Ch.7 - Covalent Bonding and Electron-Dot Structures

Problem 12

Chapter 7, Problem 12

What is the best prediction for the carbon–oxygen bond length in the carbonate anion, CO3 2-? (LO 7.14)Data for average carbon-oxygen bond lengths: (a) 143 pm (b) 132 pm(c) 121 pm(d) 118 pm

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Understand the structure of the carbonate anion, \( \text{CO}_3^{2-} \). It consists of one carbon atom bonded to three oxygen atoms, with resonance structures.

Recognize that the carbonate ion has resonance, meaning the actual structure is an average of multiple resonance forms. Each resonance form has one double bond and two single bonds.

Calculate the average bond order for the carbon-oxygen bonds in \( \text{CO}_3^{2-} \). Since there are three equivalent resonance structures, each bond is effectively \( \frac{4}{3} \) (or 1.33) bonds.

Use the bond order to predict the bond length. A bond order of 1 corresponds to a single bond, and a bond order of 2 corresponds to a double bond. The bond order of 1.33 suggests a bond length between a single and a double bond.

Compare the given bond lengths: 143 pm (single bond), 132 pm (intermediate), 121 pm (double bond), and 118 pm (triple bond). The best prediction for the bond length is the one closest to the calculated bond order of 1.33.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Resonance Structures

Resonance structures are different ways of drawing the same molecule that illustrate the delocalization of electrons. In the case of the carbonate anion (CO3 2-), it can be represented by multiple resonance forms, which contribute to the overall structure. This delocalization affects bond lengths, as the carbon-oxygen bonds are not identical but rather have an average length due to the resonance.

Bond Length and Bond Order

Bond length is the distance between the nuclei of two bonded atoms, influenced by bond order, which indicates the number of shared electron pairs. Higher bond orders typically result in shorter bond lengths. In CO3 2-, the bond order is effectively 1.33 due to resonance, suggesting that the carbon-oxygen bonds are shorter than a single bond but longer than a double bond.

Electronegativity and Atomic Size

Electronegativity is the tendency of an atom to attract electrons in a bond, while atomic size refers to the distance from the nucleus to the outermost electrons. In CO3 2-, the electronegativity of oxygen compared to carbon influences the bond characteristics. The smaller atomic size of oxygen compared to carbon contributes to the overall bond length, as shorter bonds are typically formed between atoms of differing electronegativities.

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