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Chapter 8: Problem 53

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 ordering of the C-O bond lengths in CO, CO2, and CO3虏鈦� is CO < CO2 < CO3虏鈦�, based on the bond orders calculated using molecular orbital theory (3 for CO, 2 for CO2) and resonance structures (4/3 for CO3虏鈦�), where higher bond orders correspond to shorter bond lengths.

Step by step solution

01

Use Molecular Orbital Theory for CO and CO2

Determine the bond orders of CO and CO2 using molecular orbital theory. In CO, there are 10 valence electrons forming one 蟽 bond and one 蟺 bond, making the bond order 3. In CO2, there are 16 valence electrons forming two 蟽 bonds and four 蟺 bonds, making the bond order 2 for an oxygen atom to a carbon atom in a CO2 molecule.
02

Use Resonance Structures for CO3虏鈦�

Find the bond order of CO3虏鈦� using resonance structures. Carbonate has three resonance structures, where in each structure, one of the oxygen atoms forms a double bond with the carbon atom, and the other two oxygens form a single bond. These three resonance structures equally contribute to the real structure of the carbonate ion. Thus, the bond order for a C-O bond in CO3虏鈦� will be the average of the bond orders for each resonance structure, which is equal to (1 + 1 + 2)/3 = 4/3.
03

Compare Bond Orders and Predict Bond Lengths

Compare the bond orders obtained from steps 1 and 2 to predict the ordering of the C-O bond lengths in CO, CO2, and CO3虏鈦�. Recall that a higher bond order indicates a stronger bond and a shorter bond length. The C-O bond orders are 3, 2, and 4/3 for CO, CO2, and CO3虏鈦�, respectively. Consequently, the ordering of bond lengths will be CO < CO2 < CO3虏鈦�.

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Most popular questions from this chapter

(a) What is meant by the term covalent bond? (b) Give three examples of covalent bonding. (c) A substance \(X Y\), formed from two different elements, boils at \(-33^{\circ} \mathrm{C}\). Is XY likely to be a covalent or an ionic substance? Explain.

(a) Does the lattice energy of an ionic solid increase or decrease (i) as the charges of the ions increase, (ii) as the sizes of the ions increase? (b) Using a periodic table, arrange the following substances according to their expected lattice energies, listing them from lowest lattice energy to the highest: \(\mathrm{ScN}, \mathrm{KBr}, \mathrm{MgO}\), NaF. Compare your list with the data in Table \(8.2\).

The reaction of indium, In, with sulfur leads to three binary compounds, which we will assume to be purely ionic. The three compounds have the following properties: $$ \begin{array}{lll} \hline \text { Compound } & \text { Mass \% In } & \text { Melting Point }\left({ }^{\circ} \mathrm{C}\right) \\ \hline \text { A } & 87.7 & 653 \\ \text { B } & 78.2 & 692 \\ \text { C } & 70.5 & 1050 \\ \hline \end{array} $$ (a) Determine the empirical formulas of compounds A, B, and C. (b) Give the oxidation state of In in each of the three compounds. (c) Write the electron configuration for the In ion in each compound. Do any of these configurations correspond to a noble-gas configuration? (d) In which compound is the ionic radius of In expected to be smallest? Explain. (e) The melting point of ionic compounds often correlates with the lattice energy. Explain the trends in the melting points of compounds A, B, and \(\mathrm{C}\) in these terms.

(a) Describe the molecule chlorine dioxide, \(\mathrm{ClO}_{2}\), using three possible resonance structures. (b) Do any of these resonance structures satisfy the octet rule for every atom in the molecule? Why or why not? (c) Using formal charges, select the resonance structure(s) that is (are) most important.

For the following collection of nonmetallic elements, \(\mathrm{O}\), \(\mathrm{P}, \mathrm{Te}, \mathrm{I}, \mathrm{B},(\mathrm{a})\) which two would form the most polar single bond? (b) Which two would form the longest single bond? (c) Which two would be likely to form a compound of formula \(\mathrm{XY}_{2}\) ? (d) Which combinations of elements would likely yield a compound of empirical formula \(\mathrm{X}_{2} \mathrm{Y}_{3} ?\) In each case explain your answer.
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