Periodic Trends in Properties of Elements

Periodic Trends in Physical Properties of Elements

Effective Nuclear Charge

• Between the outer most valence electrons and the nucleus of an atom, there exists finite number of shells containing electrons. 
• Due to the presence of these intervening electrons, the valence electrons are unable to experience the attractive pull of the actual number of protons in the nucleus. 
• These intervening electrons act as shield between the valence electrons and protons in the nucleus. 
• Thus, the presence of intervening (shielding) electrons reduces the electrostatic attraction between the protons in the nucleus and the valence electrons because intervening electrons repel the valence electrons. 
• The concept of effective nuclear charge allows us to account for the effects of shielding on periodic properties.
• The effective nuclear charge (Z_eff) is the charge felt by the valence electron. Z_eff is given by Z_eff = Z - s. Where Z is the actual nuclear charge (atomic number of the element) and s is the shielding (screening) constant.

Atomic Radius

An atom has no sharp boundary because the probability of finding an electron never becomes exactly zero at any finite distance. Therefore atomic radius is an operational or effective size - typically defined as the distance of closest approach between nuclei in bonded or nearest-neighbour atoms. Several radii are used depending on the context.

(A) Covalent Radius

The covalent radius (for a single bond) is one-half of the distance between the centres of two identical atoms joined by a single covalent bond. Covalent radii are most useful for non-metals and are commonly used to estimate bond lengths.

For homoatomic diatomic molecules,

For near-homonuclear (heterodiatomic with similar electronegativities),

For heteronuclear diatomic molecules with a significant electronegativity difference, Stevenson and Schomaker gave an empirical correction:

where X_A and X_B are electronegativities of atoms A and B respectively.

Example . Calculate the bond length of C-X bond, if C-C bond length is 1.54 Å, X-X bond length is 1.00 Å and electronegativity values of C and X are 2.0 and 3.0 respectively.

Sol.
C-C bond length = 1.54 Å
r_C = 1.54/2 = 0.77 Å
r_X = 1.00/2 = 0.50 Å
Using the Stevenson-Schomaker correction,

d_C-X = r_C + r_X - 0.09 (X_X - X_C)

d_C-X = 0.77 + 0.50 - 0.09(3 - 2) = 1.27 - 0.09 = 1.18 Å

Thus the C-X bond length is 1.18 Å.

(B) van der Waals Radius (Collision Radius)

The van der Waals radius is one-half of the internuclear distance between two non-bonded adjacent atoms in neighbouring molecules in the condensed phase (usually solid or liquid). It describes how close two atoms can approach when they are not chemically bonded.

van der Waals radii depend on how atoms are packed in the solid state and are not applicable to metallic bonding.

Comparison between covalent and van der Waals radii:

• van der Waals interactions are weak and the internuclear distances between non-bonded atoms are generally larger than those in covalently bonded atoms; therefore van der Waals radii are larger than covalent radii.
• Covalent bonding involves orbital overlap that brings nuclei closer together, so covalent radii are smaller.

(C) Metallic Radius (Crystal Radius)

The metallic radius is one-half of the distance between the nuclei of two adjacent metal atoms in a metallic crystal lattice. Metallic radii are usually larger than covalent radii because metallic bonding is delocalised and generally weaker than covalent bonding, producing longer internuclear distances.

For example :  

• The atomic radius of noble (inert) gases is usually given as the van der Waals radius (largest in a period) since they exist as monoatomic species; their van der Waals radii increase down the group.

• In the first transition series, covalent radii generally decrease across the series because Z increases while the added d-electrons do not shield the nuclear charge effectively; near the end there may be slight increases. Radii of Cr to Cu are very similar due to progressive addition of d-electrons which screen the 4s electrons.

• The lanthanide contraction is the steady decrease of ionic and atomic radii across the lanthanide series (4f-electron filling). It reduces the expected size increase between transition metals of successive periods; for example, covalent and ionic radii of Nb (5th period) and Ta (6th period) are almost the same because f-electrons provide poor shielding.

Ionic Radius

The ionic radius is the effective distance from the nucleus of an ion up to which it has an influence in an ionic bond. Ionic radii depend on the charge and the electron configuration of the ion.

