
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?

Interpretation:
The Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. is to be calculated. And is to be compared to the experimental values from Table 1.5.
Concept introduction:
The Boyle temperature is defined as the temperature for which the second virial coefficient, becomes zero. In other words, the Boyle temperature is the temperature at which a non-ideal gas behaves like an ideal gas. In this temperature the attractive and repulsive forces acting on the gas molecules balance each out.
Answer to Problem 1.38E
The Boyle temperature of gas are as follows;
Entry | Gas | TB (K)(calculated values) | TB (K)(experimental values) | a (atm L2 / mol2) | B (L / mol) |
1 | Carbon dioxide | 1026 | 713 | 3.592 | 0.04267 |
2 | Oxygen | 521 | 405 | 1.360 | 0.03183 |
3 | Nitrogen | 433 | 327 | 1.390 | 0.03913 |
The experimental values of Boyle temperature (TB) are compared with calculated values and found to be in low.
Explanation of Solution
The Boyle temperature (TB) is defined as the temperature for which the second virial coefficient, becomes zero. In other words, the Boyle temperature is the temperature at which a non-ideal gas behaves like an ideal gas. In this temperature the attractive and repulsive forces acting on the gas molecules balance each out. Thus ‘TB’ is given by the expression
‘a’ and ‘b’ are called as van der Waals constants and ‘a’ represents the pressure correction and it is related to the magnitude and strength of the interactions between gas particles. Similarly, ‘b’ describes the volume correction and it is having relationship to the size of the gas particles.
Since, the Boyle temperature is the temperature for which second virial coefficient becomes 0. Moreover, it is at this temperature that the forces of attraction and repulsion acting on the gas molecules balance out. Higher order be virial coefficients are smaller than the second virial coefficient, the gas likes to behave as an ideal gas over a entire range of pressures. At low pressures,
the equation transforms as,
Where, Z = Compressibility factor.
TB of carbon dioxide
Knowing a and b values of CO2 from table 1.6 TB of CO2 is calculated as follows;
R = 0.0823 L. atm / K. mol
TB of oxygen:
Knowing a and b values of oxygen from table 1.6 TB of oxygen is calculated as follows;
TB of nitrogen:
Knowing a and b values of nitrogen from table 1.6 TB of nitrogen is calculated as follows;
Moreover, the experimental Boyle temperature (table 1.5) values are compared with calculated values and the experimental values are found to be low.
Thus, the Boyle temperatures for carbon dioxide, oxygen, and nitrogen using the van der Waals constants in Table 1.6. is calculated. And compared to the experimental values from Table 1.5.
Want to see more full solutions like this?
Chapter 1 Solutions
EBK PHYSICAL CHEMISTRY
- Biological Macromolecules Naming and drawing the products of aldose oxidation and reduction aw a Fischer projection of the molecule that would produce L-ribonic acid if it were subjected to mildly oxidizing reaction conditions. Click and drag to start drawing a structure. X AP ‡ 1/5 Naor Explanation Check McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Accessibilarrow_forward● Biological Macromolecules Identifying the parts of a disaccharide Take a look at this molecule, and then answer the questions in the table below it. CH2OH O H H H OH OH OH H H CH2OH H O OH H OH H H H H OH Is this a reducing sugar? Does this molecule contain a glycosidic bond? If you said this molecule does contain a glycosidic bond, write the symbol describing it. If you said this molecule does contain a glycosidic bond, write the common names (including anomer and enantiomer labels) of the molecules that would be released if that bond were hydrolyzed. If there's more than one molecule, separate each name with a comma. Explanation Check O yes X O no ○ yes O no Uarrow_forwardThe aim of the lab is to measure the sodium content from tomato sauce using the Mohr titration method. There are two groups being: Regular Tomato sauce & Salt Reduced tomato sauce QUESTION: State how you would prepare both Regular & Salt reduced tomato sauce samples for chemical analysis using the Mohr titration methodarrow_forward
