Discus of Ionic bond

Ionic Bond

In a simplified view of an Ionic bond, the bonding electron is not shared at all, but completely transferred. In this type of bond, the outer atomic orbital of one atom has a vacancy which allows addition of one or more electrons. These newly added electrons potentially occupy a lower energy-state (effectively closer to more nuclear charge) than they experience in a different atom. Thus, one nucleus offers a more tightly bound position to an electron than does another nucleus, with the result that one atom may transfer an electron to the other. This transfer causes one atom to assume a net positive charge, and the other to assume a net negative charge. The bond thus results form electrostatic attraction between the atoms become positive or negatively charged ionic. For example consider formation of an ionic compound like sodium chloride.

Na " Na⁺ +  electron

Cl + electron " Cl^-

When sodium and chlorine react together the outer electron of the sodium atom is transferred to the chlorine atom to produce sodium ion (Na⁺) and chlorine ion (Cl^{­ -}). Electrostatic attraction between the positive and negative ionic together in the crystal Lattice. Such bonds have no particular orientation in space, since they result from equal electrostatic attraction of each ion to all ions around them. So, it is crystal clear that ionic bonds are non-directional consequently ionic compounds do not have a shape. Ionic bonds are strong and thus ionic substances require high temperatures to melt. Ionic compounds are brittle since the forces between ions are short-range, and do not easily bridge cracks and fractures.

Discus of Covalent bond

Covalent bond

In the simple view of a so-called Covalent Bond, one or more electron (often a pair of electrons) are drawn into the space between the two atomic nuclei. Here the negatively charged electron are attract to the positive charged electrons are attract to the positive of both nuclei, instead of just their own. This overcomes the repulsion between the two positively charged nuclei of the two atoms, and so this overwhelming attraction holds the two nuclei in a fixed configuration of equilibrium, even though they will still vibrate at equilibrium position. Thus, covalent bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared between them. These bonds exist between two particular same or different atoms, and have a direction in space, allowing them to be shown as single connecting lines between atoms in drawings. For Example, Two chlorine atoms react to form a Cl₂ molecule.

 Each chlorine atom gives a share of its electrons to other atom. A pair of electrons is shared equally between both atoms and each atom now has eight electrons in its outer shell (stable octet). In a similar way a molecule of tetra chloro-methane CCl₄ is made up of one carbon and four chlorine atoms.          

The carbon atom is short of four electrons so as to have noble gas structure. Consequently, it forms four bonds with the chlorine atom which themselves are short of one electron so they each form one bond. By sharing electrons in this way both carbon and all four chlorine atoms attain a noble gas structure.

A molecule of ammonia NH₃ is made up of one nitrogen and three hydrogen atom

Other example of covalent bonds includes water (with two covalent bonds) and hydrogen – fluoride (one covalent bond and three long pairs.)

  

 

In a polar covalent bond, one are more electrons are unequally shared between two nuclei. Covalent bonds often result in the formation of small collections of better-connected atoms call molecule. These molecule in solid and liquid state are bound to other molecules by inter-molecular forces that are often much weaker than the covalent bonds that hold the molecules internally together. Such weak inter-molecular bonds give organic molecule substances, such as waxes and oils, their soft bulk character, and their low melting (in liquid, molecule must case most structured or oriented contact with each other). When covalent bonds link long chain of atoms in large molecule however (as in polymers much as nylon), or when covalent bonds extend in networks through solid that are not composed of discrete molecule (such as diamond or quartz or the silicate minerals in many type of rock) then the structures that result may be both strong and tough, at least in the polymers and networks increase greatly.

How many types of chemical bond

What is a Molecule?

The elements generally do not exist in the form of atomic (except noble gases) but prefer to form group of atom called Molecules.

What is Bond? :-

The force by which the atomic attract each other to form such group is called a bond.

What is a Chemical bond?

