Lattice energy of ionic bond

                                  Lattice Energy Of Ionic Bond

    A crystal lattice is the regular arrangement of atom or ions or molecular in space and gives a  definite geometry to the solid substance.The lattice energy of crystalline solid is defined as the energy of formation of the crystal from infinite-separated ions,molecular or atoms The concept of lattice energy was  developed for rocksalt structure and shalerite structure compound like NaCl and ZnS..

                 Lattice energy is a type of potential energy which is required to break apart an ionic solid and convert its component atoms into gaseous ions. The definition cause the value of lattice energy always positive, because it is always a endothermic reaction.Again, it is defined as or other definition of lattice energy defines it is a reverse process,meaning it is the energy released when gaseous ions bind to form an ionic solid. According to this,the value of lattice energy is negative i.e it is exothermic reaction.   

                          The amount of energy released when cations and anions are united together in their respective lattice sites in a crystal from 1 mole of ionic solid is called lattice energy.  

                 

Sodium Chloride crystal lattice

                              M⁺ (g) + X⁻ (g) → MX (s) + energy released called as lattice energy.

                             cation      anion

         Its may also be defined as the energy required to break 1 mole of ionic solid crystal into cations and anions in their gaseous state.

                 MX + energy required called  → M⁺  +   X⁻

                            lattice energy               cation    anion

       The energy required and energy released in both cases in same magnitude but opposite in sign. Lattice energy cann't be measured directly but the experimental determination takes place by two ways:

1) Theoritical determination of lattice energy : Born-Lande experiment

2) Experimental determination of lattice energy : Born-Haber cycle

1. Theoritical determination of lattice energy : Born-Lande experiment                                                         Born-lande equation is a concept originally formulated in 1880 and used to calculated the lattice energy of a crystalline ionic compound. The Born-Lande eqaution states that,"the lattice energy can be derived from ionic lattice based on electrostatic potential and the potential energy due to repulsion"                                                                                                                                                      Born-Lande equation based on the assumption that the ionic lattice where ions are compressed together by mutual attraction of electrostatic change and achieve the equilibrium distance apart  due to a balancing short range rupulsion.                                                                                 

where

N_A is the Avogadro constant

M is the Madelung constant, relating to the geometry of the crystal;

z⁺ is the charge number of cation;

z⁻ is the charge number of anion;

q_e is the elementary charge , equal to 1.6022×10⁻¹⁹ C;

ε₀ is the permittivity of free space , equal to 8.854×10⁻¹² C² J⁻¹ m⁻¹;

r₀ is the distance to closest ion; and

n is the Born exponent, a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically                                                              

2.  Experimental determination of lattice energy : Born-Haber cycle                                                                  In 1919, max Born,Fritz Haber proposed the model to determine the lattice energy indirectly, by assuming that the formation of an ionic compound takes place in a series of steps and procedure is known Born Haber cycle. It is based on Hess law and relates the lattice energy of ionic compound to ionization energy, electron affinity and other atomic properties. Born Haber cycle is based on the assumption that, the formation of one mole of crystalline ionic compound,MX can occurs either by the direct combination of M(s) and half  X2(g) or by an alternative process.                                                                                                                                                                               

   Using the Born-Haber Cycle

   The values used in the Born-Haber Cycle are all predetermined changes in enthalpy for the processes described in the section above. Hess' Law allows us to add or subtract these values, which allows us to determine the lattice energy.
   
   
   

   Step 1

   Determine the energy of the metal and nonmetal in their elemental forms. (Elements in their natural state have an energy level of zero.) Subtract from this the heat of formation of the ionic solid that would be formed from combining these elements in the appropriate ration. This is the energy of the ionic solid, and will be used at the end of the process to determine the lattice energy.
   
   

   Step 2

   The Born-Haber Cycle requires that the elements involved in the reaction are in their gaseous forms. Add the changes in enthalpy to turn one of the elements into its gaseous state, and then do the same for the other element.
   
   

   Step 3

   Metals exist in nature as single atoms and thus no dissociation energy needs to be added for this element. However, many nonmetals will exist as polyatomic species. For example, Cl exists as Cl2 in its elemental state. The energy required to change Cl2 into 2Cl atoms must be added to the value obtained in Step 2.
   
