How to assign electrons in Lewis structure?

Lewis electron-Dot symbols:

Atoms interact with each forming chemical bonds in order to achieve a stable electronic configuration. The valence electrons are the only electrons that get involved in forming the chemical bond. Atoms follow octet rule when forming the chemical bond.

The octet rule is the tendency of atoms in a molecule to have eight electrons in their valence shells (two for hydrogen atoms) in order to obtain electronic configuration similar to noble gases because maximum stability occurs when an atom is isoelectronic with a noble gas.

We use Lewis dot symbols to know the number of valence electrons that can get involved in forming a chemical bond. In Lewis dot symbol the atoms or ions are represented by dots placed around the letter symbol of the element. The dots represent the electrons and written as pairs on each side of the element symbol

For example, boron electronic configuration 1s²2s²2p¹, the 2 electrons in 1s orbital are inner electrons, 2s²2p¹ are valence electrons.

Which more closely corresponds to the ground-state configuration [He]2s²2p¹. The first symbol shows boron’s chemistry, in which each single electron (single dot) tends to be involved in bond formation].

Note that in periodic table; (1) elements in the same group have similar outer electronic configurations and hence similar Lewis dot symbols. (2) For group 1 and 2, the number of valence electrons for each element is the same as the group number of elements, means for group 1 and 2 the valence electrons are equal to 1 and 2 respectively. (3) From 13 to 18, the number of valence electrons is equal to the last number. For example, Be is in group 15 so it has 5 valence electrons (five dots). (4) For lanthanides, and actinides, because the inner shells are not completely filled it is hard to anticipate the number of the valence electrons and we cannot write simple Lewis dot symbols for them.

Steps in writing Lewis structures:

Step 1: Calculate the total number of valence electrons for each atom. For anions we add the number of negative changes on this total (For CO₃^2- you add 2 because the -2 charge indicates that there are two more electrons than are provided by the neutral atoms.).

For a polyatomic cation, you subtract the number of positive charges from the total. (For NH⁴⁺  you subtract 1.)

Step 2: Write the chemical symbol of the molecule or ion and draw dots or dash between each bonded atoms.

Step 3: Distribute electrons around the central atom (or atoms) to satisfy the octet rule for these surrounding atoms.

Step 4: Distribute the remaining electrons as pairs. If there are fewer than eight electrons on the central atom, this suggests that a multiple bond is present. (Two electrons fewer than an octet suggests a double bond; four fewer suggests a triple bond or two double bonds.). Atoms that often form multiple bonds are C, N, O, and S.

Example:

Formal charge and Lewis structure:

Assigning the number of electrons an atom in a Lewis structure:

1- All the atom’s nonbonding electrons are assigned to the atom.

2- We break the bond(s) between the atom and other atom(s) and assign half of the bonding electrons to the atom.

Example: assign electrons on ozone molecules (O3) the total charge on ozone molecule is equal to zero (molecules are neutral)

Thus, the formal charges of the atoms in O₃ are:

Rule have to be regarded during assigning Lewis structure:

1. Molecules are electrically neutral so the sum of the charges must add up to zero. Example, the sum of charges on water molecule (H₂O) is equal zero.

2. For cations, the sum of formal charges must be equal to a positive value. For anions, the sum of formal charges must be equal the negative value.

Bonding and lone pair electrons in covalent compounds

The covalent bond

Like ionic bond, covalent bond forms due to the need of the atoms to reach the nearest stable electronic configuration (the nearest electron configuration of noble gas).

A covalent bond, a bond in which two electrons are shared by two atoms. In covalent compounds (contain only covalent bonds), the atoms that form covalent bond approach each other and their outer most energy levels overlap. Only valence electrons are shared in the covalent bond.

Example, the covalent bond formation between two H atoms, each atom has one electron in 1s. The two atoms approach each other, and their 1s orbitals start to overlap. Now each electron can move around the two atoms in the overlapped space between the two atoms, and the electrons are considered to be shared by the two atoms.

The electrons are attracted simultaneously by the positive charges of the two hydrogen nuclei. Because the two hydrogen atoms have the same nuclei size the electron are equally shared by the two atoms.  The shared pair of electrons is often represented by a single line [H-H].

Another example; the formation of covalent bond between two fluorine atoms [F₂ or F-F]. The electron configuration of F is [1s²2s²2p⁵]. The 1s electrons are low in energy and stay near the nucleus most of the time and do not participate in bond formation. For 2s and 2p electrons, they are considered to be the valence electrons. By that, F has 7 valence electrons. There is only one unpaired electron on F, so each F atom comes close to each other, the orbitals overlap, and the two unpaired electrons are shared between two atoms:

Bonding and lone pair electrons

For any atom to be considered a stable atom the electrons need to be paired. Let’s look again at F-F, only one electron in each atom is considered to be unpaired.

