7.5: Formal cost and reverberation (2023)

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    • 7.5: Formal cost and reverberation (1)
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    learning objective

    At the end of this section you can:

    • Calculate the formal charge of the atoms in any Lewis structure
    • Use formal charges to determine the most likely Lewis structure for a given molecule
    • Explain the concept of resonance and draw a Lewis structure representing the resonance form of the given molecule

    In the previous section, we discussed how to write Lewis structures for molecules and polyatomic ions. However, as we have seen, in some cases it is clear that a molecule has more than one valid structure. We can use the concept of formal charges to help us predict the most appropriate Lewis structure when more than one is reasonable.

    Calculate formal costs

    fromformal compensationAtoms in a molecule areimaginedIf we can distribute the electrons evenly across the bonds between the atoms, the atoms will be charged. Another way to say it is that the formal charge occurs when we take the number of valence electrons in a neutral atom, subtract the non-bonding electrons, and then subtract the number of bonds attached to that atom in the Lewis structure.

    So, we calculate the official fee as follows:

    formal compensation=# Electrons of the valence shell (free atoms)# Lonely couple12#combine electronsformal compensation=# Electrons of the valence shell (free atoms)# Lonely couple12#combine electrons

    We can check the formal cost one more time by determining the sum of the formal costs for the entire structure. The sum of the formal charges of all atoms in the molecule must be zero; the sum of the formal charges in the ion must equal the charge of the ion.

    We must remember that the formal charge calculated for an atom is not derealThe charge of atoms in a molecule. Formal debiting is only a useful accounting procedure; it does not indicate the existence of real charges.

    Example 7.6

    Calculation of formal charges from Lewis structures

    Assign formal charges to each atom in the interhalide ionpotassium chloride4.potassium chloride4.


    1. step 1.We assign bond electron pairs equally to all I-Cl bonds:
      7.5: Formal cost and reverberation (2)
    2. step 2.We attach lone electron pairs to their atomsEach Cl atom now has seven electrons, while the I atom has eight.
    3. 3rd stepSubtract that number from the number of valence electrons in the neutral atom:
      And: 7 – 8 = –1
      Classification: 7 – 7 = 0
      The sum of the formal charges of all atoms is equal to –1, which is the same as the charge (–1) of the ion.

    check your studies

    Calculate the formal charge of each atom in the carbon monoxide molecule:7.5: Formal cost and reverberation (3)


    C -1, O +1

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    Example 7.7

    Calculation of formal charges from Lewis structures

    Assign formal charges to each atom in the interhalogen molecule BrCl3.


    1. step 1.Assign one of the electrons in each Br-Cl bond to the Br atom and one electron to the Cl atom in that bond:
      7.5: Formal cost and reverberation (4)
    2. step 2.Assign lone pairs to their atoms.Each Cl atom has seven electrons, and the Br atom has seven electrons.
    3. 3rd stepSubtract this number from the number of valence electrons of the neutral atom.This gives the formal cost:
      Brom: 7 – 7 = 0
      Classification: 7 – 7 = 0
      All atoms in BrCl3The formal charge is zero and the sum of the formal charges is zero as it should be in a neutral molecule.
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    check your studies

    Determine the formal charge of each atom in NCl3.


    Number: 0; all three atoms Cl: 0

    7.5: Formal cost and reverberation (5)

    Molecular structure prediction using formal charges

    The arrangement of atoms in a molecule or ion is called the presenceMolecular structureIn many cases, following the steps to write a Lewis structure can lead to more than one possible molecular structure, such as multiple bonds and different positions of electron pairs or different arrangements of atoms. Some guidelines on formal charge can help determine the most likely structure for a particular molecule or ion:

    1. Molecular structures in which all formal charges are zero are preferred over molecular structures in which some of the formal charges are non-zero.
    2. If the Lewis structure is to have a non-zero formal charge, then the arrangement with the least non-zero formal charge is preferred.
    3. Lewis structures are preferred when neighboring forms have zero or opposite charge.
    4. When choosing between several Lewis structures with similar formal charge distributions, structures with negative formal charge on more electronegative atoms are preferred.

