Tuesday, April 7, 2020

Chapter 4.4 - Formal Charge

In the previous section, we saw the steps to draw Lewis dot structures of 'polyatomic ions'. In this section, we will see Formal charge

1. Consider the Lewis dot structure of a polyatomic ion
• We saw that, such a structure is placed inside square brackets
• Also, a charge is written at the top right corner
2. This charge is possessed by the ‘ion as a whole’
• This charge does not belong to any particular atom inside the square brackets
3. But we can assign a ‘special type of charge’ on each atom inside the square brackets
• This ‘special type of charge’ is called formal charge
4. Formal charge is applicable to molecules also
■ That is.,
    ♦ We can find the formal charge of each atom in a polyatomic ion
    ♦ We can find the formal charge of each atom in a polyatomic molecule also

Now let us see how formal charge is calculated. It can be calculated in 3 steps:
Step 1: Finding the 'number of valence electrons' owned by a 'bonded atom'
• Consider an atom in a polyatomic molecule or ion
• When it is part of a molecule or ion, it is called a 'bonded atom'
• Any bonded atom will own some valence electrons
• Write down the number of those electrons
(The method to calculate this number is explained further below)
Step 2: Finding the number of valence electrons owned by a 'free atom'
• Consider the same atom when it is not part of any ion or molecule
• We can call such an atom to be:
    ♦ A 'free atom' or
    ♦ An 'isolated atom'
• The free atom owns some valence electrons
• Write down the number of those electrons
(This number is simply the ‘number of valence electrons’ calculated from the electronic configuration of that atom)
Step 3: Finding the formal charge
• Find the following difference:
Number calculated in step (2) – Number calculated in step (1)
• This difference is the formal charge. That is:
Formal charge = Number calculated in step (2) – Number calculated in step (1)

 But we must take special care while calculating the number in step 1. Let us elaborate:
• We want to find the ‘number of valence electrons owned by a bonded atom’ in the following two cases:
    ♦ When that atom is part of a molecule
    ♦ When that atom is part of an ion
• In both cases, we use the same procedure. The procedure can be written in 3 steps:
(i) Electrons owned through lone pairs:
• If the atom has any lone pairs, all electrons in those pairs will belong to that atom
• So we can write:
The number of electrons owned through lone pairs = (Number of lone pairs × 2)
(ii) Electrons owned through bonds:
• The atom will be having covalent bonds with other atoms
    ♦ Each of those covalent bonds will contain 'two electrons'
• One of those 'two electrons' will belong to the atom under consideration
• So we can write:
The number of electrons owned through covalent bonds = Number of covalent bonds around that atom
 While counting the ‘number of covalent bonds’:
    ♦ it is important to consider a single bond as one covalent bond
    ♦ it is important to consider a double bond as two covalent bonds 
    ♦ it is important to consider a triple bond as three covalent bonds
(iii) Final number of valence electrons:
• Find the sum of the numbers obtained in (i) and (ii)
• This sum will give the ‘number of valence electrons owned by the bonded atom’

Let us see some examples where we will find the formal charge:
Example 1: O3 (ozone) molecule
• Fig.4.21(a) below, shows the Lewis dot structure of the O3 molecule
• The three O atoms are named as A, B and C
• We have to apply the steps to each of the three O atoms
Fig.4.21
First we will take atom A
Step 1Finding the 'number of valence electrons' owned by A
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (1×2) = 2
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 3
(We see a single bond and a double bond around A)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [2+3] = 5
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'A' is an O atom
• We know that, in the free state, O has 6 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (6-5) = 1

Next we will take atom B
Step 1Finding the 'number of valence electrons' owned by B
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (2×2) = 4
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 2
(We see only one double bond around B)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [4+2] = 6
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'B' is an O atom
• We know that, in the free state, O has 6 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (6-6) = 0

Finally, we will take atom C
Step 1Finding the 'number of valence electrons' owned by C
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (3×2) = 6
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 1
(We see only one single bond around C)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [6+1] = 7
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'C' is an O atom
• We know that, in the free state, O has 6 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (6-7) = -1

■ The formal charges calculated above should be marked in the Lewis dot structure. This is shown in fig.4.21(b) above

Example 2: CH3COO (acetate) ion
• Fig.4.22(a) below, shows the Lewis dot structure of the CH3COO ion
• The seven atoms are named as A, B, C, D, E, F and G 
• We have to apply the steps to each of the seven atoms
Fig.4.22
• We see that, the structure is enclosed within square brackets and a charge of '-1' is given
• This indicates that, it is an ion. Let us check:
■ Finding the number of 'available valence electrons'
• Number of valence electrons of C = 4
• Number of valence electrons of H = 1
• Number of valence electrons of O = 6
• So total number of valence electrons = [(2×4)+(3×1)+(2 × 6)] = 23
■ Finding the number of dots 
• Number of covalent bonds = 7
• Number of lone pairs = 5
• So total number of dots = [(7×2)+(5×2)] = 24
■ So there is one extra dot. This is indicated by the '-' sign at the top right