Example: Na and Cl

• Ionic sizes increase down a group for ions of the same charge 
  Li⁺ < Na⁺ < K⁺ < Rb⁺ Be²⁺ < Mg²⁺ < Ca²⁺ < Sr²⁺ F^- < Cl^- < Br^- < I^- 
• d and f orbitals shield nuclear charge poorly. As a result, sizes drop unexpectedly for elements just after filling d or f shells; this contributes to lanthanide contraction (e.g., Zr and Hf have nearly identical radii).
• Isoelectronic species are ions/atoms with the same number of electrons but different nuclear charges. For example N^3- , O^2-, F^-, Ne, Na⁺ , Mg²⁺ and Al³⁺ all have 10 electrons. Within an isoelectronic series, ionic radius decreases as nuclear charge increases (greater attraction pulls electrons closer).

• Pauling's empirical formula for ionic radius is given in the input as an illustrative relation.
• Examples of isoelectronic series: (i) S^2- Cl^- K⁺ Ca⁺² Sc⁺³   (ii) SO₂,  NO₃^-, CO₃^2-   (iii) N₂, CO,  CN^-      (iv) NH₃, H₃O^-

Ionisation Enthalpy (Ionisation Energy)

Ionisation enthalpy (IE) or ionisation energy is the energy required to remove an electron from an isolated gaseous atom (or ion) to form a cation. For successive removals we have first ionisation enthalpy IE₁, second IE₂, third IE₃, etc.

General trend: IE₁ < IE₂ < IE₃ ... because as electrons are removed the remaining electrons are held more strongly by the nucleus.

• Units of ionisation energy: kJ mol-1, kcal mol-1, or eV per atom (1 eV = 96.485 kJ mol-1 approximately, or for energy comparisons 1 eV ≈ 23.06 kcal mol-1 is used in examples).
• Factors influencing ionisation energy:
• Atomic size: IE decreases as atomic size increases because valence electrons are farther from the nucleus and less strongly held.
• Nuclear charge: IE increases with increasing nuclear charge (more protons attract electrons more strongly).
• Shielding effect: Inner electrons screen valence electrons from nuclear charge; increased shielding lowers IE.
• Penetration: Electrons in orbitals with better penetration (s > p > d > f) are held more tightly; for orbitals of the same principal quantum number IE increases with penetration.
• Electronic configuration: Atoms with fully filled or half-filled subshells have extra stability; IE values may be higher than expected (e.g., Be IE₁ > B IE₁ because Be has 2s2 configuration).
  

As noble gases have completely filled electronic configuration, they have highest ionisation energies in their respective periods.

Elements with high ionisation energies are less electropositive (less metallic); decreasing IE corresponds to increasing metallic (electropositive) character, greater reducing power and higher chemical reactivity for metals (exceptions exist, e.g., Li among alkali metals).

Example 3. First and second ionisation energies of Mg(g) are 740 and 1450 kJ mol-1. Calculate percentage of Mg+ (g) and Mg2+ (g), if 1 g of Mg(g) absorbs 50 kJ of energy.

Sol.

Sol. Number of moles of 1g of Mg =  1/24 = 0.0417

Energy required to convert Mg(g) to Mg⁺(g) = 0.0417 x 740 = 30.83 kJ
Remaining energy = 50 - 30.83 = 19.17 kJ
Number of moles of Mg²⁺ formed =  17.19/1450 = 0.0132

Thus, remaining Mg+ will be = 0.0417 -  0.0132 = 0.0285

% Mg⁺ = (0.0285/ 0.0417) × 100 = 68.35%

% Mg⁺ = 100 - 68.35 = 31.65%

Electron Gain Enthalpy (Electron Affinity)

Electron gain enthalpy (electron affinity, EA) is the enthalpy change when an electron is added to a neutral gaseous atom to form an anion. It measures the ease with which an atom accepts an electron.

Electron addition may be exothermic (negative EA) or endothermic (positive EA). The addition of a second electron to a singly charged anion is usually endothermic due to electrostatic repulsion.

EA(i) (first electron gain) is typically exothermic, but EA(ii) (second electron gain) is endothermic for most atoms.