A chemical bond is a force of attraction between atoms that allows the formation of chemical substances that contain two or more atom. The bond is caused by the electrostatic force by attraction between posstive charges or between electrons and nuclei or someetimes as a result of a dipole attration. An electron positioned between two nuclei will be attraction to both of them, and the nuclei will be attracted toward electrons in this position. This attraction constitutes the chemical bond.

Type of Bond-

As started a chenical bond is an attraction between atoms. This attraction may be seen as the result of different behaviour of the outermost electrons of atom . Although all of these behaviors merge into each other seamlessly in various bonding situations so that there is no clear lineto be drawn between them, customartily the chemical bonds are classifeid into differents types.

Atommay attain a stable electronic configuration in three different ways by lossing electron , by gaining or by shairing electron. Moreover, elements may be divided into following three type as: 

1.Electropositive elements: Whose atom give up one or more electron fairly readily:

2. Electronenegative elements: Which will accept electron.

3.Electron which have little tendency to lose or gain electrons.

The different type of bond may br formed depending on the electropositive or electronegative character of atom involved.

Electropositive element+ Electropositive element→ Metallic bond

Electropositive element+ Electronegative element→ Ionoc bond

Electonegative element+ Electronegative element→ Covalent bond

Effective Nuclear charge and slater’s RULE

Effective Nuclear charge and Slater's RULE

In quantum Chemistry, Slater’s Rules Provide numerical values for the effective nuclear charge. The rules were devised semi-empirically by John C.Slater and published in 1930. Revised values of screening constants based on computations of atomic structure by the Hartree-Fock method were obtained by Enrico Clementi and co-workers in the 1960s. For each electron in an atom, Slater’s rule provide a value for the screening constant, denoted by s, which related the effective and actual nuclear charge as:

 Z_eff – Z – s

Here, Z is the Actual Nuclear Charge and Z_eff  is the Effective Nuclear Charge.

Firstly, the electron are arrange into a sequence of group in order of increasing principle quantum number n, and for equal of increasing azimuthal quantum number l, except that p-orbitals are kept together.

[1s] [2s, 2p] [3s,3p] [3d] [4s,4p] [4d] [4f] [5s, 5p] [5d] etc.

Each group is given a different sheilding constant which depend upon the number and type of electrons in those group preceding it. The shielding constant for each group is formed as the sum of following contributions;

1.     As amount of 0.35 from each other electron within the same group except for the [1s] group, where the other electron contributes onty 0.30.

2.     If the group is the [s,p] type, an amount of 0.85 from each electron with principal quantum number (n) one less and an amoun of 1.00 for each electron with aneven smallerproincipal quantum number.

3.     If the group is of the [d] or [f]. type, an amount of 1.00 for each electron inside it. This includes,(i) Electron with a smaller principal quantum number n and (ii) Electrons with an equal principal quantum number a smaller azimuthal quantum number(l).

An example is provided below in which iron atom is considered.The screening constant and subsequently the effective nuclear charge for each electron is deduced for iron atom. Iron has a nuclear charge 26 and electronic configuration , 1s², 2s², 2p⁶, 3s², 3p⁶, 3d⁶  4s². The calculation to find out screening constants are show here:

Note:  That the effective nuclear charge is calculation by subtracting the screening constant from the corresponding atomic number.

Rules for Writing Electronic Configuration

Rules for Writing Electronic Configuration

The atom is built up by filling electrons in various orbital according to the certain rules like Aufbau principle, Pauli Exclusion Principle, Hund’s rules of maximum spin multiplicity etc. These are discussed below.

Aufbau Principle:- 

This principle state that the electrons are added one by one the various orbitals in order of their increasing energy starting with the orbital of lowest energy.  The increasing order of various atomic orbital is

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 5f, 6d, 7p………………

How to remember such a big sequence is a big deal because it appears to be highly complicated. To make it simple, there is a method to write the increasing order of the orbitals. Starting from the top, the direction of the arrows gives the order of filling of orbital as shown below,

The sequence of atomic orbital orbital shown above is based on (n+1) rule.