   

   Step 4

   Both the metal and nonmetal now need to be changed into their ionic forms, as they would exist in the ionic solid. To do this, the ionization energy of the metal will be added to the value from Step 3. Next, the electron affinity of the nonmetal will be subtracted from the previous value. It is subtracted because it is a release of energy associated with the addition of an electron. 

   *This is a common error due to confusion caused by the definition of electron affinity, so be careful when doing this calculation.
   
   

   Step 5

   Now the metal and nonmetal will be combined to form the ionic solid. This will cause a release of energy, which is called the lattice energy. The value for the lattice energy is the difference between the value from Step 1 and the value from Step 4.                                                                                                                                                         The diagram below is another representation of the Born-Haber Cycle.

                                                                                                                                                 Reference                                                                                                                                                      Wikipidea                                                                                                                                                    Ucdavis chemwiki                                                                                                                      Special thanks to Dasu Paudel

LONG FORM OF PERIODIC TABLE

                              LONG FORM OF PERIODIC TABLE

            Bohr's in 1920 modified the modern periodic table which is named  as long form of periodic table. Hence, it is an improved and extended  form of mendeleev's periodic table and is based on the modern periodic law. It states  that ," the physical and chemical properties of an electron are periodic function of their atomic number."

                Bohr's classification of elements in the periodic table divides the all known elements into different groups and subgroups. According to this classification left portion of periodic table consist of highly electropositive metal, elements right portion consists of highly electronegative known metal, some heavy metals and metalloids and the middle portion consists of transition and inner transition elements.

SIGNIFICANCE OF LONG FORM OF PERIODIC TABLE

Long form of periodic table removes some serious  drawbacks in mendeleev's periodic table and attains superior position in the classification. Some of the significance are;

1.       The arrangement of  element is based on a more fundamental basis, atomic number.

2.       The position of element in certain group or period is related to the electronic  configuration of its atom.

3.       It gives the complete separation between metals and non- metals.

4.       It is divided into four blocks depending upon the valence shell configuration of an atom such as  s,p,d,f   block.

5.       Due the separation of groups into sub-groups, dissimilar elements fall on the different group such as alkali metal and coinage metal.

6.       The position of transition metal element and inner transition metal element is suitable  due to their transitional behavior between s -block and p- block elements.                                                                                       

               DRAWBACKS/LIMITATION

Although it removes more drawbacks of mendeleev's periodic table but yet suffer from the following defects;

1.       Position of Hydrogen;

The position of hydrogen in this periodic table has not been solved completely since the valence shell configuration is same as that of alkali metals but the properties have completely different.

2.       Position of Hellium;

Since the Hellium has the same electronic configuration with alkali earth metal but the properties are similar to nobal gases even the configuration is different.

3.       Position of Lanthanides and Actinides

The Lanthanides and Actinides are given a separate place below the periodic table but can not include in the main body of periodic table.

Afbau principle

                                               Afbau Principle

    The word afbau has been derived from German word and has the meaning building or construction.It states that ,"the electron are filled in an atomic orbital in the order of their increasing energy." According to their principle the electron first enter in the subshell with minimum energy and them in the sub shell with next higher energy.

               The principle takes its name from the German, Aufbauprinzip, "building-up principle", rather than being named for a scientist. In fact, it was formulated by Neils Bohrs  and Wolfgang Pauli  in the early 1920s, and states that:

“

The orbitals of lower energy are filled in first with the electrons and only then the orbitals of high energy are filled.

”

This was an early application of  quantum mechanics to the properties of electron, and explained chemical properties in physical terms. Each added electron is subject to the electric field created by the positive charge of the atomic nucleus and the negative charge of other electrons that are bound to the nucleus. Although in hydrogen there is no energy difference between orbitals with the same principal quantum number n, this is not true for the outer electrons of other atoms.

In the old quantum theory prior to quantum mechanics, electrons were supposed to occupy classical elliptical orbits. The orbits with the highest angular momentum are 'circular orbits' outside the inner electrons, but orbits with low angular momentum (s- and p-orbitals) have high orbital eccentricity, so that they get closer to the nucleus and feel on average a less strongly screened nuclear charge.

