Chemistry
The Molar Volume of a Gas
The molar volume of a gas refers to the volume occupied by one mole of a gas at a specific temperature and pressure. It is a constant value for ideal gases at standard temperature and pressure (STP), which is 22.4 liters per mole. This concept is important in understanding the behavior of gases and is used in various gas law calculations.
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eBook - PDFIntroductory Chemistry
An Active Learning Approach
- Mark Cracolice, Edward Peters, Mark Cracolice(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
7 Given The Molar Volume of a Gas at any specified temperature and pressure, or information from which the molar volume may be determined, and either the amount in moles or the volume of a sample of that gas, calculate the other quantity. The molar volume (MV) of a gas is the volume occupied by one mole of gas molecules: MV ; V n The ideal gas equation, PV 5 nRT, can be solved for the ratio of volume to amount in moles, V/n: divide both sides by P divide both sides by n PV 5 nRT ———————— > V 5 nRT P ———————— > V n 5 RT P 5 MV MV ; V/n is the defining equa- tion for molar volume. Defining equations and their corresponding conversion factors are summarized in Section 3.11. a b Figure 14.14 Gas density and floating balloons. (a) A helium-filled balloon floats, but air-filled balloons lie on the surface of the table. The density of helium is lower than that of air at the same temperature and pressure. (b) Hot air balloons float because the higher temperature of the air enclosed in the balloon makes it less dense than the surrounding air. You improved your skill at solving ideal gas equation problems. What did you learn by solving this Active Example? Practice Exercise 14.6 The density of a gas is 2.2 g/L at 29°C and 0.966 bar. What is its molar mass? McPHOTO/AGE Fotostock Charles D. Winters 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. 528 Chapter 14 The Ideal Gas Law and Its Applications The relationship MV 5 RT/P shows that molar volume depends on temperature and pressure; T and P are both variables in the equation.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2015(Publication Date)
- Openstax(Publisher)
At STP, an ideal gas has a volume of about 22.4 L—this is referred to as the standard molar volume (Figure 9.18). Figure 9.18 Since the number of moles in a given volume of gas varies with pressure and temperature changes, chemists use standard temperature and pressure (273.15 K and 1 atm or 101.325 kPa) to report properties of gases. Chapter 9 | Gases 475 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions By the end of this section, you will be able to: • Use the ideal gas law to compute gas densities and molar masses • Perform stoichiometric calculations involving gaseous substances • State Dalton’s law of partial pressures and use it in calculations involving gaseous mixtures The study of the chemical behavior of gases was part of the basis of perhaps the most fundamental chemical revolution in history. French nobleman Antoine Lavoisier, widely regarded as the “father of modern chemistry,” changed chemistry from a qualitative to a quantitative science through his work with gases. He discovered the law of conservation of matter, discovered the role of oxygen in combustion reactions, determined the composition of air, explained respiration in terms of chemical reactions, and more. He was a casualty of the French Revolution, guillotined in 1794. Of his death, mathematician and astronomer Joseph-Louis Lagrange said, “It took the mob only a moment to remove his head; a century will not suffice to reproduce it.” [1] As described in an earlier chapter of this text, we can turn to chemical stoichiometry for answers to many of the questions that ask “How much?” We can answer the question with masses of substances or volumes of solutions. However, we can also answer this question another way: with volumes of gases. We can use the ideal gas equation to relate the pressure, volume, temperature, and number of moles of a gas. Here we will combine the ideal gas equation with other equations to find gas density and molar mass.
