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Chapter 8: Problem 55

Predict the ordering of the \(\mathrm{C}-\mathrm{O}\) bond lengths in \(\mathrm{CO}, \mathrm{CO}_{2}\), and \(\mathrm{CO}_{3}^{2-}\).

Short Answer

Expert verified
The predicted ordering of the C-O bond lengths in CO, CO2, and CO3^(2-) is: CO (bond order = 3) < CO2 (bond order = 2) < CO3^(2-) (bond order = 4/3). This is based on the molecular structures, resonance structures, and bond orders of each molecule or ion. Higher bond orders correlate with shorter bond lengths.

Step by step solution

01

Determining the Molecular Structure

To understand the bond lengths of each molecule, we need to know the structures first: 1. CO (Carbon Monoxide) - CO is a diatomic molecule where a carbon atom is triple-bonded to an oxygen atom. 2. CO2 (Carbon Dioxide) - CO2 is a linear molecule, where a carbon atom is double-bonded to two oxygen atoms on either side. 3. CO3^(2-) (Carbonate ion) - CO3^(2-) is a planar molecule in which a central carbon atom is single-bonded to three oxygen atoms, which are positioned at the vertices of an equilateral triangle.
02

Resonance Structures

In order to analyze and compare the bonds in these molecules, let's look for resonance structures: 1. CO - There is only one resonance structure for CO, with a triple bond between C and O atoms. 2. CO2 - There is only one resonance structure for CO2, with a double bond between the carbon atom and each oxygen atom. 3. CO3^(2-) - The carbonate ion has three equivalent resonance structures, where each of the three single bonds between the central carbon atom and the oxygen atoms can be replaced by one double bond in each resonance structure.
03

Bond Order

Now let's determine the bond order for the C-O bonds in each molecule/ion: 1. CO - The bond order in CO is 3, due to the triple bond between the carbon and oxygen atoms. 2. CO2 - The bond order in CO2 is 2, because of the double bond between the carbon atom and each oxygen atom. 3. CO3^(2-) - The bond order in the carbonate ion is 4/3 (4 bonds distributed over 3 C-O bonds). This value is obtained by considering the presence of one double bond and two single bonds in the resonance structures.
04

Predict the Ordering of the C-O Bond Lengths

Finally, we can predict the ordering of the C-O bond lengths. Generally, higher bond orders correlate with shorter bond lengths. Therefore, we can list the C-O bond lengths in order from shortest to longest: 1. CO (Triple bond, bond order = 3) 2. CO2 (Double bond, bond order = 2) 3. CO3^(2-) (Average of single and double bonds, bond order = 4/3) Thus, the predicted ordering of the C-O bond lengths is: CO < CO2 < CO3^(2-).

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Most popular questions from this chapter

Write the electron configuration for each of the following ions, and determine which ones possess noble-gas configura- tions: (a) \(\mathrm{Sr}^{2+},(\mathbf{b}) \mathrm{Ti}^{2+},(\mathrm{c}) \mathrm{Se}^{2-},(\mathrm{d}) \mathrm{Ni}^{2+},(\mathrm{e}) \mathrm{Br}^{-},\) (f) \(\mathrm{Mn}^{3+}\)

Use Lewis symbols and Lewis structures to diagram the formation of \(\mathrm{PF}_{3}\) from \(\mathrm{P}\) and \(\mathrm{F}\) atoms.

Consider the hypothetical molecule \(\mathrm{B}-\mathrm{A}=\mathrm{B}\). Are the following statements true or false? (a) This molecule cannot exist. (b) If resonance was important, the molecule would have identical A-B bond lengths.

(a) What is meant by the term electronegativity? (b) On the Pauling scale what is the range of electronegativity values for the elements? (c) Which element has the greatest electronegativity? (d) Which element has the smallest electronegativity?

(a) When talking about atoms in a Lewis structure, what is meant by the term formal charge? (b) Does the formal charge of an atom represent the actual charge on that atom? Explain. (c) How does the formal charge of an atom in a Lewis structure differ from the oxidation number of the atom?
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