Inorganic chemistry , For bsc first year For bsc Hons For bsc Hons chemistry For bsc chemistry For bsc Hons second semester BTech chemical sciences

1. The lattice enthalpy cannot be measured directly and so we make use
of other known enthalpies and link them together with an enthalpy
cycle.
This enthalpy cycle is the Born-Haber cycle. This cycle devised by
Born and Haber in 1919 relates the lattice energy of a crystal to other
thermochemical data.
What do we mean by lattice enthalpy?
For an ionic compound the lattice enthalpy is the enthalpy change
when one mole of solid in its standard state is formed from its ions in
the gaseous state.
The enthalpies of sublimation and dissociation and the ionization
energy are positive since energy is supplied to the system. The
electron affinity and lattice energy ate negative since energy is
evolved in these processes.

3. According to Hess's law, the overall energy change in a process depends only on
the energy of the initial and final states and not on the route taken. Thus the
enthalpy of formation of ΔHf is the algebraic sum of the terms going round the
cycle.
∆𝐻𝑓 = ∆𝐻𝑠 + 𝐼 +
1
2
∆𝐻𝑑 + 𝐸 + 𝑈
E = -348.6 kJmol-1
381.2 = +108.4 + 495.4 + 120.9 + 𝐸 − 757.3
For NaCl,
It is useful to know the lattice energy, as a guide to the solubility of the crystal.
When a solid dissolves, the crystal lattice must be broken up (which requires that
energy is put in). The ions so formed are solvated (with the evolution of energy).
When the lattice energy is high a large amount of energy is required to break the
lattice. It is unlikely that the enthalpy of solvation will be big enough (and evolve
sufficient energy to offset this), so the substance will probably be insoluble.

4. When a metal is immersed in water, or a solution containing its -own ions, the metal
tends to lose positive metal ions into the solution. Thus the metal acquires a negative
charge.
Standard Electrode Potential and Electrochemical Series
𝑀𝑛+
ℎ𝑦𝑑𝑟𝑎𝑡𝑒𝑑 + 𝑛𝑒 ↔ 𝑀(𝑠𝑜𝑙𝑖𝑑)
The tendency of an electrode to gain or loose electron when it is in contact with its
own solution is called „electrode potential‟. Tendency to gain electron is called
Reduction potential while tendency to loose electron is called Oxidation Potential.
It is not possible to determine experimentally the potential of a single electrode, it is
only the difference of potential between two electrodes that we can measure. The
standard hydrogen electrode is used for this purpose whose potential is arbitrarily
fixed to zero.
Standard Hydrogen Electrode:
Platinized platinum electrode which is saturate with hydrogen at one atmosphere
pressure and immersed in a solution of H3O+ ions at unit activity (1M concentration).

5. • If the elements are arranged in order of increasing standard electrode potentials. the
resulting Table is called the electrochemical series.
Electrochemical Series:
• In the electrochemical series the most electropositive elements are at the top and the least
electropositive. at the bottom.
• The greater the negative value of the potential. the greater isthe tendency for a metal to
ionize. Thus a metal high in the electrochemical series will displace another metal lower
down the series from solution.
• For example, iron is above copper in the. electrochemical series. and scrap iron is
sacrificed.to displace Cu2+ ions from solution of CuSO4 in the recovery of metallic copper.
Fe + Cu2+ Fe2+ + Cu
Redox couple Ox/Red Cu2+/Cu

6. • The potential suggests if the reaction is possible or not but does not suggest the kinetics of
the reaction (rate of reaction).
• The spontaneous nature of reaction can easily be predicted.
∆𝐺 = −𝑛𝐹𝐸°
ΔG = changes in Gibb‟s free energy
n = valency of the ions
F = Faraday constant
E⁰ = standard electrode potential
ΔG = negative- spontaneous
ΔG = positive- nonspontaneous
Energy Cycle for Electrode Potential:
Electrolysis: “The substances whose aqueous solution undergo decomposition into ions when
electric current is passed through them are known as electrolytes and the whole process is
known as electrolysis or electrolytic decomposition.”
Here there is conversion of electrical energy into chemical energy i.e., electrical energy is
supplied to the electrolytic solution to bring about the redox reaction (i.e., electrolysis) which
is non- spontaneous and takes place only when electrical energy is supplied.

