Chapter 9: Problem 56
Carbon dioxide \(\left(\mathrm{CO}_{2}\right),\) dinitrogen monoxide \(\left(\mathrm{N}_{2} \mathrm{O}\right),\) the azide ion \(\left(\mathrm{N}_{3}^{-}\right),\) and the cyanate ion (OCN \(^{-}\) ) have the same geometry and the same number of valence shell electrons. However, there are significant differences in their electronic structures. (a) What hybridization is assigned to the central atom in each species? Which orbitals overlap to form the bonds between atoms in each structure. (b) Evaluate the resonance structures of these four species. Which most closely describe the bonding in these species? Comment on the differences in bond lengths and bond orders that you expect to see based on the resonance structures.
Short Answer
Expert verified
All species have central atoms with sp hybridization. Resonance affects bond lengths and orders, leading to equalized or length-varying bonds.
Step by step solution
01
Determine Hybridization of Central Atoms
To find the hybridization of the central atom in each species (\( CO_2 \), \( N_2O \), \( N_3^- \), and \( OCN^- \)), use the formula: hybridization number = 1/2 (valence electrons on central atom + number of surrounding atoms + charge). - In \( CO_2 \), carbon is the central atom with a hybridization of \( sp \) as it forms two double bonds with oxygen.- In \( N_2O \), nitrogen is the central atom (middle nitrogen) and also has \( sp \) hybridization due to its linear structure.- For \( N_3^- \), the central nitrogen is solely bonded to other nitrogen atoms and thus, has \( sp \) hybridization.- In \( OCN^- \), the central atom carbon has \( sp \) hybridization due to its linear O-C-N arrangement.
02
Identify Bond Formation in Each Species
Determine the nature of orbital overlap that forms the bonds:- In \( CO_2 \), the \( sp \) orbitals of carbon overlap with \( p \) orbitals of oxygen to form sigma bonds, while the unhybridized \( p \) orbitals form pi bonds.- In \( N_2O \), the \( sp \) hybrid orbitals of the central nitrogen overlap with \( p \) orbitals of the other nitrogen and an oxygen to form sigma bonds. Pi bonds result from the overlap of remaining \( p \) orbitals.- For \( N_3^- \), the \( sp \) orbitals of the central nitrogen bond with adjacent nitrogen atoms’ \( p \) orbitals for sigma bonds; unhybridized \( p \) orbitals form pi bonds.- The bond formation in \( OCN^- \) involves \( sp \) hybrid orbital overlaps of carbon with \( p \) orbitals of oxygen and nitrogen for sigma bonds; pi bonds are formed from remaining \( p \) orbitals.
03
Evaluate Resonance Structures
Each species can have multiple resonance structures due to delocalization of electrons:- \( CO_2 \) has resonance structures with different placements of double bonds between carbons and oxygens.- \( N_2O \) has structures involving different nitrogen-oxygen bonding arrangements.- \( N_3^- \) possesses resonance where electrons are delocalized among nitrogen atoms.- \( OCN^- \) has structures with varying formal charges on atoms due to electron arrangements among oxygen, carbon and nitrogen.These resonance structures help to depict more realistic representations of electron distributions.
04
Analyze Bond Lengths and Bond Orders
Based on resonance structures:- In \( CO_2 \), bond lengths are equalized by resonance and bond order is approximately 2.- In \( N_2O \), the resonance leads to varying bond lengths and an average bond order less than a double bond, especially for N-O.- In \( N_3^- \), bond lengths are equalized, reflecting a bond order between 1 and 2.- For \( OCN^- \), resonance contributes to shorter O-C and longer C-N bond lengths, resulting in bond orders slightly altered by resonance.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Hybridization
Hybridization is a fundamental concept in understanding the molecular structure of compounds like carbon dioxide (
CO_2
), dinitrogen monoxide (
N_2O
), the azide ion (
N_3^-
), and the cyanate ion (OCN
^-
). Hybridization refers to the mixing of atomic orbitals to form new orbitals that are used in bonding. These new orbitals are typically used to explain molecule shapes that are stable and energetically favorable.
