PASS Attribution

• LibreTexts PASS Chemistry Book CHEM 1500 (2).
• Question 2.E.06 from LibreTexts PASS Chemistry Book CHEM 1500 (3) is used under a CC BY-NC 4.0 license.
  • Question 2.E.06 was adapted from 2.E.6 from LibreTexts CHEM 1500: Chemical Bonding and Organic Chemistry (4), which is under a CC BY-NC-SA 4.0 license.
  • Question 2.E.6 is question 6.1.6 from LibreTexts Chemistry 1e (OpenSTAX) (5), which is under a CC BY 4.0 license.
  • Question 6.1.6 is question 6 from from OpenStax Chemistry 2e (6), which is under a CC BY 4.0 license. Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction.

References

1. LibreTexts. 2.1: Electromagnetic Energy. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.01%3A_Electromagnetic_Energy#Electromagnetic_Radiation.

2. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1500; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500.

3. Blackstock, L.; Brewer, S.; Jensen, A. 2.1: Question 2.E.06 Pass - Energy, Wavelength, Frequency, and Colour of Emitted Lithium Photons. In PASS Chemistry Book CHEM 1500; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500.

4. OpenStax. 2.E: Quantum Theory and Electronic Structure (Exercises). In CHEM 1500: Chemical Bonding and Organic Chemistry. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.E%3A_Quantum_Theory_and_Electronic_Structure_(Exercises).

5. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX).

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

1. What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)?
2. How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?
3. Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3.
4. What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)?
5. What are the possible l and m_l values for an orbital of type (x)? Of type (y)? Of type (z)?

Guided Solution

In the complete solution the font size changes throughout and cannot figure out why. Jessica (Jan 9, 2025) - Done: Fixed content with inconsistent font styles and sizes, likely caused by copying from another document. I recommend using Cmd + Shift + V on Mac or Ctrl + Shift + V on Windows to paste without any formatting in the future. Please review the changes and let me know if anything was missed. 

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Table 2: Guided Solution

Guided Solution Ideas
This problem requires comprehension of the following concepts: 'quantum mechanics and the atom', 'shapes of atomic orbitals', and 'electronic structure of atoms'. Consider the orbitals shown below… Image description: orbital (x) consists of a single lobe and is sphere shaped, orbital (y) consists of two lobes and is dumbbell/propellor shaped, orbital (z) consists of four lobes and is 4-leaf clover/daisy shaped.   Show/Hide Resource Refer to: Libre Text 2.4, Quantum Mechanics and The Atom (1) Libre Text 2.5, The Shape of Atomic Orbitals (3) Libre Text 2.6, Electronic Structure of Atoms (Electron Configurations) (2)
Recall the quantum numbers: Show/Hide Don't Forget! Quantum numbers: [n, l, ml, ms]   What are the quantum numbers and what do they represent? what are the guidelines/rules/principles that inform each quantum number? Show/Hide Don't Forget! n (principal quantum number; represents shell energy level) must be a whole number integer (i.e., n = 1, 2, 3, ... n) bigger number = greater energy = greater distance from nucleus = larger size l (azimuthal / orbital angular momentum quantum number, represents orbital shape) must be zero or a positive whole number integer, restricted by n (i.e., l = 0, 1, 2, ... n-1; l≠n) when l=0, type s(sphere shaped: 1 lobe) when l=1, type p(propeller shaped: 2 lobes) when l=2, type d(daisy shaped: 4 lobes; or donut shaped: two lobes and a ring shape) when l=3, type f(funky shaped: 7 lobes) ml (magnetic quantum number, represents the orientation of the orbital within a subshell) must be a positive or negative whole number integer, or zero; restricted by l (i.e., ml = -l, ... -2, -1, 0, 1, 2, ... +l) for s type: l=0; ml must be 0 for p type; l=1; ml can be -1, 0, or +1 for d type; l=2; ml can be -2, -1, 0, +1, or +2 ms (spin quantum number, represents the direction of spin of the electron) They can be +½ OR -½, not restricted by any other quantum number.

Table 3: Complete Solution

Complete Solution
Part One  What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)? Think about how many electrons can you put into any orbital? Think about electron pairing. Regardless of orbital type, each orbital can contain at most 2 electrons; one electron spins in a direction (ms=+½), and the other electron spins in the opposite direction (ms=-½). Answer: type (x) = 2 electrons type (y) = 2 electrons type (z) = 2 electrons
Part Two How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?   First, identify each orbital type based on the shape in the provided figure.  Here we must consider what quantum numbers are allowed for each orbital type when n=2 type (x) - 1 lobe, sphere shaped (s); l=0 type (y) - 2 lobes, propeller shaped (p); l=1 type (z) - 4 lobes, daisy shaped (d); l=2 Consider the relationship between quantum numbers n and l when n=2; is each orbital type (i.e., x, y, and z) allowed? Recall: l must be zero or a positive whole number integer, restricted by n (i.e., l = 0, 1, 2, ... n-1). type (x) - when n=2; l=0 (allowed) type (y) - when n=2; l=1 (allowed) type (z) - when n=2; l≠2 (NOT allowed) Summary: a type (z) or 'd-type' orbital does not exist in the n=2 shell. Answer: Type (x) = 1 orbital Type (y) = 3 orbitals Type (z) = 0 orbitals
Part Three Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3. Consider what each quantum number represents? Summarize the quantum numbers you have been provided in the question.   Recall there are four distinct quantum numbers [n, l, ml, ms] The question provides the principal quantum number (n) and the shape of the orbital defines the angular momentum quantum number (l): Type (x): [n=4, l=0] Type (y): [n=2, l=1] Type (z): [n=3, l=2] What quantum numbers must be defined to answer the question? Are there any restrictions that must be considered? Is there more than one correct answer? Still need ml and ms ml must be a positive or negative whole number integer, or zero; restricted by l (i.e., ml = -l, ... -2, -1, 0, 1, 2, ... +l) ms can be +½ OR -½, not restricted by any other quantum number Yes, more than one allowed quantum number sets for each orbital type as defined in the question type (x) = [n=4, l=0, ml=0, ms=+½] ml must equal 0 because l=0 ms = -½ would also be allowed 2 correct answers the 4s orbital can hold 2 electrons, each electron has a unique set of four quantum numbers type (y) = [n=2, l=1, ml=0, ms=-½] ml = -1 and ml = +1 would also be allowed ms = +½ would also be allowed 6 correct answers the 2p orbitals can hold 6 total electrons, each electron has a unique set of four quantum numbers 2 electrons in each px, py, and pz type (z) = [n=3, l=2, ml=-1, ms=+½] ml = -2, 0, +1, and +2 would also be allowed ms = -½ would also be allowed 10 correct answers the 3d orbitals can hold 10 total electrons, each electron has a unique set of four quantum numbers 2 electrons in each dxy, dyz, dxz, dx2–y2 and dz2 Answer: type (x) = [4, 0, 0, ½] type (y) = [2, 1, 0, -½] type (z) = [3, 2, -1, ½]
Part Four What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)? Consider the relationship between quantum numbers n and l. Recall: l must be zero or a positive whole number integer, the value of l is restricted by n (i.e., l = 0, 1, 2, ... n-1; l≠n) Therefore the lowest value of n = (l+1) Recall the value of l for each type of orbital type (x):1 lobe, sphere shaped (s); l=0 type (y): 2 lobes, propeller shaped (p); l=1 type (z): 4 lobes, daisy shaped (d); l=2 Type (x): lowest n=(l+1)=(0+1)=1 Type (y): lowest n=(l+1)=(1+1)=2 Type (z): lowest n=(l+1)=(2+1)=3 Answer: Type (x): n = 1 Type (y): n = 2 Type (z): n = 3
Part Five What are the possible l and ml values for an orbital of type (x)? Of type (y)? Of type (z)?   Consider the relationship between ml and l quantum numbers. ml must be a positive or negative whole number integer, or zero; ml is restricted by l (i.e., ml = -l, ... -2, -1, 0, 1, 2, ... +l) Recall the value of l for each type of orbital type (x):1 lobe, sphere shaped (s); l=0 type (y): 2 lobes, propeller shaped (p); l=1 type (z): 4 lobes, daisy shaped (d); l=2   Type (x) = s orbital: l=0; ml must be 0 Type (y) = p orbital; l=1; ml can be -1, 0, or +1 Type (z) = d orbital; l=2; ml can be -2, -1, 0, +1, or +2 Answer: Type (x): l=0; ml must be 0 Type (y): l=1; ml can be -1, 0, or +1 Type (z): l=2; ml can be -2, -1, 0, +1, or +2

