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Chapter 8: Problem 98

Place the species below in order of the shortest to the longest nitrogen- oxygen bond. \(\begin{array}{lllll}\mathrm{H}_{2} \mathrm{NOH}, & \mathrm{N}_{2} \mathrm{O}, & \mathrm{NO}^{+}, & \mathrm{NO}_{2}^{-}, & \mathrm{NO}_{3}^{-}\end{array}\) \(\left(\mathrm{H}_{2} \mathrm{NOH}\right.\) exists as \(\left.\mathrm{H}_{2} \mathrm{~N}-\mathrm{OH} .\right)\)

Short Answer

Expert verified
The order of the nitrogen-to-oxygen bond lengths from shortest to longest for the given species is: \(NO^+ < N_2O < H_2NOH < NO_2^- < NO_3^-\)

Step by step solution

01

Identify the Bond Types

First, we need to recognize the bond types present in each species, specifically focusing on nitrogen-to-oxygen bonds. Keep in mind that multiple bonds, like double and triple bonds, are shorter and stronger than single bonds.
02

Analyze Bond Strengths and Lengths

Given the nitrogen-to-oxygen bond types, we can now analyze the bond strengths and lengths. Shorter bonds are generally stronger than longer bonds. Consider the following general guidelines: - Single bond > Double bond > Triple bond (in terms of bond length) - Triple bond > Double bond > Single bond (in terms of bond strength)
03

Arrange the Species Based on Bond Lengths

Now that we've analyzed each species, let's arrange them based on their nitrogen-to-oxygen bond lengths: 1. \(NO^+\): The nitrogen-to-oxygen bond in the \(NO^+\) ion is a triple bond, making it the shortest and strongest bond. NO^+ has the shortest nitrogen-to-oxygen bond length. 2. \(N_2O\): In dinitrogen monoxide, the nitrogen-to-oxygen bond is a double bond, which is shorter and stronger than a single bond, but longer and weaker than a triple bond. 3. \(H_2NOH\): The \(H_2NOH\) molecule exists as \(H_2N - OH\), where the nitrogen-to-oxygen bond is a single bond. 4. \(NO_2^-\): In the nitrite ion (\(NO_2^-\)), the nitrogen is connected with two oxygen atoms via resonance structures, making each nitrogen-to-oxygen bond an equivalent of one-and-a-half bond. Hence its bond length will be longer than a single bond but shorter than a double bond. 5. \(NO_3^-\): In the nitrate ion (\(NO_3^-\)), the nitrogen is connected with three oxygen atoms, and the resonance explains that nitrogen and oxygen are connected by three bonds, which are distributed among those three oxygen atoms. Thus each nitrogen-to-oxygen bond is equivalent to one and a third bond (i.e., a bond length longer than a single bond and the bond in \(NO_2^-\)).
04

Write Out the Final Order

Based on our analysis, we can write the final order of nitrogen-to-oxygen bond lengths for the given species, from shortest to longest, as follows: \(NO^+ < N_2O < H_2NOH < NO_2^- < NO_3^-\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Bonding
Chemical bonding refers to the force that holds atoms together in chemical compounds. There are several types of chemical bonds, including ionic, covalent, metallic, and hydrogen bonds. Among these, covalent bonds - the bonds between nitrogen and oxygen in the exercise - involve the sharing of electron pairs between atoms.

When discussing nitrogen-oxygen bonds, understanding the difference in bond types is crucial. Single covalent bonds involve two electrons shared between two atoms, while double bonds involve four electrons, and triple bonds, like that of the NO+ ion, involve six electrons. As the number of shared electrons increases, bonds become shorter and stronger. This explains why the NO+ ion has the shortest and strongest nitrogen-to-oxygen bond due to its triple bond nature.
Molecular Geometry
Molecular geometry, which is the three-dimensional arrangement of atoms in a molecule, has a profound effect on the bond lengths and overall molecular stability. The spatial distribution of molecules influences the bond angles and thus the length between atoms.

For example, in the nitrate ion (NO3-), resonance structures influence its molecular geometry, distributing the single and double bond character among three oxygen atoms. This delocalization of electrons results in equivalent bonds, all slightly shorter than a single bond but longer than the bond in NO2-, which has two oxygen atoms sharing resonance structures. The VSEPR theory is a model used to predict the geometry of molecules based on valence shell electron pair repulsion, which states that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsive forces.
Resonance Structures
Resonance structures are a model in chemistry used to represent the delocalization of electrons within certain molecules or ions that cannot be sufficiently described by a single Lewis structure. These structures depict possible configurations that contribute to the overall electronic structure of the molecule.

In our exercise, resonance structures significantly affect the bond length of nitrogen-oxygen bonds in the NO2- and NO3- ions. Electron delocalization in NO2- leads to each nitrogen-to-oxygen bond having a bond order of one and a half, making it shorter than a pure single bond, as seen in H2NOH. In NO3-, the bond order becomes one and a third, due to the distribution of the electron pairs across three bonds instead of two, which lengthens the bond further compared to NO2-. Understanding resonance is crucial for predicting characteristics such as bond lengths in molecules with delocalized electrons.

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Most popular questions from this chapter

Give three ions that are isoelectronic with neon. Place these ions in order of increasing size.

Use the following data to estimate \(\Delta H_{\mathrm{f}}^{\circ}\) for magnesium fluoride. Lattice energy $$ \begin{aligned} \mathrm{Mg}(s)+\mathrm{F}_{2}(g) \longrightarrow & \mathrm{MgF}_{2}(s) \\ &-2913 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ First ionization energy of \(\mathrm{Mg} \quad 735 \mathrm{~kJ} / \mathrm{mol}\) Second ionization energy of \(\mathrm{Mg} \quad 1445 \mathrm{~kJ} / \mathrm{mol}\) \(\begin{array}{ll}\text { Electron affinity of } \mathrm{F} & -328 \mathrm{~kJ} / \mathrm{mol}\end{array}\) Bond energy of \(\mathrm{F}_{2}\) \(154 \mathrm{~kJ} / \mathrm{mol}\) Enthalpy of sublimation for \(\mathrm{Mg}\) 150. \(\mathrm{kJ} / \mathrm{mol}\)

Predict the empirical formulas of the ionic compounds formed from the following pairs of elements. Name each compound. a. \(\mathrm{Al}\) and \(\mathrm{Cl}\) c. \(\mathrm{Sr}\) and \(\mathrm{E}\) b. \(\mathrm{Na}\) and \(\mathrm{O}\) d. \(\mathrm{Ca}\) and \(\mathrm{Se}\)

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The compound \(\mathrm{NF}_{3}\) is quite stable, but \(\mathrm{NCl}_{3}\) is very unstable \(\left(\mathrm{NCl}_{3}\right.\) was first synthesized in 1811 by P. L. Dulong, who lost three fingers and an eye studying its properties). The compounds \(\mathrm{NBr}_{3}\) and \(\mathrm{NI}_{3}\) are unknown, although the explosive compound \(\mathrm{NI}_{3} \cdot \mathrm{NH}_{3}\) is known. Account for the instability of these halides of nitrogen.
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