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Chapter 7. Chemical Bonding and Molecular Geometry

7.four Formal Charges and Resonance

Learning Objectives

By the end of this section, you will exist able to:

• Compute formal charges for atoms in any Lewis structure
• Use formal charges to identify the almost reasonable Lewis structure for a given molecule
• Explain the concept of resonance and draw Lewis structures representing resonance forms for a given molecule

In the previous department, nosotros discussed how to write Lewis structures for molecules and polyatomic ions. Every bit we have seen, withal, in some cases, in that location is seemingly more than ane valid construction for a molecule. We can utilize the concept of formal charges to help us predict the nigh advisable Lewis construction when more than ane is reasonable.

Calculating Formal Charge

The formal charge of an atom in a molecule is the hypothetical charge the cantlet would have if we could redistribute the electrons in the bonds evenly between the atoms. Another fashion of saying this is that formal charge results when we take the number of valence electrons of a neutral atom, subtract the nonbonding electrons, and and so subtract the number of bonds connected to that atom in the Lewis structure.

Thus, we calculate formal charge every bit follows:

[latex]\text{formal charge} = \# \;\text{valence vanquish electrons (free cantlet)} \; - \;\# \;\text{lone pair electrons}\; - \frac{1}{two} \# \;\text{bonding electrons}[/latex]

We tin can double-cheque formal charge calculations by determining the sum of the formal charges for the whole structure. The sum of the formal charges of all atoms in a molecule must be goose egg; the sum of the formal charges in an ion should equal the accuse of the ion.

We must call back that the formal charge calculated for an atom is not the actual charge of the cantlet in the molecule. Formal charge is only a useful bookkeeping procedure; it does not signal the presence of actual charges.

Example ane

Calculating Formal Charge from Lewis Structures
Assign formal charges to each atom in the interhalogen ion ICl₄ ⁻.

Solution

1. Nosotros divide the bonding electron pairs equally for all I–Cl bonds:
   
2. We assign lone pairs of electrons to their atoms. Each Cl cantlet now has seven electrons assigned to it, and the I atom has eight.
3. Subtract this number from the number of valence electrons for the neutral atom: I: 7 – 8 = –1Cl: vii – vii = 0The sum of the formal charges of all the atoms equals –1, which is identical to the accuse of the ion (–ane).

Bank check Your Learning
Summate the formal accuse for each atom in the carbon monoxide molecule:

Example 2

Calculating Formal Charge from Lewis Structures
Assign formal charges to each cantlet in the interhalogen molecule BrCl_iii.

Solution

1. Assign one of the electrons in each Br–Cl bond to the Br cantlet and one to the Cl atom in that bond:
   
2. Assign the lone pairs to their cantlet. Now each Cl cantlet has seven electrons and the Br atom has seven electrons.
3. Subtract this number from the number of valence electrons for the neutral atom. This gives the formal charge:Br: seven – 7 = 0Cl: 7 – 7 = 0

   All atoms in BrCl₃ have a formal charge of zero, and the sum of the formal charges totals zero, as it must in a neutral molecule.

Check Your Learning
Make up one's mind the formal accuse for each atom in NCl_iii.

Answer:

N: 0; all three Cl atoms: 0

Using Formal Charge to Predict Molecular Construction

The system of atoms in a molecule or ion is chosen its molecular structure. In many cases, following the steps for writing Lewis structures may atomic number 82 to more than one possible molecular construction—dissimilar multiple bail and lone-pair electron placements or different arrangements of atoms, for example. A few guidelines involving formal charge can be helpful in deciding which of the possible structures is nigh probable for a particular molecule or ion:

1. A molecular structure in which all formal charges are zero is preferable to one in which some formal charges are not zip.
2. If the Lewis structure must accept nonzero formal charges, the arrangement with the smallest nonzero formal charges is preferable.
3. Lewis structures are preferable when adjacent formal charges are naught or of the opposite sign.
4. When we must choose amid several Lewis structures with similar distributions of formal charges, the construction with the negative formal charges on the more than electronegative atoms is preferable.

To see how these guidelines apply, let us consider some possible structures for carbon dioxide, CO_ii. We know from our previous discussion that the less electronegative atom typically occupies the cardinal position, merely formal charges allow us to empathize why this occurs. Nosotros tin draw three possibilities for the structure: carbon in the center and double bonds, carbon in the center with a unmarried and triple bond, and oxygen in the centre with double bonds:

Comparing the three formal charges, we can definitively identify the construction on the left as preferable because it has only formal charges of zero (Guideline 1).

As another example, the thiocyanate ion, an ion formed from a carbon cantlet, a nitrogen atom, and a sulfur atom, could have 3 dissimilar molecular structures: CNS^–, NCS^–, or CSN^–. The formal charges present in each of these molecular structures can help united states option the most likely arrangement of atoms. Possible Lewis structures and the formal charges for each of the three possible structures for the thiocyanate ion are shown here:

Note that the sum of the formal charges in each case is equal to the charge of the ion (–ane). However, the beginning organisation of atoms is preferred considering it has the lowest number of atoms with nonzero formal charges (Guideline 2). Likewise, it places the least electronegative cantlet in the center, and the negative accuse on the more electronegative element (Guideline 4).