 

PASS Attribution

• LibreTexts PASS Chemistry Book CHEM 1500 (4).
• Question 2.3.2.E.40 from LibreTexts PASS Chemistry Book CHEM 1500 (5) is used under a CC BY-NC 4.0 license.
  • Question 2.3.2.E.40 was adapted from question 2.E.40 from LibreTexts CHEM 1500: Chemical Bonding and Organic Chemistry (6), which is under a CC BY-NC-SA 4.0 license.
  • Question 2.E.40 is question 6.3.11 in LibreTexts Chemistry 1e (OpenSTAX) (7), which is under a CC BY 4.0 license.
  • Question 6.3.11 is question 41 from OpenStax Chemistry 2e (8), which is under a CC BY 4.0 license. Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction.

Reference List

1. LibreTexts. 2.4: Quantum Mechanics and The Atom. In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.04%3A_Quantum_Mechanics_and_The_Atom

2. LibreTexts. 2.6: Electronic Structure of Atoms (Electron Configurations). In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.06%3A_Electronic_Structure_of_Atoms_(Electron_Configurations)

3. LibreTexts. 2.5: The Shape of Atomic Orbitals. In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.05%3A_The_Shape_of_Atomic_Orbitals

4. Blackstock, L.; Brewer, S.; Jensen, A. CHEM 1500: Chemical Bonding and Organic Chemistry; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500

5. Blackstock, L.; Brewer, S.; Jensen, A. 2.3: Question 2.E.40 Pass - Quantum Numbers, Orbital Characteristics. In PASS Chemistry Book CHEM 1500. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/02%3A_Quantum_Theory_and_Electronic_Structure/2.03%3A_Question_2.E.40_PASS_-_quantum_numbers_orbital_characteristics

6. OpenStax. 2.E: Quantum Theory and Electronic Structure (Exercises). In CHEM 1500: Chemical Bonding and Organic Chemistry; LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.E%3A_Quantum_Theory_and_Electronic_Structure_(Exercises)

7. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/06%3A_Electronic_Structure_and_Periodic_Properties/6.E%3A_Electronic_Structure_and_Periodic_Properties_(Exercises)

8. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

PASS Attribution (must translate details into this format, below)

• LibreTexts PASS Chemistry Book CHEM 1500 (3).
• Question 4.E.20 from LibreTexts PASS Chemistry Book CHEM 1500 (4) is used under a CC BY-NC-SA 4.0 license.
  • https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/04%3A_Chemical_Bonding_I-_Basic_Concepts/4.E%3A_Chemical_Bonding_and_Molecular_Geometry_(Exercises) (TRU question)
  • Question 4.E.20 is from page titled 7.E: Chemical Bonding and Molecular Geometry (Exercises). https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/07%3A_Chemical_Bonding_and_Molecular_Geometry/7.E%3A_Chemical_Bonding_and_Molecular_Geometry_(Exercises) shared under a CC BY 4.0 license, authored, remixed, and/or curated by OpenStax, original source https://openstax.org/books/chemistry-2e/pages/7-exercises, Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction.

References

1. LibreTexts. 4.3: Covalent Bonding. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.02%3A_Atomic_Spectroscopy_and_The_Bohr_Model.

2. ?  LibreText 4.3 Covalent Bonding (section 4.3.5 Electronegativity and Bond Type)

3. Blackstock, L.; Brewer, S.; Jensen, A. 2.2: Question 2.E.26 PASS - Bohr Model, Quantized Energy Change. In PASS Chemistry Book CHEM 1500. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/02%3A_Quantum_Theory_and_Electronic_Structure/2.02%3A_Question_2.E.26_PASS_-_Bohr_Model_quantized_energy_change.

4. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX).

5. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

PASS Attribution (must translate details into this format, below)

• LibreTexts PASS Chemistry Book CHEM 1510/1520 (X).
• Question 2.E.28 from LibreTexts PASS Chemistry Book CHEM 1510/1520 (X) is used under a CC BY-NC-SA 4.0 license.
• Question 2.E.28 was adapted from page titled 9.E Gases (Exercises),  shared under a CC BY 4.0 license  platform https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/09%3A_Gases/9.E%3A_Gases_(Exercises), original source https://openstax.org/books/chemistry-2e/pages/9-exercises, access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction) 

Unsure how to format the References List

1. LibreTexts. 2.2: Atomic Spectroscopy and The Bohr Model. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.02%3A_Atomic_Spectroscopy_and_The_Bohr_Model. [need to update with actual reference]

2. Elhitti, S.; Bonanome, M.; Carley, H.; Tradler, T.; Zhou, L. 1.3: Order of Operations. In Arithmetic and Algebra (ElHitti, Bonanome, Carley, Tradler, and Zhou). LibreTexts. 2021. https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.03%3A_The_Order_of_Operations#:~:text='PE(MD)(AS),together%20from%20left%20to%20right).

3. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

4. Blackstock, L.; Brewer, S.; Jensen, A. 2.2: Question 2.E.26 PASS - Bohr Model, Quantized Energy Change. In PASS Chemistry Book CHEM 1500. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/02%3A_Quantum_Theory_and_Electronic_Structure/2.02%3A_Question_2.E.26_PASS_-_Bohr_Model_quantized_energy_change. [need to update with actual reference]

5. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX). [need to update with actual reference]

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises. [need to update with actual reference]

PASS Attribution (must translate details into this format, below)

• LibreTexts PASS Chemistry Book CHEM 1510/1520 (X).
• Question 2.E.36 from LibreTexts PASS Chemistry Book CHEM 1510/1520 (X) is used under a CC BY-NC-SA 4.0 license.
• Question 2.E.36 was adapted from page titled 9.11: Exercises,  shared under a CC BY 4.0 license  platform https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_2e_(OpenSTAX)/09%3A_Gases/9.11%3A_Exercises, shared under a CC BY 4.0 license, authored, remixed, and/or curated by OpenStax, original source https://openstax.org/books/chemistry-2e/pages/9-exercises), Access for free at https://openstax.org/books/chemistry/pages/1-introduction)

Unsure how to format the References List [Need to edits references to match the actual content] 

1. LibreTexts. 2.2: Atomic Spectroscopy and The Bohr Model. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.02%3A_Atomic_Spectroscopy_and_The_Bohr_Model. [Reference needs to match the actual textbook link above] 

2. Elhitti, S.; Bonanome, M.; Carley, H.; Tradler, T.; Zhou, L. 1.3: Order of Operations. In Arithmetic and Algebra (ElHitti, Bonanome, Carley, Tradler, and Zhou). LibreTexts. 2021. https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.03%3A_The_Order_of_Operations#:~:text='PE(MD)(AS),together%20from%20left%20to%20right). [Reference needs to match the actual textbook link above] 

3. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

4. Blackstock, L.; Brewer, S.; Jensen, A. 2.2: Question 2.E.26 PASS - Bohr Model, Quantized Energy Change. In PASS Chemistry Book CHEM 1500. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/02%3A_Quantum_Theory_and_Electronic_Structure/2.02%3A_Question_2.E.26_PASS_-_Bohr_Model_quantized_energy_change. [Reference needs to match the actual textbook link above] 

5. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX). [Reference needs to match the actual textbook link above] 

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

PASS Attribution (must translate details into this format, below)

• LibreTexts PASS Chemistry Book CHEM 1510/1520 (X).
• Question 2.E.45 from LibreTexts PASS Chemistry Book CHEM 1510/1520 (X) is used under a CC BY-NC-SA 4.0 license.
  • https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510_1520/02%3A_Gases/2.04%3A_2.4_PASS_Ideal_Gases-_use_the_Kinetic_Molecular_Theory_to_explain_impact_on_a_gas_as_V_and_T_increased_(2.E.45) (PASS Chem LibreText link)
• Question 2.E.45 was adapted from page titled 9.E:Gases (Exercises) https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_(OpenSTAX)/09%3A_Gases/9.E%3A_Gases_(Exercises), shared under a CC BY 4.0 license, authored, remixed, and/or curated by OpenStax, original source https://openstax.org/books/chemistry/pages/9-exercises, Access for free at https://openstax.org/books/chemistry/pages/1-introduction) 

Unsure how to format the References List - Correct Information Must Still Be Filled Out

1. LibreTexts. 2.5: The Kinetic-Molecular Theory. In CHEM1510/1520:TRU: Fundamentals and Principles of Chemistry (CHEM 1510 and CHEM 1520). LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/TRU%3A_Fundamentals_and_Principles_of_Chemistry_(CHEM_1510_and_CHEM_1520)/02%3A_Gases/2.05%3A_The_Kinetic-Molecular_Theory

2. Elhitti, S.; Bonanome, M.; Carley, H.; Tradler, T.; Zhou, L. 1.3: Order of Operations. In Arithmetic and Algebra (ElHitti, Bonanome, Carley, Tradler, and Zhou). LibreTexts. 2021. https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.03%3A_The_Order_of_Operations#:~:text='PE(MD)(AS),together%20from%20left%20to%20right).

3. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

4. OpenStax. 9.E:Gases (Exercises) https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_(OpenSTAX)/09%3A_Gases/9.E%3A_Gases_(Exercises), In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX).

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

PASS Attribution (attribution & refs need work).

• LibreTexts PASS Chemistry Book CHEM 1510/1520 (X).
• Question 3.E.14 from LibreTexts PASS Chemistry Book CHEM 1510/1520 (X) is used under a CC BY-NC-SA 4.0 license.
  • (question source from page titled 3.E: Thermochemistry (Exercises), https://chem.libretexts.org/Courses/Thompson_Rivers_University/TRU%3A_Fundamentals_and_Principles_of_Chemistry_(CHEM_1510_and_CHEM_1520)/03%3A_Thermochemistry/3.E%3A_Thermochemistry_(Exercises))
• Question 3.E.14 was adapted from page titled [issue is that question no longer on page? LibreText has changed - used to be here https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/05%3A_Thermochemistry/5.E%3A_Thermochemistry_(Exercises)]

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1. LibreTexts. 2.2: Atomic Spectroscopy and The Bohr Model. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.02%3A_Atomic_Spectroscopy_and_The_Bohr_Model. [need to update with actual reference]

2. Elhitti, S.; Bonanome, M.; Carley, H.; Tradler, T.; Zhou, L. 1.3: Order of Operations. In Arithmetic and Algebra (ElHitti, Bonanome, Carley, Tradler, and Zhou). LibreTexts. 2021. https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.03%3A_The_Order_of_Operations#:~:text='PE(MD)(AS),together%20from%20left%20to%20right).

3. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

4. Blackstock, L.; Brewer, S.; Jensen, A. 2.2: Question 2.E.26 PASS - Bohr Model, Quantized Energy Change. In PASS Chemistry Book CHEM 1500. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510_1520/03%3A_Thermochemistry/3.01%3A_3.X_Template. [this LibreText link name needs fixing in LibreText then need to update here]

5. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX). [need to update with actual reference]

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises. [need to update with actual reference]

Welcome Students!

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1. Determine the change in energy (in joules) when the electron in a Li²⁺ ion moves from the n = 2 to the n = 1 orbit.
2. What is the energy (in joules) of the photon produced? 

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• LibreTexts PASS Chemistry Book CHEM 1510/1520 (3).
• Question 2.E.26 from LibreTexts PASS Chemistry Book CHEM 1500 (4) is used under a CC BY-NC-SA 4.0 license.
  • Question 2.E.26 was adapted from question 6.2.11 from LibreTexts Chemistry 1e (OpenSTAX) (5), which is under a CC BY 4.0 license.
  • Question 6.2.11 is question 11 from OpenStax Chemistry 2e (6), which is under a CC BY 4.0 license. Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction.

References

1. LibreTexts. 2.2: Atomic Spectroscopy and The Bohr Model. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.02%3A_Atomic_Spectroscopy_and_The_Bohr_Model.

2. Elhitti, S.; Bonanome, M.; Carley, H.; Tradler, T.; Zhou, L. 1.3: Order of Operations. In Arithmetic and Algebra (ElHitti, Bonanome, Carley, Tradler, and Zhou). LibreTexts. 2021. https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.03%3A_The_Order_of_Operations#:~:text='PE(MD)(AS),together%20from%20left%20to%20right).

3. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

4. Blackstock, L.; Brewer, S.; Jensen, A. 2.2: Question 2.E.26 PASS - Bohr Model, Quantized Energy Change. In PASS Chemistry Book CHEM 1500; LibreTexts, 2024. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/02%3A_Quantum_Theory_and_Electronic_Structure/2.02%3A_Question_2.E.26_PASS_-_Bohr_Model_quantized_energy_change.

5. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX).

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

1. H₂(g) + Br₂(g) → 2HBr(g)
2. CH₄(g) + I₂(g) → CH₃I(g) + HI(g)
3. C₂H₄(g) + 3O₂ → 2CO₂(g) + 2H₂O(g)

Guided Solution

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Table 2: Guided Solution

Guided Solution Ideas
This question is a calculation problem in which you must identify what bonds are broken and formed during a chemical reaction. This type of problem requires you to use a table of values to calculate the overall energy change in the reaction using bond energies. Show/Hide Resource Refer to Section 4.6: Strengths of Ionic and Covalent Bonds (1).
It can be difficult to know how many bonds are in a molecule. The easiest way to find what bonds there are is to create a Lewis Structure of the molecule. Show/Hide Resource Refer to Section 4.4 Lewis Symbols and Structures (2). 1. H2 (g) + Br2 (g) → 2HBr (g) Create Lewis structures for H2, Br2 and HBr. Show/Hide Structures    2. CH4 (g) + I2 (g) → CH3I (g) + HI (g) Create Lewis structures for CH4, I2, CH2I and HI. Show/Hide Structures 3. C2H4 (g) + 3O2 (g) → 2CO2 (g) + 2H2O (g) Create Lewis structures for C2H4, O2, CO2 and H2O. Show/Hide Structures
Recall that bonds require energy to break (start a reaction), and energy is released when bonds form (in the products of a reaction). Show/Hide Don't Forget! [latex] \Delta H=\left(\sum \text { Bonds broken }\right)-\left(\sum \text { Bonds formed }\right) [/latex] The energy of bonds formed is subtracted as they are formed in the reaction. Bond energy values, by definition, are the energy required to break the bond. By subtracting the sum of the product bonds formed, we are changing the sign of the energy to represent the opposite process (forming the bond).
When using the bond energies table, scan the table for your desired bond (i.e. (H-H)). The number beside it will be the one used in the calculation. Make sure you don’t confuse single, double, and triple bonds! Show/Hide Don't Forget! The bond energy for H-H is 436 kJ.