eBook - PDF- William R. Robinson, Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
At STP, an ideal gas has a volume of about 22.4 L—this is referred to as the standard molar volume (Figure 8.18). Figure 8.18 Since the number of moles in a given volume of gas varies with pressure and temperature changes, chemists use standard temperature and pressure (273.15 K and 1 atm or 101.325 kPa) to report properties of gases. Chapter 8 | Gases 417 8.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions By the end of this section, you will be able to: • Use the ideal gas law to compute gas densities and molar masses • Perform stoichiometric calculations involving gaseous substances • State Dalton’s law of partial pressures and use it in calculations involving gaseous mixtures The study of the chemical behavior of gases was part of the basis of perhaps the most fundamental chemical revolution in history. French nobleman Antoine Lavoisier, widely regarded as the “father of modern chemistry,” changed chemistry from a qualitative to a quantitative science through his work with gases. He discovered the law of conservation of matter, discovered the role of oxygen in combustion reactions, determined the composition of air, explained respiration in terms of chemical reactions, and more. He was a casualty of the French Revolution, guillotined in 1794. Of his death, mathematician and astronomer Joseph-Louis Lagrange said, “It took the mob only a moment to remove his head; a century will not suffice to reproduce it.” [1] As described in an earlier chapter of this text, we can turn to chemical stoichiometry for answers to many of the questions that ask “How much?” We can answer the question with masses of substances or volumes of solutions. However, we can also answer this question another way: with volumes of gases. We can use the ideal gas equation to relate the pressure, volume, temperature, and number of moles of a gas. Here we will combine the ideal gas equation with other equations to find gas density and molar mass.
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.
- Martha Mackin(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
240 Chapter Eleven 3. A mole of any gas has the same number of molecules; therefore the volume occupied by one mole of any gas has a definite fixed volume at a particular temperature. a) The molar volume of any gas is 22.4 L at STP. b) STP stands for standard temperature and pressure, which is 273 Κ (0° C) and 1 atm (760 torr, 101.3 kPa). Examples: 1. What volume is occupied by 5.36 moles of chlorine at STP? Unknown Given Connection liters Cl 2 5.36 moles Cl 2 22.4 L Cl 2 1 mole C 1 2 liters Cl 2 5.36 moles Cl 2 1 mole Cl 2 22.4 L C 1 2 22.4 L Cl liters Cl = 5 . 36 -molae-€i- x ; -r ± 2 2 ljooOe -ei-Estimate 2 χ 10 L Cl 2 5jnn1on Ph x —: — — 2 1-molc Ciri 1 x 10 L Cl Calculation 120 or 1.20 χ 10 L Cl 2 2. A sample of nitric oxide has a volume of 815 mL at STP. How many moles of gas are present? Unknown Given Connection moles NO 815 mL NO 22.4 L NO 1 mole NO 1 mole NO 22.4 L NO 1 mL -3 10 L -3 ° r 10 L 1 mL moles NO Estimate qt c τ ^ 10 Z -Zr 1 mole NO 815-mL NO -x —= x (8 χ 10 2 -mir-ΝΘ)-χ χ 22.4 -Ιτ -ΝΟ-1 mol NO 1 -m i r-2 χ 10 -L NQ--2 4 χ 10 mole NO Calculation 3.64 χ 10 mole NO What is the volume at STP of 40.6 g of 0 2 ? Unknown Given Connection liters 0 2 40.6 g 0 2 1 mole 0 2 32.0 g °2 liters 0 2 40.6 g 0 2 32.0 g 0 2 ° r 1 mole °2 1 mole 0 2 22.4 L °2 22.4 L 0 2 ° r 1 mole °2 1 -mole 0-22.4 L o„ liters 0_ = 40.6 -g-O-χ — — χ 2 2 3.20 _g Q -1 molo Ο Estimate (4 χ lo'-jg -O^) 1 -mole 0 -V 3 X 10 -^ 2 / ρ χ 10 L 0 2 1-mole 0„ = 3 χ 10 L 0_ Calculation 28.4 L 0 Λ D. 3.