The electrons participated in the formation of the covalent bond we name them bonding electrons. The other electrons that are not involved in the formation of covalent bond - nonbonding electrons - are called lone pairs. We count every two electrons together as pair thus, each F in F₂ has three lone pairs and one bonding pair:

Another example; the formation of a bond between H and Cl to produce HCl molecule [H-Cl]:

The hydrogen atom participate with its 1s orbital, for the Cl [1s²2s²2p⁶3s²3p⁶4s¹] the valence electrons are (3p⁶4s¹). 4s¹ is the only unpaired electron, so 4s¹ is the only involved electron in the formation of covalent bond with the H 1s¹ electron to form bonding pair the other valence electrons will be considered as lone pair electrons. Thus, Cl atom has 3 lone pair and one bonding pair.

Oxygen molecule:

Oxygen atom has 8 electrons, the electronic configuration of oxygen atom is [1s²2s²2p⁴]. 1s² is an inner orbital and the valence electrons of oxygen atom are [2s²2p⁴]. The p orbital has 4 electrons p_x² p_y¹ p_z¹, the py and pz are the two unpaired electrons. So, each oxygen atom has two unpaired electrons and two lone pair electrons:

When oxygen molecule forms, the two unpaired electrons in p orbital approach each other forming two bonding pairs. For that, oxygen has two bonding pairs and two lone pairs.

The rules in filling orbitals:

There are two rules in filling orbitals, the first rule is for hydrogen atom, the second rule is for the other atoms. For hydrogen atom, the energy of the electron is determined solely by its principal quantum number. Thus, the energies of hydrogen orbitals increase as follows:

1s< 2s= 2p < 3s = 3p = 3d< 4s = 4p = 4d = 4 f <…………

The electron in “1s” is in the ground state and is in the most stable condition. For 2s and 2p orbitals, the orbitals have the same energies, and the electron is in its excited state.

For other atoms, the electron distribution depends on the angular momentum quantum number and the principal quantum number. For many atoms, the 3d energy level is close to the 4s energy level. Yet, the total energy of an atom is lower when 4s subshell is filled first before 3d subshell. The reason is that the total energy of an atom depends on the sum of orbital energies and the repulsion between the electrons (each orbital can take up to 2 electrons).

For 3p and 4s, electrons would prefer to fill 3p orbital before 4s. If the 3p orbital is filled first, the repulsion between the electrons will be minimum comparing to 4s because the two electrons will fill 3p_x and 3p_y and will be unpaired. While filling 4s would mean that electrons have to be paired. For that, the repulsion between electrons in 3p orbital is less than 4s orbital.

How many electrons can fill each orbital?

Atomic orbitals

To be able to understand the atomic orbitals you need to look at the table below to see the relation between quantum numbers and atomic orbitals.

n	l	ml	Number of orbitals	Atomic orbital designations	Number of electrons filling orbital
1	0	0	1	1s	2
2	0 1	0 -1, 0, 1	1 3	2s 2px, 2py, 2pz	2 6
3	0 1 2	0 -1, 0, 1 -2, -1, 0, 1, 2	1 3 5	3s 3px, 3py, 3pz 3dxy, 3dyz, 3dxz, 3dx2-y2, 3dz2	2 6 10

From the above table you can see that when l=0, (2l +1)=1 and there is only one value of m_l, thus we have an s orbital. When l= 1, (2l+1)=3, so there are three values of m_l or three p orbitals, labeled p_x , p_y , and p_z .

1- “s” orbital:

- In “s” orbital the probability of finding electron around nucleus is a sphere like shape. (the electron density around nucleus looks like a sphere).

2- “p” orbital:

- The electron density of p orbital looks like a two loop shape.

- If n=2 this means l= 1 and m_l  =-1, 0, 1 so we have three p orbitals that have same shape, size and energy only differ in their orientation.

- “p” consists of three orbitals p_x, p_y and p_z.

3- “d” orbital:

- For l = 2 the m_l  value will be -2, -1, 0, 1, 2 means five; (d_xy, d_yz, d_xz, d_x²_-y² and d_z²).

- “d” contains 5orbitals that is why it can be filled with 10 electrons.

4- “f” orbitals:

There are 7 f orbitals each can be filled with 2 electrons that is why f orbitals can be filled with        14 electrons.

                                                 

Quantum numbers

Quantum numbers

The simplest definition of Quantum mechanics is that quantum mechanics is the part of science that explain the distribution of the electrons around the nucleus and calculate the energy of electrons.

There are four quantum numbers used to describe the distribution of the electrons in any atom. These numbers are derived from the mathematical solution of the Schrödinger equation for the hydrogen atom. The four quantum numbers are called:

a- The principal quantum number

b. The angular momentum quantum number

c. The magnetic quantum number

d. The spin quantum number

The first three are used to describe atomic orbitals and to label electrons that reside in them. The fourth quantum number describes the behavior of a specific electron and completes the description of electrons in atoms.

a. The Principal Quantum Number (n)

The principal quantum number (n) have to be an integer number (1, 2, 3,…….). For hydrogen atom only, the value of n determines the energy of an orbital. The principle quantum number can give information about the average distance of the electron from the nucleus is a particular orbital. The larger n is, the greater the average distance of an electron in the orbital from the nucleus and therefore the larger the orbital.