For example, in CO_2 , the carbon atom undergoes sp hybridization because it forms two double bonds in a linear structure. This mixing of one s and one p orbital creates two equivalent sp orbitals that align linearly.
Similarly, N_2O also uses sp hybridization at its central nitrogen due to its linear structure, despite being surrounded by another nitrogen and an oxygen atom. For the N_3^- , the central nitrogen also adopts sp hybridization, while in OCN^- the central carbon uses this hybridization for the linear arrangement of atoms. This consistency in hybridization highlights the challenging yet fascinating nature of predicting and understanding molecule geometries.
For example, in CO_2 , the carbon atom undergoes sp hybridization because it forms two double bonds in a linear structure. This mixing of one s and one p orbital creates two equivalent sp orbitals that align linearly.
Similarly, N_2O also uses sp hybridization at its central nitrogen due to its linear structure, despite being surrounded by another nitrogen and an oxygen atom. For the N_3^- , the central nitrogen also adopts sp hybridization, while in OCN^- the central carbon uses this hybridization for the linear arrangement of atoms. This consistency in hybridization highlights the challenging yet fascinating nature of predicting and understanding molecule geometries.
Orbital Overlap
The overlap of atomic orbitals is crucial for bond formation. It is the foundation of molecular structure in compounds, dictating the type of bonds that form between atoms. When orbitals overlap, they can form either sigma (σ) bonds or pi (π) bonds, depending on the type of orbitals and the geometry of the overlap.
In CO_2 , carbon's sp hybrid orbitals interact with the p orbitals of oxygen to form sigma bonds. Meanwhile, the unhybridized p orbitals of both carbon and oxygen create pi bonds. This dual bonding results in strong double bonds between carbon and oxygen.
In N_2O , the central nitrogen's sp hybrid orbitals overlap with the p orbitals of the adjacent nitrogen and oxygen atoms, forming sigma bonds, while remaining p orbitals engage in pi bonding.
For the N_3^- deficit ion, similar orbital interactions occur amongst the nitrogen atoms, establishing both sigma and pi bonds. In the cyanate ion (OCN ^- ), the carbon's sp hybrid orbitals overlap with oxygen’s and nitrogen’s p orbitals, forming robust sigma bonds along with pi bonds due to leftover p orbital interactions.
Understanding these overlaps provides insight into the robust nature and the geometry stability in these molecules.
In CO_2 , carbon's sp hybrid orbitals interact with the p orbitals of oxygen to form sigma bonds. Meanwhile, the unhybridized p orbitals of both carbon and oxygen create pi bonds. This dual bonding results in strong double bonds between carbon and oxygen.
In N_2O , the central nitrogen's sp hybrid orbitals overlap with the p orbitals of the adjacent nitrogen and oxygen atoms, forming sigma bonds, while remaining p orbitals engage in pi bonding.
For the N_3^- deficit ion, similar orbital interactions occur amongst the nitrogen atoms, establishing both sigma and pi bonds. In the cyanate ion (OCN ^- ), the carbon's sp hybrid orbitals overlap with oxygen’s and nitrogen’s p orbitals, forming robust sigma bonds along with pi bonds due to leftover p orbital interactions.
Understanding these overlaps provides insight into the robust nature and the geometry stability in these molecules.
Resonance Structures
Resonance structures are alternative ways to draw a molecule, which illustrate different possible distributions of electrons. These structures are used to represent molecules because electrons are often delocalized. Delocalization refers to the spreading of electrons across several atoms, which is more stable than having electrons situated on one atom.
In CO_2 , resonance is observed in different placements of double bonds between the carbon and oxygen atoms. Although they change positions in drawing, no molecule is exactly like any one structure; instead, the actual structure is a hybrid of all possible resonance structures.
Dinitrogen monoxide ( N_2O ) is similar, having resonance structures with various nitrogen-oxygen configurations, affecting electron distribution and bond characterization.
With the azide ion ( N_3^- ), resonance involves electron delocalization among nitrogen atoms, creating a balance in electron distribution.
In the cyanate ion (OCN ^- ), resonance structures show variations in electron placement between oxygen, carbon, and nitrogen, impacting their formal charges and bonding characteristics. These resonance structures offer clearer insights into the true, yet complex, electronic structure of molecules, emphasizing the flexibility and variability in electron assignment.