Instance 3

Using Formal Charge to Determine Molecular Structure
Nitrous oxide, N₂O, unremarkably known as laughing gas, is used equally an anesthetic in small surgeries, such as the routine extraction of wisdom teeth. Which is the likely structure for nitrous oxide?

Solution
Determining formal charge yields the following:

The structure with a terminal oxygen atom all-time satisfies the criteria for the most stable distribution of formal charge:

The number of atoms with formal charges are minimized (Guideline two), and there is no formal accuse larger than one (Guideline 2). This is again consistent with the preference for having the less electronegative atom in the key position.

Check Your Learning
Which is the about likely molecular structure for the nitrite (NO₂ ⁻) ion?

Resonance

You may accept noticed that the nitrite anion in Example 3 can have two possible structures with the atoms in the same positions. The electrons involved in the N–O double bond, however, are in different positions:

If nitrite ions do indeed contain a single and a double bond, we would look for the two bond lengths to be different. A double bond between 2 atoms is shorter (and stronger) than a single bond between the same ii atoms. Experiments bear witness, however, that both Due north–O bonds in NO₂ ⁻ have the same force and length, and are identical in all other properties.

It is not possible to write a single Lewis structure for NO_ii ⁻ in which nitrogen has an octet and both bonds are equivalent. Instead, we use the concept of resonance: if two or more Lewis structures with the same arrangement of atoms tin exist written for a molecule or ion, the actual distribution of electrons is an average of that shown by the various Lewis structures. The actual distribution of electrons in each of the nitrogen-oxygen bonds in NO_ii ⁻ is the average of a double bond and a single bail. Nosotros call the private Lewis structures resonance forms. The actual electronic structure of the molecule (the average of the resonance forms) is called a resonance hybrid of the individual resonance forms. A double-headed arrow between Lewis structures indicates that they are resonance forms. Thus, the electronic structure of the NO_ii ⁻ ion is shown every bit:

We should remember that a molecule described as a resonance hybrid never possesses an electronic structure described past either resonance form. It does non fluctuate between resonance forms; rather, the actual electronic structure is always the average of that shown past all resonance forms. George Wheland, one of the pioneers of resonance theory, used a historical analogy to depict the human relationship between resonance forms and resonance hybrids. A medieval traveler, having never earlier seen a rhinoceros, described it as a hybrid of a dragon and a unicorn because it had many backdrop in common with both. Just as a rhinoceros is neither a dragon sometimes nor a unicorn at other times, a resonance hybrid is neither of its resonance forms at any given time. Like a rhino, information technology is a existent entity that experimental evidence has shown to exist. Information technology has some characteristics in common with its resonance forms, but the resonance forms themselves are convenient, imaginary images (like the unicorn and the dragon).

The carbonate anion, CO_three ⁱⁱ⁻, provides a 2d example of resonance:

1 oxygen atom must have a double bond to carbon to complete the octet on the central atom. All oxygen atoms, however, are equivalent, and the double bond could grade from whatever ane of the 3 atoms. This gives rise to three resonance forms of the carbonate ion. Because nosotros can write three identical resonance structures, nosotros know that the actual organisation of electrons in the carbonate ion is the average of the three structures. Again, experiments testify that all iii C–O bonds are exactly the same.

The online Lewis Construction Brand includes many examples to do drawing resonance structures.

Key Concepts and Summary

In a Lewis construction, formal charges tin can be assigned to each atom past treating each bond as if one-one-half of the electrons are assigned to each cantlet. These hypothetical formal charges are a guide to determining the nearly advisable Lewis structure. A structure in which the formal charges are every bit shut to zero as possible is preferred. Resonance occurs in cases where two or more than Lewis structures with identical arrangements of atoms but different distributions of electrons can be written. The actual distribution of electrons (the resonance hybrid) is an average of the distribution indicated by the individual Lewis structures (the resonance forms).