• Group 17 elements (halogens) have large negative electron gain enthalpies because they achieve noble gas configuration by gaining one electron.
• Noble gases have large positive (or less negative) electron gain enthalpies because the incoming electron must occupy a new shell.
• O and F have less negative EA than S and Cl respectively because in the n = 2 shell added electrons experience stronger electron-electron repulsion in the smaller volume.
• Alkaline earth metals have small or positive electron gain enthalpies as the extra electron must enter a filled s-orbital.
• Across a period left to right EA generally becomes more negative (higher tendency to gain electrons) due to increasing Z_eff. Down a group EA becomes less negative (weaker tendency) because added electron would be farther from nucleus.
• (i) Electron affinity

  (ii) Electron affinity ∞ Effective nuclear charge (z_eff)

  (iii) Electron affinity

Key relations noted in the input:

• Electron affinity correlates with effective nuclear charge Z_eff.
• Stability of half-filled and completely filled subshells lowers the tendency to accept an extra electron; EA values may be less negative in those cases.

Example 4. How many Cl atoms can you ionise in the process [reaction shown in image] if the energy liberated for the process [image] for one Avogadro number of atoms. Given IP = 13.0 eV and EA = 3.60 eV.

Sol.
Let n atoms be ionised. 6.02 × 10²³ × EA = n × IP

Example 5. The first ionisation potential of Li is 5.4 eV and the electron affinity of Cl is 3.6 eV. Calculate ΔH in kcal mol-1 for the reaction [image].

Sol.
The overall reaction is written into two partial equations 

= 1.8 × 23.06 kcal mol-1 = 41.508 kcal mol-1

Example 6. For the gaseous reaction [image] the value was calculated to be 19 kcal under conditions where cations and anions were prevented by electrostatic separation from combining with each other. The ionisation potential of K is 4.3 eV. What is the electron affinity of F?

Sol.

Example 7. The electron affinity of chlorine is 3.7 eV. How much energy in kcal is released when 2 g of chlorine is completely converted to Cl- ion in the gaseous state? (1 eV = 23.06 kcal mol-1)

Sol.

35.5 3.7 × 23.06 kcal

l .'. Energy released for conversion of 2 g gaseous chlorine into CI^- ions

 × 2 = 4.8 kcal

Hydration Enthalpy

Hydration enthalpy (hydration energy) is the energy released when one mole of gaseous ions becomes surrounded by water molecules and forms hydrated ions in aqueous solution. It is an important component of solvation and helps determine solubility and reaction energetics in aqueous phase.

• Hydration enthalpy is proportional to the charge density of the ion: smaller ions with higher charge have larger (more negative) hydration enthalpies.
• Hydration enthalpy decreases down a group because ionic size increases, reducing ion-water interactions.
• For example, Mg²⁺ has a higher hydration enthalpy than Na+ because Mg²⁺ has higher charge density.
• Hydration process is exothermic; large hydration enthalpies stabilise solvated ions and affect solubility trends (e.g., solubility of Group 2 hydroxides changes down the group because lattice enthalpy and hydration enthalpy change at different rates).

Note: Hydration enthalpy decreases down the group because ions become larger and their charge density decreases; lattice enthalpy often decreases faster (due to r-1 dependence in many lattice energy approximations), so overall solubility trends result from the balance between lattice and hydration enthalpies.

Lattice Enthalpy

Lattice enthalpy is the energy associated with formation of one mole of an ionic solid from its gaseous ions. It is a measure of the strength of the ionic lattice and strongly influences melting point, hardness, solubility and other physical properties of ionic compounds.

• Lattice enthalpy is large and exothermic when oppositely charged ions are brought together to form a crystal; its magnitude depends on the charges and sizes of the ions and on the crystal structure.
• High lattice enthalpy generally means low solubility and high melting point; the competition between lattice enthalpy and hydration enthalpy determines solubility in water.

Electronegativity

Electronegativity is the tendency of an atom (in a bonded molecule) to attract shared electrons towards itself. It is a dimensionless quantity and cannot be measured directly; several scales have been proposed to quantify it.

The magnitude of electronegativity depends on ionisation potential and electron affinity; higher IE and more negative EA typically indicate higher electronegativity.

• Electronegativity generally decreases with increasing atomic size (the valence electrons are farther from the nucleus).
• Electronegativity generally increases with increasing effective nuclear charge and with increasing oxidation state (higher positive charge on an atom increases its polarising power and electronegativity).