Table 3: Complete Solution

Complete Solution
The following equation will be used for each of the reactions: [latex] \Delta H=\left(\sum \text { Bonds broken }\right)-\left(\sum \text { Bonds formed }\right) [/latex] For a reaction to occur, bonds need to break, and new bonds need to form. When bonds break, energy is absorbed. When bonds form, energy is released. We use this to calculate the sum of the energy change over the reaction. How do we know which bonds are breaking and which are forming? Show/Hide Don't Forget! In a reaction, the bonds to the left of the arrow will break, and the bonds to the right will form. ___(break)___ → ___(form)___
1. H2 (g) + Br2 (g) → 2HBr (g) [latex] \Delta H=\left(\sum \text { Bonds broken }\right)-\left(\sum \text { Bonds formed }\right) [/latex] The bond between the two hydrogen and the two bromine atoms breaks. Two product molecules form, each with a hydrogen bonded to a bromine. Show/Hide Structures [latex] \Delta \mathrm{H}=(1 \operatorname{mol}\mathrm{(H-H)+1} \operatorname{mol}\mathrm{(B r-B r))-(2} \operatorname{mol}\mathrm{(H-B r))} [/latex] Using Table 4.6.1: Bond Energies (kJ/mol) from Section 4.6: Strengths of Ionic and Covalent Bonds (1), the values for each bond energy replaces their respective bonds in the equation. [latex] \Delta \mathrm{H=(1} \mathrm{~mol}(436 \mathrm{~kJ} / \mathrm{mol})+1 \mathrm{~mol}(190 . \mathrm{kJ} / \mathrm{mol}))-(2 \mathrm{~mol}(370 . \mathrm{kJ} / \mathrm{mol})) [/latex] When solving inside the brackets, keep stoichiometry in mind. [latex] \Delta \mathrm{H=(626 k J)-(740 . k J)} [/latex] The energy released from the bonds formed is subtracted from the energy absorbed by the bonds broken. ΔH=-114 kJ The calculated value is negative, meaning the reaction was exothermic.
2. CH4 (g) + I2 (g) → CH3I (g) + HI (g) [latex] \Delta \mathrm{H}=\left(\sum \text { Bonds broken }\right)-\left(\sum \text { Bonds formed }\right) [/latex] Four carbon-hydrogen and one iodine-iodine bonds break. Three carbon-hydrogen bonds, one carbon-iodine and one hydrogen-iodine, are formed. Show/Hide Think About This! Make sure you have the correct bonds for CH4 and CH3I. Show/Hide Structures [latex] \Delta \mathrm{H=(4(C-H)+(I-I))-(3(C-H)+(C-I)+(H-I))} [/latex] Using Table 4.6.1: Bond Energies (kJ/mol) from Section 4.6: Strengths of Ionic and Covalent Bonds (1), the values for each bond energy replaces their respective bonds in the equation. [latex] \begin{align} \Delta& \mathrm{H=(4mol(415 kJ/mol)+1 mol(150. kJ/mol))-(3 mol(415 kJ/mol)\\+1 mol(240. kJ/mol)+1 mol(295 kJ/mol))} \\\\ \Delta& \mathrm{H=((1660 kJ)+(150. kJ))-((1245 kJ)+(240. kJ)+(295 kJ))} \end{align} [/latex] When solving inside the brackets, keep stoichiometry in mind. [latex] \Delta \mathrm{H=(1810 kJ)-(1780 kJ)} [/latex] The energy released from the bonds formed is subtracted from the energy absorbed by the bonds broken. ΔH=30 kJ The calculated value is positive, meaning the reaction was endothermic
3. C2H4 (g) + 3O2 (g) → 2CO2 (g) + 2H2O (g) [latex] \Delta \mathrm{H}=\left(\sum \text { Bonds broken }\right)-\left(\sum \text { Bonds formed }\right) [/latex] Two hydrogen-carbon, one carbon-carbon double, and three oxygen-oxygen double bonds break. Two molecules of CO2 form that contain two carbon-oxygen double bonds and two molecules, each containing two hydrogen-oxygen bonds. Show/Hide Think About This! Make sure you have the correct bonds for C2H4, O2 and CO2. Show/Hide Structures [latex] \begin{gathered} \Delta \mathrm{H=(4(C-H)+(C=C)+3(O=O))-(2(2(C=O))+2(2(H-O)))} \end{gathered} [/latex] Using Table 4.6.1: Bond Energies (kJ/mol) from Section 4.6: Strengths of Ionic and Covalent Bonds (1), the values for each bond energy replaces their respective bonds in the equation. [latex] \begin{gathered} \Delta \mathrm{H=(4 mol(415 kJ/mol)+1 mol(611 kJ/mol)\\ +3 mol(498 kJ/mol))-(4 mol(741 kJ/mol)\\ +4 mol(464 kJ/mol))} \end{gathered} [/latex] When solving inside the brackets, keep stoichiometry in mind. [latex] \begin{align} \Delta& \mathrm{H=((1660 kJ)+(611 kJ)+(1494 kJ))-((2964 kJ)+(1856 kJ))} \\\\ \Delta& \mathrm{H=(3765 kJ)-(4820 kJ)} \end{align} [/latex] The energy released from the bonds formed is subtracted from the energy absorbed by the bonds broken. ΔH= -1055 kJ = 1.055 x 103 kJ The calculated value is negative, meaning the reaction was exothermic.

1. CS₂
2. Cl₂CO (C is the central atom)
3. Cl₂SO (S is the central atom)
4. SO₂F₂ (S is the central atom)
5. XeO₂F₂ (Xe is the central atom)

Solution

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Show/Hide Solution

1. CS₂ 16 valence electrons, C central atom     This molecule has a linear electron-pair geometry: sp hybridized (s + p)

2. Cl₂CO (C is the central atom) 24 valence electrons     This molecule has a trigonal planar electron-pair geometry: sp² hybridized (s + p + p)

3.Cl₂SO (S is the central atom) 26 valence electrons     This molecule has a tetrahedral electron-pair geometry: sp³ hybridized (s + p + p + p)

4. SO₂F₂ (S is the central atom) 32 valence electrons     This molecule has a tetrahedral electron-pair geometry: sp³ hybridized (s + p + p + p)

5. XeO₂F₂ (Xe is the central atom) 34 valence electrons     This molecule has a trigonal bipyramidal electron-pair geometry: sp³d hybridized (s + p + p + p + d)

Guided Solution

Do you want more help? The guided solution below will give you the reasoning for each step to get your answer, with reminders and hints.

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Table 2: Guided Solution

Guided Solution Ideas
This question is a theory problem where you use your knowledge of molecular bonding and identify atomic orbital hybridization. Show/Hide Resource Refer to Section 5.3 Hybrid Atomic Orbitals (1).
What is the pattern associated with atomic orbital hybridization? Show/Hide Think About This! The hybridization of the centre atom will be determined by the electron-pair geometry, not the atom itself. For example, the centre atoms hybridization will always be sp in a linear molecule. Number of electron domains (as determined by the number of bonding directions and lone pairs in the best Lewis structure) = Number of atomic orbitals required for hybridization. Number of hybrid orbitals = Number of orbitals mixed. Hybrid orbitals are named by type and number of orbitals mixed. Show/Hide Don't Forget! Recall the atomic orbitals: for n=2 there is 1 's' orbital (l=0) and 3 degenerate 'p' orbitals (l=1). Note that 'd' orbitals (l=2) can only exist when n is greater than or equal to 3. 2 domains = 2 atomic orbitals must be hybridized = s + p = sp hybridization = linear electron domain geometry (EDG) 3 domains = 3 atomic orbitals must be hybridized = s + p + p = sp2 hybridization = trigonal planar EDG 4 domains = 4 atomic orbitals must be hybridized = s + p + p + p = sp3 hybridization = tetrahedral EDG 5 domains = 5 atomic orbitals must be hybridized = s + p + p + p + d = sp3d hybridization = trigonal bipyramidal EDG 6 domains = 6 atomic orbitals must be hybridized = s + p + p + p + d + d = sp3d2 hybridization = octahedral EDG

Table 3: Complete Solution

Complete Solution
CS2 16 valence electrons, C central atom   This molecule has a linear electron-pair geometry: sp hybridized
2. Cl2CO (C is the central atom) 24 valence electrons     This molecule has a trigonal planar electron-pair geometry : sp2 hybridized
3. Cl2SO (S is the central atom) 26 valence electrons     This molecule has a tetrahedral electron-pair geometry : sp3 hybridized
4. SO2F2 (S is the central atom) 32 valence electrons     This molecule has a tetrahedral electron-pair geometry : sp3 hybridized
5. XeO2F2 (Xe is the central atom) 34 valence electrons     This molecule has a trigonal bipyramidal electron-pair geometry: sp3d hybridized

Check Your Work

Verify that:

• Your Lewis structure has all the valence electrons.
• You have counted the central atom's electron domains correctly.

