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1.38. Calculate the Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. How close do they come to the experimental values from Table 1.5?

1.38. Calculate the Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. How close do they come to the experimental values from Table 1.5?

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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1.38. Calculate the Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. How close do they come to the experimental values from Table 1.5?
Transcribed Image Text:1.38. Calculate the Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. How close do they come to the experimental values from Table 1.5?
1.4 The second virial coefficient B ol) at various temperatures erature (K) He -3.34 7.4 11.7 12.2 12.3 12.0 11.5 10.7 Ne Ar -35.4 -6.0 -183.5 3.2 -86.2 7.6 -47.4 11.3 -15.5 12.8 -1.0 13.8 12.0 J. S. Winn, Physical Chemistry, HarperCollins, ork, 1994 Z=1+ 0 TABLE 1.5 Boyle temperatures for various gases + is called the Boyle temperature, TB, of the gas. At that temperature, the com- ibility is Gas H₂ He Ne Ar N₂ 0₂ CO₂ CH₁ Source: J. S. Winn, Physical Chemistry, HarperCollins, New York, 1994 TB (K) 110 25 127 410 327 405 713 509 e the additional terms will be neglected. This means that Z=1 nRT is acting like an he nonideal gas is acting like an ideal ideal gas. Table 1.5 lists Boyle temperatures of nonideal gases. The existence of Boyle temperature allows us to use nonideal s to study the properties of ideal gases-if the gas is at the right temperature, successive terms in the virial equation are negligible. ne model of ideal gases is that (a) they are composed of particles so tiny compared e volume of the gas that they can be considered zero-volume points in space, and here are no interactions, attractive or repulsive, between the individual gas par- However, real gases ultimately have behaviors due to the facts that (a) gas atoms molecules do have a size, and (b) there is some interaction between the gas par- 5, which can range from minimal to very large. In considering the state variables of 5, the volume of the gas particles should have an effect on the volume V of the gas. interactions between gas particles would have an effect on the pressure p of the gas. aps a better equation of state for a gas should take these effects into account. 1873, the Dutch physicist Johannes van der Waals (Figure 1.9) suggested ected version of the ideal gas law. It is one of the simpler equations of state for gases, and is referred to as the van der Waals equation: an² (V (p+ an)(v - nb) (1.20) ere n is the number of moles of gas, and a and b are the van der Waals con- ts for a particular gas. The van der Waals constant a represents the pressure rection and is related to the magnitude of the interactions between gas parti- The van der Waals constant b is the volume correction and is related to the of the gas particles. Table 1.6 lists van der Waals constants for various gases, ch can be determined experimentally. Unlike a virial equation, which fits be- ior of real gases to a mathematical equation, the van der Waals equation is a thematical model that attempts to predict behavior of a gas in terms of real sical phenomena (that is, interaction between gas molecules and the physical es of atoms). s otherwise noted, all art on this page is Cengage Learning 2014. FIGURE 1.9 Johannes van der Waals (1837-1923), Dutch physicist who pro- posed a new equation of state for gases. He won a 1910 Nobel Prize for his work. TABLE 1.6 Van der Waals parameters for various gases Gas Acetylene, C₂H₂ Ammonia, NH3 Carbon dioxide, CO₂ Ethane, C₂H6 Ethylene, C₂H₁ Helium, He Hydrogen, H₂ Hydrogen chloride, HCl Krypton, Kr Mercury, Hg Methane, CH4 Neon, Ne Nitric oxide, NO Nitrogen, N₂ Nitrogen dioxide, NO₂ Oxygen, O₂ Propane, C3H8 Sulfur dioxide, SO₂ Xenon, Xe Water, H₂O a b (atm-L²/mol) (L/mol) 0.05136 4.390 4.170 3.592 5.489 4.471 0.03508 0.244 3.667 2.318 8.093 2.253 0.2107 1.340 1.390 5.284 1.360 8.664 6.714 4.194 5.464 0.03707 0.04267 ⒸMary Evans Picture Library/The Image Works 0.0638 0.05714 0.0237 0.0266 0.04081 0.03978 0.01696 0.0428 0.01709 0.02789 0.03913 0.04424 0.03183 0.08445 0.05636 0.05105 0.03049 Source: D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 82nd ed., CRC Press, Boca Raton, Fla., 2001.