(n+1) Rule:-

The energy of an orbital depends upon the sum of value of the principle quantum number (n) and the azimuthal quantum number (l). This is called (n+1) rule. According to rule, “ In neutral isolated atom, the lower the value of (n+1) for an orbital, lower will be its energy However, if the two different type of orbital have same value of (n+1), the orbital lower value of n has lower energy”.

Pauli’s Exclusion Principle:-

According to this principle “no two electron in an atom will have same value of all four quantum number”.

If one electron in an atom has the quantum number n=1, l=0, m=0 and s= +1/2, no other electrons can have the same four quantum numbers.  In other word , one cannot place two electron with the same value of spin quantum number (s) in a 1s orbital. So, the orbital diagram ##(1s) is not possible arrangement of electrons. Rather, the correnct representation must be #$(1s).

Hund’s Rule of Maximum spin multiplicity:-

This rule deal with the filling of electron in the orbital having equal energy also known as degenerate orbital’s. According to this rule “Degenerate orbital must be single occupied before the spin pairing stars”.

This due to the fact that electrons being identical in charge, repel each other when present in the same orbital. This repulsion can however be two electrons move as far as by possible by occupying different degenerate orbital’s. Moreover all the unpaired electrons in a degenerate set of orbital’s must have the same spin.

Electronic Configuration of Various Elements:-

Electronic configuration is the distribution of electrons into orbitals or shells, subshell orbitals an atom. Keeping in view the above mention rule, electronic configuration of any orbital can be simply represented by the notation.                                 n l ^x

Where- n= Principal quantum number

               l= Symbol of subshell or orbital (s, p, d, f)

              x= Number of electrons in the subshell

To write the electronic configuration, one must know (1) The atomic number (2) The order which orbital are to be filled (3) Maximum number of electrons that can occupies in a shell, sub-shell or orbital. Some more fundamental aspects are

1.      Each orbital can accommodate two electrons.

2.     The number of electrons to be accommodated in a subshell is 2 × number of       degenerate orbitals.

3.    The maximum number of electrons in each shell ( K, L, M, N…) is given by 2n².   When, n is the principal quantum number.

Factors Responsible for the Extra Stability of Half-Filled and completely filled Subshell

 1. Symmetrical distribution:-

It is well known fact that symmetry leads to stability. Thus the electronic configuration in which all the orbitals of the same subshell are either completely filled or are exactly half filled are more stable because of Symmetrical Distribution of electrons.

2.Exchange energy:-        

The electrons with parallel spins present in the degenerate orbital tend to exchange their position. The energy released during this exchange is called Exchange Energy. The number of exchanges that can take place is maximum when the degenerate orbital are exactly half-filled or completely filled. As a result, the exchange is maximum and is the stability.

 

Shapes of Atomic Orbital’s

Shapes of Atomic Orbital’s

An orbital is the region of shape around the nucleus within which the probability of finding an electron of a given energy is maximum (90-95%). The shape or contour diagram of this region of electron cloud gives the shape of the orbital. It is fundamentally determined by the Azimuthal quantum number (l), while the orientation of orbital depends on the magnetic quantum number (m). Let us now see the shapes of different orbital in the various subshells.

s-orbital’s(l=o) 

These orbital are spherical and symmetrical about the nucleus. The probability of finding the electron is zero near the nucleus keep on increasing as the distance from nucleus increase, becomes maximum and thereafter decreases.

The size of the orbital depends upon the value of principal quantum number (n). Greater the value of n, large is the zero of the orbital. Therefore, 2s orbital is large the 1s orbital but both of them are non-direction and spherically symmetrical is shape.

Closer inspection of 2s orbital suggests that there is vacant space between two successive s-orbital know as radial node or nodal surface. So, 2s orbital suggest is characterized with one radial node. However, there is no radial node for 1s orbital since it is starting from the nucleus.

p-orbital(l=1)

The probability of finding the p-electron is maximum in two lobes on the opposite side of the nucleus. This gives rise to a dumb- bell shape for the p-shape the p-orbital. For p-orbital l = 1. Hence, m = -1, o, +1.  Thus, p-orbital have three different orientations. These are designated as p_x , p_y, and p_z depending upon whether the density of electron is maximum along the x, y, and z- axis, respectively. They are symmetrical but have direction characters. The two lobes of p-orbital are separated by a nodal plane, where the probability of finding electron is zero.