- Leo J. Malone, Theodore O. Dolter, Steven Gentemann(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
These and other properties, including what are known as “the gas laws,” become obvious from an understanding of the kinetic molecular theory applied to gases. The major assumptions of this theory are: (1) Gas molecules have negligible volume. (2) Gas molecules undergo random collisions with each other and with the walls of the container, thus exerting pressure. (3) The total energy of all of the collisions is conserved. (4) Gas molecules have negligible interactions with each other. (5) The average kinetic energy of the molecules is proportional to the temperature. An immediate consequence of the last point of kinetic theory is that the average velocity of a gas is related to its formula weight (or molar mass) since K.E. = 1/2mv 2 . The extension of this principle to the effusion and diffusion of gases is known as Graham’s law. The lower the molar mass of a gas, the higher is its average velocity as well as rates of effusion and diffusion. It seems obvious now, but the understanding of the nature of gases began with the demonstration that the atmosphere exerts pressure that can be measured with a barometer. Pressure is the weight of the gas (the force) applied per unit area. The pressure of a gas is measured in many different units but all can be compared to the standard unit, which is the average pressure of the atmosphere at sea level (one atmosphere). The most common unit of pressure in chemistry calculations besides atmosphere is torr, which is the same as mm of mercury. One atmosphere is the pressure that supports a column of Hg 760 mm high, which is thus 760 torr. 185 The gas laws discussed in this part of the review relate the pressure, temperature, and number of moles to the volume of a gas. The laws can be used to calculate how one parameter changes as the others are varied.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
524 CHAPTER 10 Properties of Gases Integrated Chemistry Example In Chapter 10, we learned that gases are a system that have a few guiding principles. The first guiding principle is the kinetic molecular model of gases and the second is the equation for the ideal gas law and how the equation developed from the discovery of a series of gas laws that related one property of a gas to another property. All of these were integrated to be able to answer some very important questions at the molecular and macroscopic levels that apply to many different sciences. Also, in many sciences, the use of reagents for chemical reactions requires a knowledge of the molar mass of these compounds. In this chapter, we brought these two together and started exploring the many methods that are available to determine the molar mass of a compound. For instance, the molar mass of a gas can be readily determined from its density. Perhaps a full gas cylinder only had the label “HIGHLY POISONOUS” and it was important to determine the iden- tity of the poisonous gas. One way to determine the identity of the poisonous compound is to know its molar mass. To determine the density of a gas, a vessel with a known volume can be evacuated and then weighed and filled with the poisonous gas and reweighed to obtain the mass of the gas. Knowing the volume and mass, we can calculate the density of the gas and then the molar mass. Using this method, a gas vessel with a volume of 500.0 cm 3 was evacuated, weighed, and found to be 545.23 g. When the vessel was filled with the poisonous gas, the total mass was 589.32 g. The temperature of the system was 26.3 °C and the pressure was 688 torr. What is the molar mass of the poisonous gas? Analysis: This question is asking for the determination of the molar mass of the unknown gaseous substance. We know that the molar mass can be determined by rearranging the ideal gas law equation.
eBook - PDFChemistry
The Molecular Nature of Matter
- James E. Brady, Neil D. Jespersen, Alison Hyslop(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
Lavoisier was unable to extend the study of this behavior of hydrogen and oxygen to other gas reac- tions because he was beheaded during the French Revolution. (See Michael Laing, The Journal of Chemical Education, February 1998, page 177.) 