The name of our electron pair geometry and number of electron domains leads us to the correct hybridization. Does your answer make chemical sense?

Show/Hide Answer

Hybrid orbitals form due to the covalent bonding within molecules. When 2 or more atoms create a covalent bond, their atomic orbitals will overlap to form these hybrid orbitals. In this case, we are looking at the hybridization of the centre atom to see what kind of hybridization is happening to overlap with all the atoms. When molecules grow and involve more atoms, more bonds form, and thus, more orbitals become involved. This is why a linear molecule only uses two orbitals (s + p), while an octahedral molecule uses six (s + p + p + p + d + d).

PASS Attribution

• LibreTexts PASS Chemistry Book CHEM 1510/1520 (4).
• Question 5.E.59 from LibreTexts PASS Chemistry Book CHEM 1510/1520 (5) is used under a CC BY-NC-SA 4.0 license.
  • Question 5.E.59 is question 8.E.1.1 (b to f) from LibreTexts Chemistry 1e (OpenSTAX) (6), which is under a CC BY 4.0 license.
  • Question 8.E.1.1 (b to f) is question 27 (b to f) from OpenStax Chemistry (7), which is under a CC BY 4.0 license. Access for free at https://openstax.org/books/chemistry/pages/1-introduction.

References

1. OpenStax. 5.3: Hybrid Atomic Orbitals. In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500:_Chemical_Bonding_and_Organic_Chemistry/05:_Chemical_Bonding_II-_Molecular_Geometry_and_Hybridization_of_Atomic_Orbitals/5.03:_Hybrid_Atomic_Orbitals. 2. OpenStax. 4.4: Lewis Symbols and Structures. In General Chemistry 1. LibreTexts, 2020. https://chem.libretexts.org/Courses/Nassau_Community_College/General_Chemistry_1/04%3A_Chemical_Bonding_and_Molecular_Geometry/4.04%3A_Lewis_Symbols_and_Structures. 3. OpenStax. 5.1: Molecular Structure and Polarity. In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/05%3A_Chemical_Bonding_II-_Molecular_Geometry_and_Hybridization_of_Atomic_Orbitals/5.01%3A_Molecular_Structure_and_Polarity.

4. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

5. Blackstock, L.; Brewer, S.; Jensen, A. 5.3: Question 5.E.59 PASS - Identify Central Atom Hybridization. In PASS Chemistry Book CHEM 1510/1520. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/05%3A_Chemical_Bonding_II_-_Molecular_Geometry_and_Hybridization_of_Atomic_Orbitals/5.03%3A_Question_5.E.59_PASS_-_identify_central_atom_hybridization. 6. OpenStax. 8.E: Advanced Theories of Covalent Bonding (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2022. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/08%3A_Advanced_Theories_of_Covalent_Bonding/8.E%3A_Advanced_Theories_of_Covalent_Bonding_(Exercises). 7. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 8 Exercises. In Chemistry. OpenStax, 2015. https://openstax.org/books/chemistry/pages/8-exercises.

1. H₂O, HCl, SiH₄
2. Br₂, Cl₂, F₂
3. C₂H₆, CH₄, C₃H₈

1. How many sigma and pi bonds does it have?
2. What orbitals overlap to form the C-H sigma bonds?
3. What orbitals overlap to form the C-C sigma bonds?
4. What orbitals overlap to form the C-N sigma bonds?
5. What orbitals overlap to form the C-N pi bonds?
6. What orbital contains the lone pair electrons on nitrogen?
7. Sketch the molecule showing the hybridized atomic orbital ‘cloud’ overlap.

Show/Hide Answer

1. 5 sigma and 2 pi.
2. A sp³ hybrid orbital from carbon and an s orbital from hydrogen.
3. A sp³ hybrid orbital from one carbon and a sp hybrid orbital from another carbon.
4. A sp hybrid orbital from carbon and a sp orbital from nitrogen.
5. A p_y and a p_z orbital from carbon and a p_y and p_z orbital from nitrogen.
6. A sp hybrid orbital.
7. Sketch below:

Solution

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Show/Hide Solution

a. 5 sigma (single bonds) and 2 pi (one double and one triple bond).

b. A sp³ hybrid orbital from carbon and an s orbital from hydrogen. The hydrogen atoms are all unhybridized.

c. A sp³ hybrid orbital from one carbon and a sp hybrid orbital from another carbon. Both carbons are hybridized, but their electron domain geometries are not the same, meaning their hybridizations are different.

d. A sp hybrid orbital from carbon and a sp orbital from nitrogen. Both carbon and nitrogen have a sp hybridization.

e. A p_y and a p_z orbital from carbon and a p_y and p_z orbital from nitrogen. The ‘Y’ and ‘Z’ mean they have slightly different orientations.

f. A sp hybrid orbital. Nitrogen has a linear electron domain geometry, meaning it has a sp hybridization in both directions.

g. Hand-drawn sketch below:

 

Guided Solution

Do you want more help? The guided solution below will give you the reasoning for each step to get your answer, with reminders and hints.

Show/Hide Guided Solution

Table 2: Guided Solution

Guided Solution Ideas
This is a theory type problem that tests your knowledge on atomic orbital hybridization. You must correctly identify the hybridization of multiple atoms in a molecule and sketch the orbital overlaps. Show/Hide Resource Refer to Section 7.1.7: sp Hybrid Orbitals and the Structure of Acetylene (1).
What are sigma and pi bonds? Recall that: Sigma bonds are your single bonds. Pi bonds are your double and triple bonds. Show/Hide Don't Forget! There is at least one sigma bond between each atom. Look at the bonds between your carbon and your nitrogen. How many lines do you see?
How do you identify atomic orbital hybridization? Identify the electron domain geometry of your central atom. (in this case, the center atoms are carbons). Your electron domain geometry will tell you the number of bonding directions attached to your atom. Each bonding direction represents an orbital needed. Show/Hide Think About This! For instance, a tetrahedral must make four bonds, so it has an s+p+p+p (sp3) hybridization. Identify if your outer atoms require hybridization (if they do, they will also have multiple bonding directions, including lone pairs).
How do you know which orbitals are overlapping? Show/Hide Think About This! Each bond that is between the atoms will be an overlap. The hybridization of the orbitals will depend on the two atoms the bond is between.
How do you sketch the orbital overlaps? Begin by drawing your center atom with its orbitals in the shape of its electron domain geometry. (it is okay if they look like “sausages” if you label them with their hybridization) Overlap these orbitals with orbitals representing the outer atoms. Label these as sigma bonds. The orbitals that overlap to form pi bonds are longer and skinnier than the sigma bonds. They overlap sideways, and therefore, connect above and below the sigma bond.