                          The relative energy of an orbital is determine by the principle and azimuthal quantum number and popularly known as n+l rule. It has two parts;

1.     The higher value of n+l have higher energy level and lower value have lower energy level. For example;                                                                                       Subshell                                     n+l                                                                                 1s                                           1+0=1                                                                              2s                                           2+0=2                                                                              2p                                           2+1=3                                                                            3s                                           3+0=3                                                                              3p                                           3+1=4                                                                            3d                                           3+2=5                                                                            4s                                           4+0=4                                                                              4p                                           4+1=5                                                                            4d                                           4+2=6                                                                            4f                                            4+3=7                                                                                                                          and so on.                                                                                   Hence,the order of energy level in different orbitals is, 1s<2s<2p<3s<3p<4s<3d<4p<5s<4d and so on. Therefore, the 4s orbital filled before 3d.                      

2.     In case of same value of (n+l), the lower value of n has the lower energy level and higher ones have higher energy level.                                                                            For ex; 2p (2+1=3) orbitals are filled before 3s (3+0=3)                                                          3p(3+1=4) orbitals are filled before 4s (4+0=4)                                                            3d (3+2=5) orbitals are filled before 4p (4+1=5)                                                                                                                                                                                                                            Hence, the lower energy level are better place for the electrons and occupied first.The relative energy of different orbitals can be shown below;                                                                               

1s

           2s           2p

                          3s          3p       3d

                                         4s        4p          4d           4f

                                                                     5s            5p             5d            5f

                                                                                      6s              6p           6d            6f

                                                                                                                                                                                                                                                                                                          and so on.  

                    

Reference                                                                                      

Wikipidea                                                                                     

Dasu Paudel                                                                                  

ionic bond

                                                        Bohr's Atomic Model

          Neil Bohr in 1913 A.D.,formulated on atomic model by based on planks quantum theory of radiation and some classed concept of physician the early 20th century, experiments by Ernest Rutherford  established that atoms consisted of a diffuse cloud of negatively

charged electrons surrounding a small, dense, positively charged nucleus. Given this experimental data, Rutherford naturally considered a planetary-model atom, the Rutherford model of 1911 – electrons orbiting a solar nucleus – however, said planetary-model atom has a technical difficulty. The laws of classical mechanics (i.e. the Larmor formula), predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds. This atom model is disastrous, because it predicts that all atoms are unstable.

Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster. This would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharge have shown that atoms will only emit light (that is, electromagnetic radiation) at certain discrete frequencies.

To overcome this difficulty, Neils Bohrs  proposed, in 1913, what is now called the Bohr model of the atom..This atomic model has following assumptions:

1. Electron revolves arround the nucleus in a selected circular path called orbit.                                                                                                         
                                                                                                                                                                                                                                                            
2. Electrons  doesnt loose or gains energy when revolves around the nucleus. Such a state of electron is called stationary state.Stationary means energy of electron is constant but its motion change with time.The postulate justify about the statibility of atom.
3. The centrifugal force of electron, which tends to pull away electron from its orbit is balanced by electrostatic force of attraction between nucleus and electron,                                                                                       where m_e is the electron's mass, e is the charge of the electron, k_e is coulombs constant and Z is the atom's atomic number.             
4. Electron can revolve only in those orbit in which angular momentum of revolving electron is an integral multiple of h/2π. This postulates shows that the angular momentum is quantized.
5. Electron can absorb or emit energy when electron absorbs energy. It gets excited.The excited of electron/atom is highly unstable, so electron jumps from higher energy level to lower energy level by emitting energy in the form quantum of radiation which can be calculated by using planks's quantum theory of radiation.                                                                                                              where h= planck constant                                                                  
The radius of electron can be determined by using formula:




It also determines the electron's total energy at any radius:

Ionic Bond

    A bond formed by the complete transference of electron from one atom to another is called as electrovalent or ionic bond.It is a type of chemical bond in which the electrostatic atrraction exists between oppositely charged ion. Element which have the tendency to loose the electron is called electropositive element (generally metal ) and the element which have the tendency to gain the electron is called electronegative element ( generally non -metal ) and forms cation and anion respectively.Hence, electrostatic force of attraction exist between two oppositely charged particle ( cation and anion ) is called ionic bonding.
                          To form the ionic bond ,there must be greater difference of electronegativity between two combining molecule.All the ionic compound have some of the character of covalent bonding.Thus, ionic bonding is seen only when the ionic character of atom should be greater than covslent character.Bond with partial or equal character of both ionic and covalent character are called polar covalent bond.        
        Formation of NaCl takes place only when electropositive element Na loose its valence electron and Na+ ion (cation) and the electronegative element Cl- ion accept that electron to forms chloride ion to attain the stable nearest noble gas configuration.

