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Chapter 11: Problem 63

Methyl nitrate, \(\mathrm{CH}_{3} \mathrm{NO}_{3}\), is used as a rocket propellant. The skeletal structure of the molecule is \(\mathrm{CH}_{3} \mathrm{ONO}_{2}\). The N and three O atoms all lie in the same plane, but the \(\mathrm{CH}_{3}\) group is not in the same plane as the \(\mathrm{NO}_{3}\) group. The bond angle \(\mathrm{C}-\mathrm{O}-\mathrm{N}\) is \(105^{\circ},\) and the bond angle \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) is \(125^{\circ} .\) One nitrogen-to-oxygen bond length is \(136 \mathrm{pm},\) and the other two are \(126 \mathrm{pm}\) (a) Draw a sketch of the molecule showing its geometric shape. (b) Label all the bonds in the molecule as \(\sigma\) or \(\pi\), and indicate the probable orbital overlaps involved. (c) Explain why all three nitrogen-to-oxygen bond lengths are not the same.

Short Answer

Expert verified
The Geometry of the \(CH_3NO_3\) molecule depicts that nitrogen and three oxygen atoms lie in the same plane and the \(CH_3\) group does not lie in the same plane as the \(NO_3\) group. The entire molecule has a combination of \(\sigma\) and \(\pi\) bonds, formed from different types of orbital overlaps. The reason that not all nitrogen-to-oxygen bonds are the same length is due to the resonance in the \(NO_3\) group.

Step by step solution

01

Drawing the Sketch of the Molecule

It is given that nitrogen and three oxygen atoms are in the same plane and the \(CH_3\) group is not in the same plane as the \(NO_3\) group. This means, firstly, complete the molecule by drawing a nitrogen atom bonded with three oxygen atoms in a trigonal planar arrangement, then attach the \(CH_3\) above the plane. Since, the bond angle \(C-O-N\) is \(105^{\circ}\), and the bond angle \(O-N-O\) is \(125^{\circ}\), it should be reflected in your sketch.
02

Labeling the Bonds

Observe your sketch. A single bond between two atoms usually represents a \(\sigma\) bond. So, the \(C-H\) bonds in the \(CH_3\) group and the \(C-O\), \(N-O\) (single) bonds are all \(\sigma\) bonds, formed by end-to-end overlap of orbitals. Double bond between \(N\) and \(\(O_2\)\) is composed of one \(\sigma\) bond and one \(\pi\) bond (formed by sideways overlap of p orbitals). Label all these on your sketch accordingly.
03

Explaining the Bond Lengths

Lastly, it is required to explain why all three nitrogen-to-oxygen bonds are not the same length. This is because of the presence of a resonance structure in \(NO_3\) group which causes the double bond to spread over the three \(N-O\) bonds, making the bond length shorter than a normal \(N-O\) single bond, but longer than a normal \(N-O\) double bond. Therefore, one nitrogen-to-oxygen bond length is \(136pm\) (longer) and the other two have \(126pm\) (shorter).

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Most popular questions from this chapter

Propose a hybridization scheme to account for bonds formed by the central carbon atom in each of the following molecules: (a) hydrogen cyanide, HCN; (b) methyl alcohol, \(\mathrm{CH}_{3} \mathrm{OH} ;\) (c) acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\) (d) carbamic acid,

The energy gap, \(\Delta E\), for silicon is \(110 \mathrm{kJ} / \mathrm{mol}\). What is the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon? In what region of the electromagnetic spectrum is this light?

Furan, \(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O},\) is a substance derivable from oat hulls, corn cobs, and other cellulosic waste. It is a starting material for the synthesis of other chemicals used as pharmaceuticals and herbicides. The furan molecule is planar and the \(\mathrm{C}\) and \(\mathrm{O}\) atoms are bonded into a fivemembered pentagonal ring. The H atoms are attached to the C atoms. The chemical behavior of the molecule suggests that it is a resonance hybrid of several contributing structures. These structures show that the double bond character is associated with the entire ring in the form of a \(\pi\) electron cloud. (a) Draw Lewis structures for the several contributing structures to the resonance hybrid mentioned above. (b) Draw orbital diagrams to show the orbitals that are involved in the \(\sigma\) and \(\pi\) bonding in furan. [Hint: You need use only one of the contributing structures, such as the one with no formal charges.] (c) How many \(\pi\) electrons are there in the furan molecule? Show that this number of \(\pi\) electrons is the same, regardless of the contributing structure you use for this assessment.

Lewis theory is satisfactory to explain bonding in the ionic compound \(\mathrm{K}_{2} \mathrm{O},\) but it does not readily explain formation of the ionic compounds potassium superoxide, \(\mathrm{KO}_{2}\), and potassium peroxide, \(\mathrm{K}_{2} \mathrm{O}_{2}\) (a) Show that molecular orbital theory can provide this explanation. (b) Write Lewis structures consistent with the molecular orbital explanation.

Use the valence molecular orbital configuration to determine which of the following species is expected to have the lowest ionization energy: (a) \(\mathrm{C}_{2}^{+} ;\) (b) \(\mathrm{C}_{2}\) (c) \(\mathrm{C}_{2}^{-}\)
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