Table 3: Complete Solution

Complete Solution
a. 5 sigma (single bonds) and 2 pi (one double bond and one triple bond). There will always be a single bond between each atom in the molecule. A second or third line next to the single bond represents a double or triple bond. Count these in your Lewis structure form to identify the sigma and pi bonds.
b. A sp3 hybrid orbital from carbon and an s orbital from hydrogen. This carbon atom makes bonds in four directions, which gives it a sp3 hybridization. Three of these directions are hydrogen atoms. All of these hydrogens are unhybridized and have s orbitals. When the orbitals from the hydrogens and carbon overlap, they form a sigma bond.
c. A sp3 hybrid orbital from one carbon and a sp hybrid orbital from another carbon. Although both atoms are hybridized, they have a different number of bonding directions, and therefore, one is sp3 and the other is sp.
d. A sp hybrid orbital from carbon and a sp orbital from nitrogen. Both atoms bond in two different directions giving them sp orbital hybridization.
e. A py and a pz orbital from carbon and a py and pz orbital from nitrogen. These are the pi bonds. They are labelled with ‘Y’ and ‘Z’ as they have slightly different orientations on the axis. Pi orbitals make bonds above and below the sigma bond as they overlap sideways.
f. A sp hybrid orbital. Nitrogen has two electron domain directions. One is towards the carbon in a triple bond, and the other is towards its lone pair; therefore, it has two hybridized sp orbitals. The orbital that contains nitrogen's lone pair is an sp orbital.
g. Hand-drawn sketch below:

PASS Attribution

• LibreTexts PASS Chemistry Book CHEM 1510/1520 (2)
• Question 7.17 from LibreTexts CHEM1500: Chemical Bonding and Organic Chemistry (1) is used under a CC BY-SA 4.0 license.
  • Question 7.17 is question 1 from LibreTexts Organic Chemistry (Morsch et al.) (3), which is under a CC BY-SA 4.0 license.

Media Attributions

• Figure 1: Acetonitrile by Farmer et al. from LibreTexts CHEM1500: Chemical Bonding and Organic Chemistry (1) is modified and used under a CC BY-SA 4.0 license.
• Figure 2, by the authors (Brewer S. and Blackstock L.), is free to use under a CC0 license.

References

1. Farmer, S.; Kennepohl, D.; Cunningham, K.; Soderburg, T.; Reusch, W. 7.1.7: sp Hybrid Orbitals and the Structure of Acetylene. In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/07%3A_Organic_Chemistry_I_-_Bonding_and_Structure/7.01%3A_Bonding_and_Structure_I-_Review_of_Bonding/7.1.07%3A_sp_Hybrid_Orbitals_and_the_Structure_of_Acetylene.

2. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1510/1520; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

3. Farmer, S.; Kennepohl, D.; Cunningham, K.; Soderburg, T.; Reusch, W. 1.9: sp Hybrid Orbitals and the Structure of Acetylene. In Organic Chemistry (Morsch et al.). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Organic_Chemistry_(Morsch_et_al.)/01%3A_Structure_and_Bonding/1.09%3A_sp_Hybrid_Orbitals_and_the_Structure_of_Acetylene.

1. [caption id="attachment_690" align="alignnone" width="103"] Compound A[/caption]
2. [caption id="attachment_691" align="alignnone" width="64"] Compound B[/caption]
3. [caption id="attachment_692" align="alignnone" width="76"] Compound C[/caption]

Guided Solution

Do you want more help? The guided solution below will give you the reasoning for each step to get your answer, with reminders and hints.

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Table 2: Guided Solution

Guided Solution Ideas
This question is a theory problem where you assign the correct configuration to a carbon stereocenter (R or S). Show/Hide Resource Refer to Section 8.4: Absolute Configuration- R-S Sequence Rules (1).
For the following compounds, assign R or S configurations for each stereocenter. [caption id="attachment_690" align="alignnone" width="103"] Compound A[/caption] [caption id="attachment_691" align="alignnone" width="64"] Compound B[/caption] [caption id="attachment_692" align="alignnone" width="76"] Compound C[/caption]
The rules to assign priority to substituents: First, examine the atoms directly attached to the stereocenter of the compound. An atom with a higher atomic number takes precedence over an atom with a lower number. Hydrogen is the lowest possible priority atom because it has the lowest atomic number. Ensure that the lowest priority group is pointed away (dashed back) If two or more substituents have the same element directly attached to chiral carbon, proceed along the substituent chains until you find a point of difference. Determine which chain has the first connection to an atom with the highest priority (the highest atomic number). That chain has the higher priority. For assigning priority, treat multiple bonds as if each bond of the multiple bond is bonded to a unique atom. For example, an alkene substituent (CH2=CH-) has a higher priority than an ethyl substituent (CH3CH2-). Show/Hide Resource Refer to Section 8.4: Absolute Configuration- R-S Sequence Rules (1).
R vs S configuration To identify the configuration of a stereocenter, you must identify if your order of priority goes in the clockwise or counterclockwise direction. Clockwise = R Counterclockwise = S

Table 3: Complete Solution

Complete Solution
a. Compound A [caption id="attachment_690" align="alignnone" width="103"] Compound A[/caption] Bromine is the first priority (atomic number 35). Oxygen is the second priority (atomic number 8). Carbon is the third priority (atomic number 6). It goes counterclockwise around the stereocenter. Answer: S
b. Compound B [caption id="attachment_691" align="alignnone" width="64"] Compound B[/caption] Iodine is the first priority (atomic number 53). Fluorine is the second priority (atomic number 9). Carbon is the third priority (atomic number 6). It goes clockwise around the stereocenter. Answer: R
c. Compound C [caption id="attachment_692" align="alignnone" width="76"] Compound C[/caption] Hydrogen is wedged forward, so you must rotate the molecule or reverse the stereochemistry determined, as drawn below. [caption id="attachment_437" align="alignnone" width="127"] Rotated Compound C[/caption] Hydrogen, the lowest priority group, is now dashed back. Iodine is the first priority (atomic number 53). Oxygen is the second priority (atomic number 8). Carbon is the third priority (atomic number 6). It goes counterclockwise around the stereocenter in the original figure. It goes clockwise in the rotated molecule. Answer: R

PASS Attribution

• Questions 8.4.E.1 from LibreTexts PASS Chemistry Book CHEM 1500 (2) is used under a CC BY-NC 4.0 license.