In CO_2 , resonance is observed in different placements of double bonds between the carbon and oxygen atoms. Although they change positions in drawing, no molecule is exactly like any one structure; instead, the actual structure is a hybrid of all possible resonance structures.
Dinitrogen monoxide ( N_2O ) is similar, having resonance structures with various nitrogen-oxygen configurations, affecting electron distribution and bond characterization.
With the azide ion ( N_3^- ), resonance involves electron delocalization among nitrogen atoms, creating a balance in electron distribution.
In the cyanate ion (OCN ^- ), resonance structures show variations in electron placement between oxygen, carbon, and nitrogen, impacting their formal charges and bonding characteristics. These resonance structures offer clearer insights into the true, yet complex, electronic structure of molecules, emphasizing the flexibility and variability in electron assignment.
Bond Length
Bond length refers to the average distance between the nuclei of two bonded atoms. It is an important concept in the study of molecular structures because it affects the physical and chemical properties of a molecule.
Resonance can often modify bond lengths by causing them to average out between extremes in differing structures. In CO_2 , for instance, resonance ensures that the bond lengths of the carbon-oxygen bonds remain equal and are consistent with a double-bond character.
For N_2O , the resonance causes a variety of bond lengths, potentially inducing a slightly longer bond with more single-bond character.
In N_3^- , resonance results in nearly equal bond lengths due to the delocalization of electrons over the nitrogen atoms, reflecting an intermediate bond order that balances single and double bond traits.
In OCN^- ion, the effect of resonance leads to shorter O-C bonds but longer C-N bond lengths than one would expect if looking at single, static structures. This equalization or variation in bond lengths illustrates how resonance contributes to the stability and structure of molecules.
Resonance can often modify bond lengths by causing them to average out between extremes in differing structures. In CO_2 , for instance, resonance ensures that the bond lengths of the carbon-oxygen bonds remain equal and are consistent with a double-bond character.
For N_2O , the resonance causes a variety of bond lengths, potentially inducing a slightly longer bond with more single-bond character.
In N_3^- , resonance results in nearly equal bond lengths due to the delocalization of electrons over the nitrogen atoms, reflecting an intermediate bond order that balances single and double bond traits.
In OCN^- ion, the effect of resonance leads to shorter O-C bonds but longer C-N bond lengths than one would expect if looking at single, static structures. This equalization or variation in bond lengths illustrates how resonance contributes to the stability and structure of molecules.
Bond Order
Bond order is a numerical value that represents the number of chemical bonds between a pair of atoms. It provides an average count of bonds, often reflecting a fraction when resonance structures are involved.
In CO_2 , each carbon-oxygen bond has a bond order of approximately 2 due to the resonance between different positions of double bonds.
For N_2O , the presence of resonance means bond orders might be somewhat less defined but typically ranging below 2, indicative of more single-bond character on average, particularly in the N-O bonds.
Within the azide ion ( N_3^- ), the delocalization from resonance yields bond orders between 1 and 2, balancing the bonding situation among nitrogen atoms.
In OCN ^- , varied resonance structures modify bond orders from those expected for simple single or double bonds, usually indicating slightly reduced or enhanced bond strength depending on specific atom pairs. Understanding bond order is crucial as it correlates directly with the strength and stability of bonds, influencing molecular reactivity and interaction.
In CO_2 , each carbon-oxygen bond has a bond order of approximately 2 due to the resonance between different positions of double bonds.
For N_2O , the presence of resonance means bond orders might be somewhat less defined but typically ranging below 2, indicative of more single-bond character on average, particularly in the N-O bonds.
Within the azide ion ( N_3^- ), the delocalization from resonance yields bond orders between 1 and 2, balancing the bonding situation among nitrogen atoms.
In OCN ^- , varied resonance structures modify bond orders from those expected for simple single or double bonds, usually indicating slightly reduced or enhanced bond strength depending on specific atom pairs. Understanding bond order is crucial as it correlates directly with the strength and stability of bonds, influencing molecular reactivity and interaction.