The three p-orbital belonging to a particular energy shell have have equal energies and are called degenerate orbital.-

d-orbital’s(l = 2) :-

For d –orbital’s, l = 2, Hence m = -2, -1, 0, +1, +2 5 different values of m suggests that there are 5d-orbital’s--  d_xy d_yz d_zx p_z²  and d_x²_-y² . They have relatively complex geometry. Out of the five orbitals, the three (d_xy d_yz d_zx) project in between the axis and the other two and the other two p_z² and d_x²_-y² lie along the axis.

f-orbital’s :--

Foe f-orbitals, l = 3, Hence m = -3, -2, -1, 0, +1,+2, +3. Thus there are 7 f-orbital. They have relatively complex geometry.

What is Schrödinger Wave Equation?,

The Schrödinger Wave Equation:-

Schrodinger Wave Equation is given by Erwin Schrodinger in 1926 and based on dual nature of electron. In it electron is described as a three dimensional wave in the electron field of a positively charge nucleus. The probability of finding an electron at any point around the nucleus can be determined by the help of Schrodinger wave equation. It Schrodinger’s  wave model of an atom, the discrete energy levels of orbits proposed by Bohr are replace by mathematical function, Ψ, which are related to the probability of finding electrons at various around the nucleus.

Physical Significance of Ψ and Ψ2:-

The wave function Ψ represent the amplitude of the electron wave. The amplitude Ψ is thus a function of space co-ordinate and times. Mathematically it can be expressed as Ψ= Ψ(x, y, z……times), Ψ² refers to the probability density of finding electron. So, for single particle, the square of the wave function (Ψ²) at any point  is If Ψ₂ is maximum than probability of finding e^- is maximum around nucleus and the place where probability of finding e^- is maximum is called an atom orbital . Ψ² can be converted into probability of finding electron, if it is multiple by volume. So, If Ψ(x) is the wave function of a particle, then the probability of finding the particle within the range from x to x+dx is given by:

                                                      P(x)dx = Ψ Ψdx =| Ψ |² dx

Where Ψ^* denotes the complex conjugate of Ψ. Note that P(x)dx is the probability and P(x)  is the probability density.

When this concept is applied to electrons, the expressed for the probability of finding the electron in a spherical shell of thickness dr at distance r from the nucleus is given by:

                                                   P(x)dr = 4π| Ψ|² r²dr

Radial Nodes:--     

Radial nodes occur when the wave function for the electron is zero on a spherical surface of a particle radius  -  hence the name radial node. Shown on the right is a plot of the probability of the 3s wave function. The two radial surfaces are indicate in the figure.

Number of radial or spherical nodes = n – l – 1.

Number of peaks in radial distribution curve = n – l.

Angular Nodes:-- 

Angular nodes occur when the wave function for the electron is zero along direction specified by a particular angle (…hence the name angular node.)Shown on the left is a plot of the probability of the 2p wave function. The angular nodes surface indicated in the figure is a plane that makes a 90⁰ angle with the z-axis.

Number of Angular nodes = l

The three dimensional view of the same angular nodes can be shown like below in case of

1       1.   A 2p orbital which has one angular node

                                                   

2. A 3d orbital has two angular nodes:

 Eigen Function and Eigen values:--

Eigen is a German word which means Unique. In genral, an eigen function can be obtained when one operates on a function and get the same function back multiblied by a constant, as said here wavw function are ternmes and eigen function each corresponding energy is the eigen value.Moving into a bit more detailed explaination,the Schrödinger equation can have serval solution, not all of which correspond to any physical or chemical reality. Such solution or wave function are, therefore, not acceptable.