8.  However, hydrogen and other gases often require a considerably higher voltage than the
theoretical potential before they discharge. For hydrogen, this extra or over-voltage may be
0.8 volts, and thus it is possible to electrolyse zinc salts in aqueous solution.
 When a solution is electrolysed the externally applied potential must overcome the
electrode potential. The minimum voltage necessary to cause deposition is equal and
opposite in sign to the potential between the solution and the electrode.
 Elements low down in the series discharge first; thus Cu2+ discharges before H+, so copper
may be electrolysed in aqueous solution.
Several factors affect the value of the standard potential. The conversion of M to M+ in
aqueous solution may be considered in a series of steps:
1. sublimation of a solid metal
2. Ionization of a gaseous metal atom
3. Hydration of a gaseous ion
These are best considered in a Born-Haber type of cycle

9. The enthalpy of sublimation and the ionization energy are positive since energy must be put
into the . system, and the enthalpy of hydration is negative since energy is evolved. Thus
𝑬 = +∆𝑯𝒔 + 𝑰 + ∆𝑯𝒉

10. Why Group I and II metals are more reactive as compared to transition metal ions?
Consider first a transition metal; Most transition metals have high melting points: hence the
enthalpy of sublimation is high. Similarly they are fairly small atoms and have high ionization
energies. Thus the value for the electrode potential E is low; and the metal has little tendency
to form ions: hence it is unreactive or noble.
In contrast the s-block metals (Groups I and II) have low melting points (hence low
enthalpies of sublimation), and the atoms are large and therefore have low ionization
energies. Thus the electrode potential E is high and the metals are reactive.
The most powerful oxidizing agents have a large positive oxidation potential and strong
reducing agents have a large negative potential.

11. Oxidation-Reduction Reactions:
Oxidation is the removal of electrons from an atom, and reduction is the addition of electrons
to an atom.
Corrosion and Galvanization
Galvanized iron is iron which has been coated with zinc to prevent rusting.
Consider the corrosion that may occur when a sheet of galvanized is scratched.
Standard potential and half cell reaction for both the metals
𝐹𝑒2+
+ 2𝑒 → 𝐹𝑒
𝑍𝑛2+
+ 2𝑒 → 𝑍𝑛
E⁰= -0.44 volts
E⁰= -0.76 volts
When in contact with water. either metal might be oxidized and lose metal ions, so we
require the reverse reactions, and the potentials for these are called oxidation potentials, and
have the same magnitude but the opposite sign to the reduction potentials.

12. Plainly, since Zn - Zn2+ produces the largest positive E⁰ value, and since
ΔG = -nFE⁰
it will produce the largest negative ΔG value. Thus it is energetically more favourable for the
Zn to dissolve, and hence the Zn will corrode away in preference to the Fe.
It is possible that when the galvanized steel is scratched, the air may oxidize some iron. The
Fe2+ so produced is immediately reduced to iron by the zinc, and rusting does not occur.
Thus the coating of zinc serves two purposes - first it covers the iron and prevents its
oxidation (rather like a coat of paint) and second it provides anodic protection. ·
• What species will oxidize or reduce.
• It gives an idea about the stability of oxidation state with respect to solvent.
• It suggests the possibility of disproportionation.

13. A great-deal of useful information about an element can be shown by the appropriate half
reactions and reduction potentials. Consider some half reactions involving iron:
Fe (VI), Fe(III), Fe(II), Fe(0)
Materials which are generally accepted as oxidizing agents have E⁰ values above +0.8 volts,
those such as Fe3+→Fe2+ of about 0.8 volts are stable (equally oxidizing and reducing), and
those below +0.8 volts become increasingly reducing.

14. 𝐹𝑒3+ + 𝑒 → 𝐹𝑒2+
E⁰= +0.77 volts
𝐹𝑒2+
+ 2𝑒 → 𝐹𝑒 E⁰= -0.47 volts
ΔG = -1 (+0.77)F = -0.77F
ΔG = -2 (-0.47)F = +0.94F
𝐹𝑒3+
+ 3𝑒 → 𝐹𝑒
ΔG = +0.17F
Now we can calculate E⁰ using the formula for Gibb‟s free energy
∆𝐺 = −𝑛𝐹𝐸0
𝐸0
= −
∆𝐺
𝑛𝐹
= −
0.17𝐹
3𝐹
= −0.057𝑉

15. One of the most important facts which can be obtained from a reduction potential diagram is
whether any of the oxidation states are unstable with regard to disproportionation.
Disproportionation is where one oxidation state decomposes, forming some ions in a higher
oxidation state, and some in a lower oxidation state. This happens when a given oxidation
state is a stronger oxidizing agent than the next highest oxidation state and this situation
occurs when a reduction potential on the right is more positive than one on the left.
𝐶𝑢+ + 𝑒 → 𝐶𝑢 E⁰= +0.50volts
𝐶𝑢+
→ 𝐶𝑢2+
+ 𝑒 E⁰= -0.15volts
ΔG = -1 (+0.50)F = -0.50F
ΔG = -1 (-0.15)F = +0.15F
2𝐶𝑢+ → 𝐶𝑢 + 𝐶𝑢2+ ΔG = -0.35F
Example1:
+0.35

16. Now we can calculate E⁰ using the formula for Gibb‟s free energy
∆𝐺 = −𝑛𝐹𝐸0
𝐸0 = −
∆𝐺
𝑛𝐹
= −
−0.35𝐹
𝐹
= +0.35𝑉
Example2:
+IV
+V
+VI +III 0
+IV
+V
+VI +III 0
1.74V
1.726V