Transcribed Image Text:1.4 The second virial coefficient B ol) at various temperatures erature (K) He -3.34 7.4 11.7 12.2 12.3 12.0 11.5 10.7 Ne Ar -35.4 -6.0 -183.5 3.2 -86.2 7.6 -47.4 11.3 -15.5 12.8 -1.0 13.8 12.0 J. S. Winn, Physical Chemistry, HarperCollins, ork, 1994 Z=1+ 0 TABLE 1.5 Boyle temperatures for various gases + is called the Boyle temperature, TB, of the gas. At that temperature, the com- ibility is Gas H₂ He Ne Ar N₂ 0₂ CO₂ CH₁ Source: J. S. Winn, Physical Chemistry, HarperCollins, New York, 1994 TB (K) 110 25 127 410 327 405 713 509 e the additional terms will be neglected. This means that Z=1 nRT is acting like an he nonideal gas is acting like an ideal ideal gas. Table 1.5 lists Boyle temperatures of nonideal gases. The existence of Boyle temperature allows us to use nonideal s to study the properties of ideal gases-if the gas is at the right temperature, successive terms in the virial equation are negligible. ne model of ideal gases is that (a) they are composed of particles so tiny compared e volume of the gas that they can be considered zero-volume points in space, and here are no interactions, attractive or repulsive, between the individual gas par- However, real gases ultimately have behaviors due to the facts that (a) gas atoms molecules do have a size, and (b) there is some interaction between the gas par- 5, which can range from minimal to very large. In considering the state variables of 5, the volume of the gas particles should have an effect on the volume V of the gas. interactions between gas particles would have an effect on the pressure p of the gas. aps a better equation of state for a gas should take these effects into account. 1873, the Dutch physicist Johannes van der Waals (Figure 1.9) suggested ected version of the ideal gas law. It is one of the simpler equations of state for gases, and is referred to as the van der Waals equation: an² (V (p+ an)(v - nb) (1.20) ere n is the number of moles of gas, and a and b are the van der Waals con- ts for a particular gas. The van der Waals constant a represents the pressure rection and is related to the magnitude of the interactions between gas parti- The van der Waals constant b is the volume correction and is related to the of the gas particles. Table 1.6 lists van der Waals constants for various gases, ch can be determined experimentally. Unlike a virial equation, which fits be- ior of real gases to a mathematical equation, the van der Waals equation is a thematical model that attempts to predict behavior of a gas in terms of real sical phenomena (that is, interaction between gas molecules and the physical es of atoms). s otherwise noted, all art on this page is Cengage Learning 2014. FIGURE 1.9 Johannes van der Waals (1837-1923), Dutch physicist who pro- posed a new equation of state for gases. He won a 1910 Nobel Prize for his work. TABLE 1.6 Van der Waals parameters for various gases Gas Acetylene, C₂H₂ Ammonia, NH3 Carbon dioxide, CO₂ Ethane, C₂H6 Ethylene, C₂H₁ Helium, He Hydrogen, H₂ Hydrogen chloride, HCl Krypton, Kr Mercury, Hg Methane, CH4 Neon, Ne Nitric oxide, NO Nitrogen, N₂ Nitrogen dioxide, NO₂ Oxygen, O₂ Propane, C3H8 Sulfur dioxide, SO₂ Xenon, Xe Water, H₂O a b (atm-L²/mol) (L/mol) 0.05136 4.390 4.170 3.592 5.489 4.471 0.03508 0.244 3.667 2.318 8.093 2.253 0.2107 1.340 1.390 5.284 1.360 8.664 6.714 4.194 5.464 0.03707 0.04267 ⒸMary Evans Picture Library/The Image Works 0.0638 0.05714 0.0237 0.0266 0.04081 0.03978 0.01696 0.0428 0.01709 0.02789 0.03913 0.04424 0.03183 0.08445 0.05636 0.05105 0.03049 Source: D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 82nd ed., CRC Press, Boca Raton, Fla., 2001.
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