First we will take atom A
Step 1Finding the 'number of valence electrons' owned by A
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (2×2) = 4
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 2
(We see only one double bond around A)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [4+2] = 6
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'A' is an O atom
• We know that, in the free state, O has 6 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (6-6) = 0

Next we will take atom B
Step 1Finding the 'number of valence electrons' owned by B
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (0×2) = 0
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 4
(We see two single bonds and one double bond around B)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [0+4] = 4
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'B' is a C atom
• We know that, in the free state, C has 4 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (4-4) = 0

Next we will take atom C
Step 1Finding the 'number of valence electrons' owned by C
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (3×2) = 6
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 1
(We see only one single bond around C)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [6+1] = 7
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'C' is an O atom
• We know that, in the free state, O has 6 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (6-7) = -1

Next we will take atom D
Step 1Finding the 'number of valence electrons' owned by D
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (0×2) = 0
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 1
(We see only one single bond around D)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [0+1] = 1
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'D' is a H atom
• We know that, in the free state, H has 1 valence electron
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (1-1) = 0

Next we will take atom E
Step 1Finding the 'number of valence electrons' owned by E
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (0×2) = 0
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 4
(We see four single bonds around E)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [0+4] = 4
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'E' is a C atom
• We know that, in the free state, C has 4 valence electrons
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (4-4) = 0

Next we will take atom F
Step 1Finding the 'number of valence electrons' owned by F
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (0×2) = 0
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 1
(We see only one single bond around F)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [0+1] = 1
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'F' is a H atom
• We know that, in the free state, H has 1 valence electron
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (1-1) = 0

Finally, we will take atom G
Step 1Finding the 'number of valence electrons' owned by G
(i) Electrons owned through lone pairs:
• The number of electrons owned through lone pairs = (Number of lone pairs × 2) = (0×2) = 0
(ii) Electrons owned through bonds:
• The number of electrons owned through covalent bonds = Number of covalent bonds = 1
(We see only one single bond around G)
(iii) Final number of valence electrons:
• The sum [(i)+(ii)] = [0+1] = 1
Step 2: Finding the number of valence electrons owned by the 'free atom'
• Atom marked as 'G' is a H atom
• We know that, in the free state, H has 1 valence electron
Step 3: Finding the formal charge
• Formal charge = Number calculated in step (2) – Number calculated in step (1)
= (1-1) = 0


■ The formal charges calculated above should be marked in the Lewis dot structure. This is shown in fig.4.22(b) above

Now we will see 5 important points related to formal charges:
1. The formal charges do not indicate the real charge separation within the molecule or ion
This can be explained with examples:
■ In fig.4.21, we cannot say these:
    ♦ The O atom marked as A, 'has a +1 charge'
    ♦ The O atom marked as C, 'has a -1 charge'
■ In fig.4.22, we cannot say this:
    ♦ The O atom marked as C, 'has a -1 charge'
2. Marking the charges in the Lewis dot structure help us to keep track of the electrons
This can be explained with examples
■ In fig.4.21, the O atom marked as A has +1 written near it
• This indicates that, the O atom has lost one electron when compared to the free state
    ♦ In the free state, an O atom will own 6 valence electrons
    ♦ But this particular O atom has only 5 electrons around it
          ✰ 3 electrons from the 3 covalent bonds
          ✰ 2 electrons from the single lone pair
■ In fig.4.21, the O atom marked as C has -1 written near it
• This indicates that, the O atom has gained one electron when compared to the free state
    ♦ In the free state, an O atom will own 6 valence electrons
    ♦ But this particular O atom has 7 electrons around it
          ✰ 1 electron from the single covalent bond
          ✰ 6 electrons from the three lone pairs
■ In fig.4.22, the O atom marked as C has -1 written near it
• This indicates that, the O atom has gained one electron when compared to the free state
    ♦ In the free state, an O atom will own 6 valence electrons
    ♦ But this particular O atom has 7 electrons around it
          ✰ 1 electron from the single covalent bond
          ✰ 6 electrons from the three lone pairs
3. Selecting the suitable structure
• For some molecules and ions, more than one Lewis dot structure is possible
• In such cases, we will want to find ‘the structure with the lowest energy’
• Formal charges will help us in this situation
• ‘The structure with the lowest energy’ is that structure which has the smallest formal charges on the atoms
(We will see the application of this procedure in later sections)
4. Formal charge is based on the following assumptions:
• The bonds between atoms are pure covalent bonds
• In such bonds, the ‘electrons in the pairs’ are shared equally by the neighboring atoms
• If the pair moves towards any one atom, the formal charge will become invalid
5. Sum of formal charges
• Sum of the formal charges in all the atoms in a polyatomic molecule will be zero
• Sum of the formal charges in all the atoms in a polyatomic ion will be equal to the charge of that ion

In the next section, we will see the limitations of the octet rule

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