17. Example3:
Detailed calculation for both the cases was done in class.

18. The lattice energy ( U) of a crystal is the energy evolved when one gram molecule of the crystal
is formed from gaseous ions.
Lattice energy is defined as the energy required to separate a mole of an ionic solid into
gaseous ions.
Lattice energy cannot be measured empirically, but it can be calculated using electrostatics or
estimated using the Born-Haber cycle.
Theoretical values for lattice energy may be calculated. The ions are treated as point charges,
and the electrostatic ( coulombic) energy E between two ions of opposite charge is calculated:
𝐸 = −
𝑧+𝑧−𝑒2
𝑟
where
z+ and z- are the charges on the positive and negative ions
e is the charge on an electron
r is the inter-ionic distance

19. For more than two ions the electrostatic energy depends on the number of ions and also on A
their arrangement in space. For one mole the attractive energy is:
𝐸 = −
𝑁0𝐴𝑧+𝑧−𝑒2
𝑟
N₀is the Avogadro constant - the number of molecules in a mole. Which has the value 6. 023 ×
1023 mol-1
A is the Madelung constant, which depends on the geometry of the crystal.

20. • When the inter-ionic distance becomes small enough for the ions to touch, they begin to
repel each other. This repulsion originates from the mutual repulsion of the electron clouds
on the two atoms or ions.
• The repulsive forces increase rapidly as r decreases. The repulsive force is given by B/rn
where B is a constant that depends on the structure, an n is a constant called the Born
exponent. For one gram molecule the total repulsive force is (N0 B)/rn. The Born exponent
may be determined from compressibility measurements.
• The Born exponent value varies from 5-12, however chemists use a value of 9.
The total energy holding the crystal together is U the lattice energy. This is the sum of the
attractive and the repulsive forces.
𝑈 = −
𝑁0𝐴𝑧+𝑧−𝑒2
𝑟
+
𝑁0𝐵
𝑟𝑛
Attractive forces Repulsive forces
(A is the Madelung constant and B is a repulsion coefficient, which is constant which is
approximately proportional to the number of nearest neighbours.)

21. The equilibrium distance between ions is determined by the balance between the attractive and
repulsion terms. At equilibrium, dU/dr = 0, and the equilibrium distance r = r₀
𝑑𝑈
𝑑𝑟
=
𝑁0𝐴𝑧+𝑧−𝑒2
𝑟₀2
−
𝑛𝑁0𝐵
𝑟₀𝑛+1
= 0
Rearranging this gives an equation for the repulsion coefficient B.
Substituting the value of B in the formula for lattice energy
𝑈 = −
𝑁0𝐴𝑧+
𝑧−
𝑒2
𝑟₀
1 −
1
𝑛
This equation is called the Born-Lande equation. It allows the lattice energy to be
calculated from a knowledge of the geometry of the crystal, and hence the Madelung
constant, the charges z+ and z-, and the interionic distance.
When using. SI units, the equation takes the form:
𝑈 = −
𝑁0𝐴𝑧+
𝑧−
𝑒2
4𝜋𝜀₀𝑟₀
1 −
1
𝑛
where e₀ is the permittivity of free space = 8.854 x 10-12 Fm -1

22. Factors affecting Lattice Energy:
 The lattice becomes stronger (i.e. the lattice energy U becomes more negative), as r the
interionic distance decreases. U is proportional to 1/r.
 The lattice energy depends on the product of the ionic charges, and U is proportional to (z+
. z-).
 There are two opposing factors in the equation. Increasing the inter-ionic distance r reduces
the lattice energy. It is .almost impossible to change r without changing the structure, and
therefore changing the Madelung constant A. Increasing A increases the lattice energy:
hence the· effects of changing rand A may largely cancel each other.

23. For a change of coordination number from 6 (NaCl structure} to 8 (CsCl structure) the inter-
ionic distance increases by 3.7%, and the Madelung constants (NaCl A = 1.74756, and CsCl A
= 1.76267) change by only 0. 9% . Thus a change in coordination number from 6 to 8 would
result in a reduction in lattice energy, and in theory the NaCl structure should always be more
stable than the CsCI structure. In a similar way reducing the coordination number from 6 to 4
decreases r by 4.9%. The decrease in A is 6.1% or 6.3% (depending on whether a zinc blende
or wurtzite structure is formed), but in either case it more than compensates for the change in r,
and in theory coordination number 6 is more stable than 4.
Reference:
1.Basic Inorganic Chemistry, F. A Cotton, G. Wilkinson, and Paul L. Gaus, 3rd
Edition (1995), John Wiley & Sons, New York.
2.Concise Inorganic Chemistry, J. D. Lee, 5th Edition (1996), Chapman & Hall, London.