- Using the conditions of spontaneity to deduce the signs of AH and AS Use the observations about each chemical reaction in the table below to decide the sign (positive or negative) of the reaction enthalpy AH and reaction entropy AS. Note: if you have not been given enough information to decide a sign, select the "unknown" option. reaction observations conclusions A The reverse of this reaction is always spontaneous but proceeds faster at temperatures above -48. °C. ΔΗ is (pick one) ✓ AS is (pick one) B This reaction is spontaneous except below 114. °C but proceeds at a slower rate below 135. °C. ΔΗ is (pick one) AS is (pick one) ΔΗ is C This reaction is exothermic and proceeds faster at temperatures above -43. °C. (pick one) AS is (pick one) v Х 5 ? 18 Ararrow_forwardion. A student proposes the following Lewis structure for the perchlorate (CIO) io : :0: : Cl : - - : :0: ك Assign a formal charge to each atom in the student's Lewis structure. atom central O formal charge ☐ top O ☐ right O ☐ bottom O ☐ Cl ☐arrow_forwardDecide whether these proposed Lewis structures are reasonable. proposed Lewis structure Yes. Is the proposed Lewis structure reasonable? Cl- : 2: :Z: :Z: N—N : 0: C C1: O CO No, it has the wrong number of valence electrons. The correct number is: ☐ No, it has the right number of valence electrons but doesn't satisfy the octet rule. The symbols of the problem atoms are:* ☐ Yes. No, it has the wrong number of valence electrons. The correct number is: ☐ No, it has the right number of valence electrons but doesn't satisfy the octet rule. The symbols of the problem atoms are:* | Yes. No, it has the wrong number of valence electrons. The correct number is: No, it has the right number of valence electrons but doesn't satisfy the octet rule. The symbols of the problem atoms are:* | If two or more atoms of the same element don't satisfy the octet rule, just enter the chemical symbol as many times as necessary. For example, if two oxygen atoms don't satisfy the octet rule, enter "0,0". ☑arrow_forward
- Use the observations about each chemical reaction in the table below to decide the sign (positive or negative) of the reaction enthalpy AH and reaction entropy AS. Note: if you have not been given enough information to decide a sign, select the "unknown" option. reaction observations conclusions ΔΗ is (pick one) A This reaction is faster above 103. °C than below. AS is (pick one) ΔΗ is (pick one) B This reaction is spontaneous only above -9. °C. AS is (pick one) ΔΗ is (pick one) C The reverse of this reaction is always spontaneous. AS is (pick one) 18 Ararrow_forwardUse the observations about each chemical reaction in the table below to decide the sign (positive or negative) of the reaction enthalpy AH and reaction entropy AS. Note: if you have not been given enough information to decide a sign, select the "unknown" option. reaction observations conclusions A The reverse of this reaction is always spontaneous but proceeds slower at temperatures below 41. °C. ΔΗ is (pick one) AS is (pick one) ΔΗ is (pick one) B This reaction is spontaneous except above 94. °C. AS is (pick one) This reaction is always spontaneous, but ΔΗ is (pick one) C proceeds slower at temperatures below −14. °C. AS is (pick one) Х 00. 18 Ar 무ㅎ B 1 1arrow_forwardDraw the product of the reaction shown below. Ignore inorganic byproducts. + H CH3CH2OH HCI Drawingarrow_forward
- please explain this in simple termsarrow_forwardK Most Reactive Na (3 pts) Can the metal activity series (shown on the right) or a standard reduction potential table explain why potassium metal can be prepared from the reaction of molten KCI and Na metal but sodium metal is not prepared from the reaction of molten NaCl and K metal? Show how (not). Ca Mg Al с Zn Fe Sn Pb H Cu Ag Au Least Reactivearrow_forward(2 pts) Why is O2 more stable as a diatomic molecule than S2?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Chemistry for Engineering StudentsChemistryISBN:9781337398909Author:Lawrence S. Brown, Tom HolmePublisher:Cengage LearningGeneral Chemistry - Standalone book (MindTap Cour...ChemistryISBN:9781305580343Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; DarrellPublisher:Cengage Learning
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage Learning