    To see how these guidelines apply, let's look at some possible structures for carbon dioxide, CO22.We know from the previous discussion that the less electronegative atom usually occupies the central position, but the formal charge allows us to understandWhySometimes it happens. We can deduce three possibilities for the structure: middle carbon and double bond, middle carbon and single and triple bonds, and middle oxygen and double bond:

    7.5: Formal cost and reverberation (6)

    Comparing the three formal fees, we can definitively determine that the structure on the left is preferable because there is no formal fee (guideline 1).

    Another example: the thiocyanate ion, an ion formed from carbon, nitrogen and sulfur atoms, can have three different molecular structures: NCS, Central nervous system, China Southern Airlines.The formal charges present in each molecular structure can help us choose the most likely arrangement of atoms. Here are the possible Lewis structures and formal charges for each of the three possible structures of the thiocyanate ion:

    7.5: Formal cost and reverberation (7)

    Note that the sum of the formal charges in each case is equal to the ion charge (–1). However, the first arrangement of atoms is preferred because it has the least number of atoms with a non-zero formal charge (Guideline 2). In addition, it places the least electronegative atom in the center and negative charges on the more electronegative elements (guideline 4).

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    Example 7.8

    Determination of molecular structure using formal charges

    Larchgas, N2O, commonly known as nitrous oxide, is used as an anesthetic during minor procedures, such as the routine extraction of wisdom teeth. What is the most likely structure of nitric oxide?7.5: Formal cost and reverberation (8)


    Determination of official fees gives the following results:7.5: Formal cost and reverberation (9)

    Structures with terminal oxygen atoms best meet the criteria for the most stable form of charge distribution:

    7.5: Formal cost and reverberation (10)

    The smallest number of atoms with a formal charge (criterion 2), there is no formal charge greater than 1 (criterion 2), the negative formal charge is on the more electronegative element (guideline 4), and the less electronegative atoms are on the middle class.

    check your studies

    This is the most likely molecular structure of nitrite(East Europe2)(East Europe2)ion?7.5: Formal cost and reverberation (11)


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    Note that the more likely structure is for the nitrite anionExample 7.8It can actually be drawn in two different ways, the difference being in the position of the N-O and N=O bonds:

    7.5: Formal cost and reverberation (12)

    If the nitrite ion contains both a single and a double bond, we would expect the two bond lengths to be different. A double bond between two atoms is shorter (and stronger) than a single bond between the same two atoms. However, experiments have shown that both N-O bonds are presentEast Europe2East Europe2they have the same strength and length, and all other properties are the same.

    It is not possible to specify a single Lewis structureEast Europe2East Europe2Where nitrogen has an octet, the two bonds are equivalent. Instead we use the conceptresonance: If two or more Lewis structures with the same arrangement of atoms can be written for a molecule or ion, the actual electron distribution isAverageThose shown by various Lewis structures. The actual distribution of electrons in each nitrogen-oxygen bondEast Europe2East Europe2is the average of double and single bonds. We name individual Lewis structuresform of resonance.The actual electronic structure of the molecule (average of resonance forms) is calledresonant bastardpersonal echo. The double arrows between the Lewis structures indicate that these are resonance forms.

    7.5: Formal cost and reverberation (13)

    We must remember that molecules are described as resonance hybridsno wayIt has an electronic structure described by two forms of resonance. It does not fluctuate between resonance forms; the actual electronic structure isconstantlyAverage value shown for all resonance forms. George Wheland, one of the pioneers of resonance theory, used a historical analogy to describe the relationship between resonant shapes and resonant mixtures. A medieval traveler who had never seen a rhinoceros before described it as a cross between a dragon and a unicorn, as it shared many characteristics with both. Just as a rhinoceros is sometimes not a dragon and sometimes a unicorn, the resonant hybrid is at no time one of its resonant forms. Like the rhinoceros, it is a real entity that experimental evidence suggests exists. It shares some characteristics with its resonance form, but the resonance form itself is a nice image (like the unicorn and the dragon).

    carbonate anion,carbon monoxide32-,carbon monoxide32-,Give another example of resonance:

    7.5: Formal cost and reverberation (14)

    An oxygen atom must have a double bond with carbon to complete the octet on the central atom. However, all oxygen atoms are equivalent and double bonds can form from any of the three atoms. This produces three resonance forms of the carbonate ion. Since we can write three identical resonance structures, we know that the actual electron arrangement in the carbonate ion is the average of the three structures. Again, experiments show that all three C-O bonds are identical.

    study link

    use itonline QPractice the skills of drawing resonance structures and estimating formal charges.

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