10.4 | Stoichiometry Using Gas Volumes 479 follows: When measured at the same temperature and pressure, equal volumes of gases contain equal numbers of moles. A corollary to Avogadro’s principle is that the volume of a gas is directly proportional to its number of moles, n. V µ n (at constant T and P) Standard Molar Volume Avogadro’s principle implies that the volume occupied by one mole of any gas—its molar volume—must be identical for all gases under the same conditions of pressure and tem- perature. To compare the molar volumes of different gases, scientists agreed to use 1 atm and 273.15 K (0 °C) as the standard conditions of temperature and pressure, 6 or STP, for short. If we measure the molar volumes for a variety of gases at STP, we find that the values fluctuate somewhat because the gases are not “ideal.” Some typical values are listed in Table 10.1, and if we were to examine the data for many gases we would find an average of around 22.4 L per mole. This value is taken to be the molar volume of an ideal gas at STP and is now called the standard molar volume of a gas. For an ideal gas at STP: 1 mol gas Û 22.4 L gas Avogadro’s principle was a remarkable advance in our understanding of gases. His insight enabled chemists for the first time to determine the formulas of gaseous elements. 7 Stoichiometry Problems For reactions involving gases, Avogadro’s principle lets us use a new kind of stoichiometric equivalency, one between volumes of gases. Earlier, for example, we noted the following reaction and its gas volume relationships.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
With the aid of the ideal gas law, it can be shown that one mole of an ideal gas occupies a volume of 22.4 liters at a temperature of 273 K (0 8C) and a pressure of one atmosphere (1.013 3 10 5 Pa). These conditions of temperature and pressure are known as standard temperature and pressure (STP). Conceptual Example 3 discusses another interesting application of the ideal gas law. *“Particles” is not an SI unit and is often omitted. Then, particles/mol 5 1/mol 5 mol 21 . EXAMPLE 2 | The Physics of Oxygen in the Lungs In the lungs, a thin respiratory membrane separates tiny sacs of air (absolute pressure 5 1.00 3 10 5 Pa) from the blood in the capillaries. These sacs are called alveoli, and it is from them that oxygen enters the blood. The average radius of the alveoli is 0.125 mm, and the air inside contains 14% oxygen. Assuming that the air behaves as an ideal gas at body temperature (310 K), find the number of oxygen molecules in one of the sacs. Reasoning The pressure and temperature of the air inside an alveolus are known, and its volume can be determined since we know the radius. Thus, the ideal gas law in the form PV 5 NkT can be used directly to find the number N of air particles inside one of the sacs. The number of oxygen molecules is 14% of the number of air particles. Solution The volume of a spherical sac is V 5 4 3 pr 3 , where r is the radius. Solving Equation 14.2 for the number of air particles, we have N 5 PV kT 5 (1.00 3 10 5 Pa) [ 4 3 p (0.125 3 10 23 m) 3 ] (1.38 3 10 223 J/K)(310 K) 5 1.9 3 10 14 The number of oxygen molecules is 14% of this value, or 0.14N 5 2.7 3 10 13 . Problem-Solving Insight In the ideal gas law, the temperature T must be expressed on the Kelvin scale. The Celsius and Fahrenheit scales cannot be used. 372 Chapter 14 | The Ideal Gas Law and Kinetic Theory Historically, the work of several investigators led to the formulation of the ideal gas law.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
Consider the following calculation of the number of H 2 mol- ecules in 50 mL of hydrogen gas, for example. 0.005 g H 2 * 1 mol H 2 2.02 g H 2 * 6.02 * 10 23 molecules 1 mol = 1 * 10 21 H 2 molecules V r n (T and P constant) NH 3 (g) + HCl(g) ¡ NH 4 Cl(s) 6.12 AVOGADRO’S HYPOTHESIS 235 Fig. 6.12 Apparatus used to demonstrate Avogadro’s hypothesis. Table 6.5 Experimental Data for the Mass of 50-mL Samples of Different Gases (T and P are Constant) Mass of Molecular Weight Number of Molecules Compound 50 mL Gas (g) of Gas (g/mol) in 50 mL Gas H 2 0.005 2.02 1 10 21 N 2 0.055 28.01 1.2 10 21 O 2 0.061 32.00 1.1 10 21 CO 2 0.088 44.01 1.2 10 21 C 4 H 10 0.111 58.12 1.15 10 21 CCl 2 F 2 0.228 120.91 1.14 10 21 The last column in Table 6.5 summarizes the results obtained when the cal- culation is repeated for each gas. The number of significant figures in the answer changes from one calculation to the next. But the number of molecules in each sample is the same, within experimental error. We therefore conclude that equal volumes of different gases collected under the same conditions of temperature and pressure do in fact contain the same number of particles. 6.13 The Ideal Gas Equation So far, gases have been described in terms of four variables: pressure (P), vol- ume (V ), temperature (T ), and the number of moles of gas (n). In the course of this chapter, five relationships between pairs of these variables have been dis- cussed. In each case, two of the variables were allowed to change while the other two were held constant. The discussion of the bicycle tire, for example, showed that the pressure of a gas is directly proportional to the moles of gas when the temperature and volume of the gas are held constant. Other relationships between pairs of variables include the following.
