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Chapter 9: Problem 83

What type of molecular orbital would result from the in-phase combination of two \(d_{x z}\) atomic orbitals shown below? Assume the \(x\) -axis is the internuclear axis.

Short Answer

Expert verified
The resulting molecular orbital from the in-phase combination of two d_xz atomic orbitals is a σ_d_xz molecular orbital.

Step by step solution

01

Understand the d_xz atomic orbital shape

The d_xz atomic orbital is part of the d-orbital set and has a distinctive shape, with two lobes located on opposite sides of the x-z plane. It is easiest to visualize this as a four-leaf clover pattern on the x-z plane (with the x-axis being the internuclear axis).
02

Visualize the in-phase combination of two d_xz orbitals

When combining atomic orbitals to form molecular orbitals, we consider both in-phase and out-of-phase combinations. In the in-phase combination, the lobes of the same sign (positive or negative) on both orbitals overlap constructively resulting in a new molecular orbital.
03

Combine the two d_xz orbitals in-phase

Let's visualize the two d_xz atomic orbitals along the x-axis (the internuclear axis), with one on the left (orbital 1) and one on the right (orbital 2). To combine them in-phase, arrange it so that the positive lobes of orbital 1 overlap with the positive lobes of orbital 2, and the same for negative lobes. This will result in only two lobes along the x-axis, one positive and one negative.
04

Identify the type of molecular orbital formed

The in-phase combination of two d_xz atomic orbitals has created a new molecular orbital with only two lobes along the x-axis. This type of molecular orbital is called a σ (sigma) orbital. In this case, since it's formed from two d_xz orbitals combination, it will be called a σ_d_xz molecular orbital. In conclusion, the resulting molecular orbital from the in-phase combination of two d_xz atomic orbitals is a σ_d_xz molecular orbital.

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Most popular questions from this chapter

Describe the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-},\) and \(\mathrm{NO}\) using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

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Cyanamide \(\left(\mathrm{H}_{2} \mathrm{NCN}\right),\) an important industrial chemical, is produced by the following steps: $$ \begin{array}{c}{\mathrm{CaC}_{2}+\mathrm{N}_{2} \longrightarrow \mathrm{CaNCN}+\mathrm{C}} \\ {\mathrm{CaNCN} \stackrel{\mathrm{Acid}}{\longrightarrow} \mathrm{H}_{2} \mathrm{NCN}} \\\ {\mathrm{Cyanamide}}\end{array} $$ Calcium cyanamide (CaNCN) is used as a direct-application fertilizer, weed killer, and cotton defoliant. It is also used to make cyanamide, dicyandiamide, and melamine plastics: a. Write Lewis structures for \(\mathrm{NCN}^{2-}, \mathrm{H}_{2} \mathrm{NCN}\) , dicyandiamide, and melamine, including resonance structures where appropriate. b. Give the hybridization of the C and N atoms in each species. c. How many \(\sigma\) bonds and how many \(\pi\) bonds are in each species? d. Is the ring in melamine planar? e. There are three different \(C-N\) bond distances in dicyandiamide, \(\mathrm{NCNC}\left(\mathrm{NH}_{2}\right)_{2}\) , and the molecule is nonlinear. Of all the resonance structures you drew for this molecule, predict which should be the most important.

Although nitrogen trifluoride \(\left(\mathrm{NF}_{3}\right)\) is a thermally stable compound, nitrogen triodide \(\left(\mathrm{N} \mathrm{I}_{3}\right)\) is known to be a highly explosive material. \(\mathrm{NI}_{3}\) can be synthesized according to the equation $$ \mathrm{BN}(s)+3 \mathrm{IF}(g) \longrightarrow \mathrm{BF}_{3}(g)+\mathrm{NI}_{3}(g) $$ a. What is the enthalpy of formation for \(\mathrm{NI}_{3}(s)\) given the enthalpy of reaction \((-307 \mathrm{kJ})\) and the enthalpies of formation for $\mathrm{BN}(s)(-254 \mathrm{kJ} / \mathrm{mol}), \operatorname{IF}(g)(-96 \mathrm{kJ} / \mathrm{mol})\( and \)\mathrm{BF}_{3}(g)(-1136 \mathrm{kJ} / \mathrm{mol}) ?$ b. It is reported that when the synthesis of \(\mathrm{NI}_{3}\) is conducted using 4 moles of IF for every 1 \(\mathrm{mole}\) of \(\mathrm{BN}\) , one of the by-products isolated is \(\left[\mathrm{IF}_{2}\right]^{+}\left[\mathrm{BF}_{4}\right]^{-} .\) What are the molecular geometries of the species in this by-product? What are the hybridizations of the central atoms in each species in the by-product?

The molecules \(\mathrm{N}_{2}\) and \(\mathrm{CO}\) are isoelectronic but their properties are quite different. Although as a first approximation we often use the same MO diagram for both, suggest how the \(\mathrm{MOs}\) in \(\mathrm{N}_{2}\) and \(\mathrm{CO}\) might be different.
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