated per molecular basis in contrast with the universal Gas Constant R, which is calculated on a per mole basis. The values of k in some system of units are listed in Table 1.3. 1.15 The Gas Density p = mn (e.g., kg m -3 ) O-H) = pM/RT (1.14a) = pm/kT (1.14b) = M/V M (1.14c) For the expressions of n and m, see Eqs. 1.8 and 1.10. The values of R and k in some system of units are listed in Table 1.3. The density of gas p depends on temperature and pressure. Therefore, these parameters must be specified when quoting the gas density.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
Explain why the volumes need to be measured at a constant temperature and pressure. 10.10 Explain why two liters of hydrogen gas and one liter of oxygen gas react to form two liters of water, when the pressures and temperatures are held constant. Ideal Gas Law 10.11 State the ideal gas law in the form of an equation. What is the value of the Gas Constant in units of L atm mol -1 K -1 ? 10.12 Using the ideal gas law, show that at STP, the molar volume of an ideal gas is 22.4 L. 10.13 The molar mass of a gas can be determined from its mass, volume, pressure, and temperature. Derive the equation from the ideal gas law and the definition of molar mass. Dalton’s law of partial pressures (Section 10.6) P total = P A + P B + P C + . . . When a gas is collected over water, P total = P water + P gas Mole fraction and mole fraction related to partial pressure (Section 10.6) X A = n A n total = P A P total Graham’s law of effusion (Section 10.6) effusion rate (A) effusion rate (B) = Å d B d A = Å M B M A van der Walls equation of state for real gases (Section 10.8) a P meas + n 2 a V 2 b (V meas - nb) = nRT = WileyPLUS, an online teaching and learning solution. Note to instructors: Many of the end-of-chapter problems are available for assignment via the WileyPLUS system. www.wileyplus.com. Review Problems are presented in pairs separated by blue rules. Answers to problems whose numbers appear in blue are given in Appendix B. More challenging problems are marked with an asterisk . Review Problems 509 10.14 The density of a gas can vary with pressure, volume, and temperature. Develop an equation for density from the ideal gas law. Dalton’s Law of Partial Pressures 10.15 What is partial pressure? 10.16 State Dalton’s law of partial pressures in the form of an equation. 10.17 Define mole fraction. How is the partial pressure of a gas related to its mole fraction and the total pressure? 10.18 Consider the diagrams below that illustrate three mix- tures of gases A and B.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Actually, we shall derive two expressions. One is for the case in which the volume of the gas remains constant as energy is trans- ferred to or from it as heat. The other is for the case in which the pressure of the gas remains constant as energy is transferred to or from it as heat. The symbols for these two molar specific heats are C V and C p , respectively. (By convention, the capital letter C is used in both cases, even though C V and C p represent types of specific heat and not heat capacities.) Molar Specific Heat at Constant Volume Figure 19-9a shows n moles of an ideal gas at pressure p and temperature T, confined to a cylinder of fixed volume V. This initial state i of the gas is marked on the p-V diagram of Fig. 19-9b. Suppose now that you add a small amount of energy to the gas as heat Q by slowly turning up the temperature of the thermal reservoir. The gas temperature rises a small amount to T + ∆T, and its pressure rises to p + ∆p, bringing the gas to final state f. In such experiments, we would find that the heat Q is related to the temperature change ∆T by Q = nC V ∆T (constant volume), (19-39) where C V is a constant called the molar specific heat at constant volume. Substi- tuting this expression for Q into the first law of thermodynamics as given by Eq. 18-26 (∆E int = Q − W ) yields ∆E int = nC V ∆T − W. (19-40) With the volume held constant, the gas cannot expand and thus cannot do any work. Therefore, W = 0, and Eq. 19-40 gives us C V = ΔE int n ΔT . (19-41) From Eq. 19-38, the change in internal energy must be ΔE int = 3 2 nR ΔT. (19-42) Substituting this result into Eq. 19-41 yields C V = 3 2 R = 12.5 J/mol · K (monatomic gas). (19-43) As Table 19-2 shows, this prediction of the kinetic theory (for ideal gases) agrees very well with experiment for real monatomic gases, the case that we have assumed.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
As expected, the value of absolute zero obtained by extrapolating the data in Table 6.4 is essentially the same as the value obtained from the graph of pressure versus temperature in the preceding section. Absolute zero can therefore be more accurately defined as the temperature at which the pressure and the volume of a gas both extrap- olate to zero. When the temperatures in Table 6.4 are converted from the Celsius to the Kelvin scale, a plot of the volume versus the temperature of a gas becomes a straight line that passes through the origin. Any two points along the line can therefore be used to construct the following equation, which is known as Charles’ law. V 1 V 2 = T 1 T 2 V a T (n and P constant) 6.10 CHARLES’ LAW 233 ➤ CHECKPOINT What relationship can be derived by combining Boyle’s and Amontons’ laws? Fig. 6.10 Charles’ law can be demonstrated with a simple apparatus. When the flask is removed from the ice bath and placed in a warm-water bath, the gas in the flask expands, slowly pushing up on the piston of the syringe. Syringe Clamp Thermometer 250-mL Erlenmeyer flask Ice-water bath Clamp Block Ring stand Table 6.4 Dependence of the Volume of a Gas on Its Temperature Temperature (C) Volume (mL) 0 107.9 5 109.7 10 111.7 15 113.6 20 115.5 25 117.5 30 119.4 35 121.3 40 123.2 Before you use this equation, however, it is important to remember to convert temperatures from C to K. 6.11 Gay-Lussac’s Law Joseph Louis Gay-Lussac (1778–1850) studied the volume of gases consumed or produced in a chemical reaction because he was interested in the reaction between hydrogen and oxygen to form water. Gay-Lussac found that 199.89 parts by vol- ume of hydrogen were consumed for every 100 parts by volume of oxygen. Thus hydrogen and oxygen seemed to combine in a simple 2:1 ratio by volume. 2 volumes 1 volume Gay-Lussac found similar whole-number ratios for the reactions between other pairs of gases.
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.