- Armand Berman(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
1 Ideal Gases 1.1 The Ideal Gas Law If an ideal gas, specified by the quantities p { (pressure) and V! (volume) at temperature 7, changes its state to another set of quantities p 2 > ^2 a t ^ 2 » t n e n , ,/ , =p 2 V 2 /T 2 (1.1) where T is the thermodynamic temperature measured in degrees Kelvin (see Appendix, Table A.20). 1.2 Boyle's Law For a given mass of gas, held at T = const. p x V x = p 2 V 2 = const. (1.2) 13 Charles's Law For a given mass of gas, held at p = const. Vi/ T i = V 2 /T 2 = const. (1.3) IA Gay-Lussac'sLaw For a given mass of gas, held at V = const. f>i/ T i = Pi/^i = const. (1.4) 1 2 1 Ideal Gases 1.5 Mole Amount The amount of moles n M in a given mass W t of substance having a molar mass M is n M = W t /M [mol (moles)] (1.5) The molar mass M of a substance (also known as moiar weight) is the mass divided by the amount of substance. The SI base unit is kg mol -1 , and the practical unit is g mol -1 (Compendium of Chemical Technology, 1987, p. 260). 1.6 Dalton's Law In a mixture of gases, each component exerts the pressure that it would exert if it were present alone at the same temperature in the volume occupied by the gas mixture. The total pressure p of a gas mixture is the sum of partial pressures Pv Pv - -· » Pi °f t n e individual components. P = Px + Pi + *·· +ft = ÎPi (1.6) The partial pressure of each component is equal to the total pressure multiplied by its mole fraction c, in the mixture (for c,·, see Eq. 1.7c). Dalton's law holds true for ideal gases. At pressures below atmosphere, gas mixtures can be regarded as ideal gases.
eBook - PDFPhysical Chemistry
Thermodynamics
- Horia Metiu(Author)
- 2006(Publication Date)
- Taylor & Francis(Publisher)
The calculations of the molar volume, using several equations of state, have been performed in Workbook T3.2 and the results are shown in Table 3.2. Since the pressure is up to 10 atm and the temperature is reasonably high, all equations perform fairly well. Exercise 3.4 One of the many functional forms proposed for the equation of state is the second-order virial equation p = RT 1 v + B 2 ( T ) v 2 (3.6) The second virial coefficient a B 2 ( T ) for ethane at 400 K is − 0.095 liter/mol. Use this equation to calculate the molar volume at p = 10 atm. Compare to the experimental result given in Appendix 2. Solution . v = 3.18408 liter/mol (see Workbook T3.2). a The virial coefficients are tabulated in J.H. Dymond and E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Oxford University Press, Oxford, 1980. 40 How to Use the Equation of State Exercise 3.5 Calculate the molar volumes of ethane at a temperature of 350 K and pressures of 15, 25, 35, 45, 55, 65, 75, 85, and 95 atm. Compare your results to the experimental values given in Appendix 2. Use the van der Waals, the Beattie–Bridgeman, and the Benedict–Webb–Rubin equations of state. Calculate Temperature When You Know Molar Volume and Pressure §8. When Do You Need Such Calculations? You are in charge of gas reservoirs and you hear that a great heatwave is coming. You worry that if the temperature gets to be too high, the pressure in the reservoir may exceed the limit p 0 that the reservoir can withstand. You know the number of moles n of gas in the reservoir (hence you know the molar volume v = V / n ) and you know the maximum pressure p 0 . You can calculate from the equation p 0 = f ( T , V / n ), the maximum temperature that you can have in the reservoir, beyond which the tank explodes. §9. Example. To solve this type of problem you insert the known values of v and p in the equation of state and obtain an equation for T .
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