Media Attributions

• Compound A by Blackstock et al. from LibreTexts PASS Chemistry Book CHEM 1500 (2) is used under a CC BY-NC 4.0 license.
• Compound B by Blackstock et al. from LibreTexts PASS Chemistry Book CHEM 1500 (2) is used under a CC BY-NC 4.0 license.
• Compound C by Blackstock et al. from LibreTexts PASS Chemistry Book CHEM 1500 (2) is used under a CC BY-NC 4.0 license.
• Rotated Compound C by Blackstock et al. from LibreTexts PASS Chemistry Book CHEM 1500 (2) is used under a CC BY-NC 4.0 license.

References

1. LibreTexts. 8.4: Absolute Configuration- R-S Sequence Rules. In CHEM1500: Chemical Bonding and Organic Chemistry. LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM1500%3A_Chemical_Bonding_and_Organic_Chemistry/08%3A_Organic_Chemistry_II_-_Stereochemistry/8.04%3A_Absolute_Configuration-_R-S__Sequence_Rules.

2. Blackstock, L.; Brewer, S.; Jensen, A. 8.2. Question 8.4.E.1 PASS - Stereocenter Configuration R or S. In PASS Chemistry Book CHEM 1500. LibreTexts, 2024. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/08%3A_Organic_Chemistry_II_-_Stereochemistry/8.2._Question_8.4.E.1_PASS_-_stereocenter_configuration_R_or_S.

1. Draw the simple line structure.
2. Draw the two chair confirmations numbering the carbons and labelling the positions as axial/equatorial.
3. Identify which is the more stable structure.

Solution

Do you want to see the steps to reach the answer? Check out this solution.

Show/Hide Solution

a. Simple Line Structure This molecule is trans, meaning one bromine is dashed back, and one is wedged forward. These bromines are on a six-carbon ring and attached to carbons one and two.

b. Chair conformations

1. Conformation 1 — Both bromines are in axial positions.
2. Conformation 2 — Both bromines are in equatorial positions.

c. Conformation 2 is the most stable. It has the least 1,3-diaxial interactions between the bromine groups and surrounding atoms.

 

Guided Solution

Do you want more help? The guided solution below will give you the reasoning for each step to get your answer, with reminders and hints.

Show/Hide Guided Solution

Table 2: Guided Solution Ideas

Guided Solution
This question is a theory problem where you test your understanding of cycloalkane naming and chair conformations. Show/Hide Resource Refer to Section 9.4: Cyclohexane- A Strain-Free Cycloalkane (1).
Recall how to sketch a line structure: 1. Identify if the structure is Cis or Trans. Show/Hide Think About This! Trans 1,2-dibromocyclohexane This means one substituent is dashed back, and one is wedged forward. 2. Determine if the parent chain is in the form of a chain or ring. (This will be at the end of the name). Show/Hide Don't Forget! [caption id="attachment_745" align="alignnone" width="66"] Cyclohexane[/caption] Trans 1,2-dibromocyclohexane 3. Identify substituent atoms and which carbons they are connected to. Show/Hide Don't Forget! [caption id="attachment_718" align="alignnone" width="91"] Trans 1,2-dibromocyclohexane[/caption] Trans 1,2-dibromocyclohexane.
How to draw the chair conformation: Draw two slightly offset parallel lines. Draw another pair of parallel lines from the ends of the first pair. Connect with the third set of parallel lines. Start the first pair of lines at the opposite angle to draw its ring-flip conformer. Show/Hide Don't Forget!   [caption id="attachment_1082" align="alignnone" width="1024"] How to draw a chair conformation (Farmer et al. / LibreTexts) CC BY-SA license[/caption]
Identify the axial and equatorial positions.  Identify if the structure is Cis or Trans. Show/Hide Don't Forget! Axial positions in red: [caption id="attachment_750" align="alignnone" width="84"] Conformation 1 axial positions[/caption]   [caption id="attachment_751" align="alignnone" width="94"] Conformation 2 axial positions[/caption]   Equatorial Positions in blue: [caption id="attachment_752" align="alignnone" width="93"] Conformation 1 equitorial positions[/caption]   [caption id="attachment_753" align="alignnone" width="86"] Conformation 2 equitorial positions[/caption]
Convert your simple line structure to your chair conformation: 1. Match the numbered carbons from your line structure to your template. 2. Recall that substituents wedged forward will be on the higher ('up') position and the substituent dashed backwards will be on the lower ('down') position. Show/Hide Watch Out! [caption id="attachment_719" align="alignnone" width="105"] Simple line structure converted to a chair conformation[/caption]
Identify the more stable conformation. Show/Hide Don't Forget! The most stable conformation is the one that has the least number of interactions between substituent atoms. The larger, more electronegative atoms are favoured in the equatorial positions as they will be impacted by fewer interactions with surrounding atoms. Show/Hide Resource Refer to Section 9.5: Substituted Cyclohexanes (2).

Table 3: Complete Solution

Complete Solution
a. Simple Line Structure This molecule is trans, meaning one bromine is dashed back and one is wedged forward. These bromines are on a six-carbon ring and attached to carbons one and two.
b. Chair Conformations i. Conformation 1 Both bromines are in axial positions. The bromine on carbon one is in the highest position, and the bromine on carbon two is in the lowest position. ii. Conformation 2 Both bromines are in equatorial positions. All axial and equatorial positions switch. The bromine on carbon one is in the highest position, and the bromine on carbon two is in the lowest position.
c. The equatorial conformation is the most stable. It has the fewest interactions between the bromine groups and surrounding atoms because they are both in equatorial positions.