     Ionic compound have high melting and Boiling point. This is due to the strong force of attraction between two oppositely charged particle.Solid Crystalline compound of ionic compound do not conduct heat and electricity due to absence of free electron.

Valence-Shell Electron Pair Repulsion(VSEPR) Theory

            In 1940,Sidgwick and Powell first the theory of valence-shell electron pair repulsion theory and was developed by Gillespie and Nyholm later in 1957.They explain the molecular shape and bond angle more exactly.According to them,geometry of a molecule depends on the number of bonding and non bonding electron pair in a central atom so as to maintain the minimum repulsion between them.These electron pair arrange themself in one orientation of orbitals corresponding to minimum energy and attain a definite shape.
                                       The idea of correlatin between the molecular geometry and the number of valence electrons (both shared and unshared) was originally proposed in 1939 by Ryutaro Tsuchida in Japan, and was independently presented in a Bakerain Lecturein 1940 Nevil Sidgwick and Herbert Powell of the University of oxford In 1957, Ronald Gillespie and Ronald Sydney Nyhlom of University college of London refined this concept into a more detailed theory, capable of choosing between various alternative geometries.
              Rule;
    

• IF the central atom of the molecule is surrounded by only bonding electron pair and not by non bonding electron pair, the geometry of the molecule will be regular as predicted by hybridization.
• When the central atom in a molecule is surrounded by both bond and lone pair, the molecule doesnt have regular shape.
• Presence of lone pair on the central atom cause slight distortion of the bond angle from the ideal shape. The extent of repulsion between different electron pair is in the order of;                            l.p-l.p repulsion> l.p-b.p repulsion>b.p-b.p repulsion
• The magnitude of a repulsion between bonding pairs of electrons depends  on the electronegativity difference between the central atom and other atoms.
• Double bond cause more repulsion than single bond and triple bond cause more repulsion than double bond.                                                                                                                                                                     

Molecule Type	Shape[12]	Electron arrangement†[12]	Geometry‡[12]	Examples
AX2E0	Linear			BeCl2,[1] HgCl2,[1] CO2[11]
AX2E1	Bent			NO− 2,[1] SO2,[12] O3,[1] CCl2
AX2E2	Bent			H2O,[12] OF2[17]
AX2E3	Linear			XeF2,[12] I− 3,[18] XeCl2
AX3E0	Trigonal planar			BF3,[12] CO2− 3,[19] NO− 3,[1] SO3[11]
AX3E1	Trigonal pyramidal			NH3,[12] PCl3[20]
AX3E2	T-shaped			ClF3,[12] BrF3[21]
AX4E0	Tetrahedral			CH4,[12] PO3− 4, SO2− 4,[11] ClO− 4,[1] XeO4[22]
AX4E1	Seesaw (also called disphenoidal)			SF4[12][23]
AX4E2	Square planar			XeF4[12]
AX5E0	Trigonal bipyramidal			PCl5[12]
AX5E1	Square pyramidal			ClF5,[21] BrF5,[12] XeOF4[11]
AX5E2	Pentagonal planar			XeF− 5[14]
AX6E0	Octahedral			SF6,[12] WCl6[24]
AX6E1	Pentagonal pyramidal			XeOF− 5,[13] IOF2− 5[13]
AX7E0	Pentagonal bipyramidal[11]			IF7[11]
AX8E0	Square antiprismatic[11]			IF− 8, ZrF4− 8, ReF− 8
AX9E0	Tricapped trigonal prismatic (as drawn) OR capped square antiprismatic			ReH2− 9[15]

    

•       Reference:
• Dasu Paudel
• Wikipedia
• Advance Inorganic Chemistry