Fundamental Equations

• [latex]\text{formal charge} = \# \;\text{valence shell electrons (gratuitous atom)} \; - \;\# \;\text{alone pair electrons}\; - \frac{1}{2} \# \;\text{bonding electrons}[/latex]

Chemistry End of Chapter Exercises

1. Write resonance forms that describe the distribution of electrons in each of these molecules or ions.

   (a) selenium dioxide, OSeO

   (b) nitrate ion, NO₃ ⁻

   (c) nitric acrid, HNO₃ (N is bonded to an OH grouping and two O atoms)

   (d) benzene, C₆H₆:

   

   (east) the formate ion:

   

2. Write resonance forms that draw the distribution of electrons in each of these molecules or ions.

   (a) sulfur dioxide, And then₂

   (b) carbonate ion, CO_three ²⁻

   (c) hydrogen carbonate ion, HCO₃ ⁻ (C is bonded to an OH group and 2 O atoms)

   (d) pyridine:

   

   (due east) the allyl ion:

   

3. Write the resonance forms of ozone, O_three, the component of the upper atmosphere that protects the Globe from ultraviolet radiation.
4. Sodium nitrite, which has been used to preserve bacon and other meats, is an ionic compound. Write the resonance forms of the nitrite ion, NO₂ ^–.
5. In terms of the bonds nowadays, explain why acetic acrid, CH₃CO₂H, contains two distinct types of carbon-oxygen bonds, whereas the acetate ion, formed by loss of a hydrogen ion from acetic acid, only contains one blazon of carbon-oxygen bond. The skeleton structures of these species are shown:
   
6. Write the Lewis structures for the following, and include resonance structures where appropriate. Betoken which has the strongest carbon-oxygen bond.

   (a) CO_ii

   (b) CO

7. Toothpastes containing sodium hydrogen carbonate (sodium bicarbonate) and hydrogen peroxide are widely used. Write Lewis structures for the hydrogen carbonate ion and hydrogen peroxide molecule, with resonance forms where advisable.
8. Determine the formal charge of each chemical element in the following:

   (a) HCl

   (b) CF₄

   (c) PCl_iii

   (d) PF_v

9. Decide the formal accuse of each element in the following:

   (a) H_threeO⁺

   (b) And then₄ ²⁻

   (c) NH₃

   (d) O₂ ²⁻

   (e) H_twoO₂

10. Calculate the formal accuse of chlorine in the molecules Cl₂, BeCl_two, and ClF₅.
11. Calculate the formal charge of each chemical element in the following compounds and ions:

    (a) F₂CO

    (b) NO^–

    (c) BF₄ ⁻

    (d) SnCl₃ ⁻

    (eastward) H_iiCCH_ii

    (f) ClF_iii

    (g) SeF_half-dozen

    (h) PO₄ ³⁻

12. Describe all possible resonance structures for each of these compounds. Decide the formal charge on each atom in each of the resonance structures:

    (a) O_iii

    (b) Then₂

    (c) NO₂ ⁻

    (d) NO_iii ⁻

13. Based on formal charge considerations, which of the following would likely be the right system of atoms in nitrosyl chloride: ClNO or ClON?
14. Based on formal charge considerations, which of the post-obit would likely be the right arrangement of atoms in hypochlorous acid: HOCl or OClH?
15. Based on formal charge considerations, which of the post-obit would likely be the correct arrangement of atoms in sulfur dioxide: OSO or SOO?
16. Draw the structure of hydroxylamine, H₃NO, and assign formal charges; await up the structure. Is the actual construction consistent with the formal charges?
17. Iodine forms a series of fluorides (listed here). Write Lewis structures for each of the four compounds and decide the formal charge of the iodine atom in each molecule:

    (a) IF

    (b) IF_iii

    (c) IF₅

    (d) IF_vii

18. Write the Lewis construction and chemic formula of the compound with a molar mass of about 70 g/mol that contains 19.7% nitrogen and 80.3% fluorine by mass, and decide the formal charge of the atoms in this compound.
19. Which of the following structures would we expect for nitrous acrid? Determine the formal charges:
    
20. Sulfuric acrid is the industrial chemic produced in greatest quantity worldwide. About 90 billion pounds are produced each year in the Usa alone. Write the Lewis structure for sulfuric acid, H₂SO₄, which has 2 oxygen atoms and ii OH groups bonded to the sulfur.

Glossary

formal charge

charge that would upshot on an atom past taking the number of valence electrons on the neutral cantlet and subtracting the nonbonding electrons and the number of bonds (half of the bonding electrons)

molecular structure

organisation of atoms in a molecule or ion

resonance

situation in which one Lewis structure is insufficient to describe the bonding in a molecule and the average of multiple structures is observed

resonance forms

2 or more Lewis structures that accept the same arrangement of atoms only different arrangements of electrons

resonance hybrid

average of the resonance forms shown by the individual Lewis structures

Solutions

Answers to Chemistry End of Chapter Exercises

ii. (a)

(b)

(c)

(d)

(due east)

four.

6. (a)

(b)

CO has the strongest carbon-oxygen bail because in that location is a triple bond joining C and O. CO_ii has double bonds.

eight. (a) H: 0, Cl: 0; (b) C: 0, F: 0; (c) P: 0, Cl 0; (d) P: 0, F: 0

10. Cl in Cl₂: 0; Cl in BeCl₂: 0; Cl in ClF₅: 0

12. (a)
;

(b)
;

(c)
;

(d)

14. HOCl

xvi. The structure that gives zero formal charges is consistent with the actual structure:

xviii. NF₃;

xx.

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