The Angular Momentum Quantum Number (l)

The angular momentum quantum number (l) give information about the “shape” of the orbitals. From the value of “n” we can determine the number of ‘l” value. For a given value of n, l has possible integral values from 0 to ( n -1). For example, If n = 1, there is only one possible value of l; ( l = n - 1 = 1 - 1 = 0). Another example, if n = 2, there are two values of l (l = 0 and 1). If n = 3, there are three values of l (l= 0, 1, and 2). The value of l is generally designated by the letters s , p , d , f, and so on.

l	0	1	2	3	4	5
Name of orbital	s	p	d	f	g	h

If n=1, l= 0 we have s orbital

If n=2, l=0 and 1 we have s and p orbitals

If n=3, l=0, 1 and 2 we have s, p and d orbitals and so on……………

( “s” stand for the spectral lines of atomic emission spectra, “p” stand for the strong emission of principal lines, “d” for the diffuse of the atomic emission spectra, and “f” for fundamental atomic spectra emission). After letter “f” the naming of orbital followed alphabetical order.

A collection of orbitals “l” with the same value of “n” is frequently called a shell. If one or more orbitals with the same “n” and “l” values are referred to as a subshell. For example, the shell with n= 2 is composed of two subshells, l= 0 and 1 (the allowed values for n= 2). These subshells are called the 2s and 2p subshells where 2 denotes the value of n , and s and p denote the values of l.

The principle quantum no.	The Angular Momentum Quantum Number (l)	Orbital	Subshell
n=1	l=0	s orbital	1s
n=2	l= 0 and 1	s and p orbitals	1s, 2s, 2p

The Magnetic Quantum Number (m_l)

The magnetic quantum number (m_l) describes the orientation of the orbital in space. Within a subshell, the value of m_l depends on the value of the angular momentum quantum number, l.

For a certain value of l, there are (2l+1) integral values of m_l as follows:

- l, (-l+1),       0,           (+l-1), + l

Example: for l=0 m_l=0

If l =1 then no. of m_l= (1X2)+1=3  m_l will have three values= -1, 0, 1

If l=2, then no. of m_l = (2X2)+1 = 5 values, m_l = -2, -1, 0 ,1, 2.

The number of m_l values indicates the number of orbitals in a subshell with a particular l value.

The Electron Spin Quantum Number (m_s )

The electromagnetic theory postulated that, a spinning charge generates a magnetic field, and it is this motion that causes an electron to behave like a magnet. The two possible spinning motions of an electron, one clockwise and the other counter clockwise.

The fourth quantum number, called the electron spin quantum number (m_s ), which has a value of +½ , -½

Otto Stern and Walther Gerlach in 1924 experiment showed that the interaction between an electron and the magnetic field causes the atom to be deflected from its straight-line path. Because the spinning motion is completely random, the electrons in half of the atoms will be spinning in one direction, and those atoms will be deflected in one way; the electrons in the other half of the atoms will be spinning in the opposite direction, and those atoms will be deflected in the other direction. Thus, two spots of equal intensity are observed on the detecting screen.

Gas Pressure units

Gas Pressure units:

Pressure is an expression of force exerted on a surface per unit area. Pressure is one of measurable properties of a gas. To drive the unit of pressure we begin with velocity and acceleration.

Velocity is defined as the change in distance with elapsed time; that is,

Velocity = distance moved / elapsed time

The SI unit for velocity is m/s or cm/s.

Acceleration is the change in velocity with time, or:

Acceleration = change in velocity /time

Force = mass X acceleration

Acceleration is measured in m/s² (or cm/s²). The second law of motion, formulated by Sir Isaac Newton in the late seventeenth century, defines another term, from which the units of pressure are derived, namely, force. According to this law,

1N = 1kgm/s²

In this context, the SI unit of force is the newton (N), where:

Pressure = force / area

The SI unit of pressure is the pascal (Pa), defined as one newton per square meter:

1Pa = 1N/m²

1atmosphere = 1bar

1atmosphere=101.325kilopascal

1bar = 100000 pascal

The bonding of carbon and optical isomerism

The bonding of carbon:

Carbon has four valence electrons. For Carbon to fulfil octet rule it binds to four additional electrons.

By that, carbon can form single, double and triple bonds to achieve filled octet. The possible bonding combination for carbon are:

Carbon atoms may be bonded to each other or to other nonmetal atoms, such as hydrogen, a halogen, oxygen, or nitrogen.

                          

Optical isomerism of carbon:

A chiral molecule/ion is non-superposable on its mirror image.

Carbon characterized by its ability to form compounds with optical isomerism. The chiral carbon atom means, carbon has four different substitution. The carbon atom is considered to be “Achiral” if the carbon atom has similar substitution. The presence of an asymmetric carbon centre is one of several structural features that induce chirality in organic and inorganic molecules.