No single direct experimental method exists to determine electronegativity; common scales are:

(a) Pauling Scale

Linus Pauling introduced a semi-empirical scale based on bond dissociation energies. The difference in Pauling electronegativities is related to extra stabilization (ionic character) in an A-B bond compared to the average of A-A and B-B bonds.

(b) Mulliken Scale

Mulliken proposed that electronegativity can be taken as the arithmetic mean of ionisation energy (IE) and electron affinity (EA):

When IE and EA are in electron-volts, Mulliken values may be converted to the Pauling scale by an empirical factor (Mulliken values are larger numerically by a factor ≈ 2.8 compared to Pauling values).

(c) Allred-Rochow Scale

Allred and Rochow defined electronegativity as the electrostatic force exerted by the nucleus on valence electrons, proportional to effective nuclear charge divided by the square of an appropriate radius:

where Z_effective is the effective nuclear charge and r is the covalent radius (in Å).

• Francium (Fr) has a slightly higher effective nuclear charge compared to cesium (Cs), resulting in subtle differences in some scales; however, both are among the least electronegative elements.
• Noble gases (in their ground state, isolated atoms) are often assigned zero electronegativity in Pauling terminology since electronegativity is primarily a property of bonded atoms.

Example 8. Ionisation potential and electron affinity of fluorine are 17.42 eV and 3.45 eV respectively. Calculate the electronegativity of fluorine according to Mulliken.

Sol.

When both IP and EA are taken in eV, Mulliken electronegativity = (IP + EA) / 2.

Applications of Electronegativity

(I) Nomenclature. In binary compounds of two non-metals, the more electronegative element is named last with the suffix -ide. The less electronegative element is named first.

Example 9. Write correct formula and name of the following:

(a) ICl or ClI (b) FCl or ClF (c) BrCl or ClBr (d) BrI or IBr (e) OF2 or F2O (f) Cl2O or OCl2

Sol.
(a) ICl : Iodine chloride (I+ Cl-)
(b) ClF : Chlorine fluoride (Cl+ F-)
(c) BrCl : Bromine chloride (Br+ Cl-)
(d) IBr : Iodine bromide
(e) OF2 : Oxygen difluoride (oxygen is less electronegative than fluorine so O is written first)
(f) Cl2O : Dichlorine monoxide

(II) Nature of bond. If the difference of electronegativities is ≳ 1.7 (Pauling criterion) the bond is largely ionic; if the difference is less, the bond is largely covalent. (HF is an exception: although Δχ ≈ 1.9, the bond is largely covalent.)

(III) Metallic and nonmetallic character. Metals have low electronegativity; nonmetals have high electronegativity.

(IV) Partial ionic character in covalent bonds. Difference in electronegativities produces partial ionic character. Hanni and Smith provided an empirical relation to estimate percentage ionic character from Δχ.

Percentage ionic character =

where Δ = X_A - X_B, with X being electronegativity values.

(V) Bond length. Increasing difference of electronegativities generally shortens bond length due to increased bond polarity (Shoemaker and Stephenson equation referenced in the input).

(VI) Bond strength and stability. Bond strength A-B increases with increasing difference of electronegativities; for example, H-F > H-Cl > H-Br > H-I.

Example 10. Electronegativity is highest for which?
(1) -CH₃(sp₃)
(2) H₂C = CH₂(sp₂)  
 (3) CH ≡ CH(sp)
 (4) Equal in all 

Ans. (3)

Ex.11 CF₃NH₂ is not a base, whereas CH₃NH₂ is a base. What is the reason ?

Sol. Fluorine atoms are strongly electronegative and withdraw electron density from nitrogen through inductive effect, reducing availability of the lone pair on N for protonation; hence CF3NH2 is a much weaker base than CH3NH2.

Example 12. OF₂ is called oxygen difluoride, whereas Cl₂O is called dichlorine monoxide. Why?

Sol. In OF₂, fluorine is more electronegative than oxygen, so O carries positive character and is written first. In Cl₂O, oxygen is more electronegative than chlorine, so Cl appears first as positive centres and O last as negative centre.

Example 13. Calculate electronegativity of fluorine from the following data:
E_{H - H} = 104.2 kcal mol-1,
E_F-F = 36.6 kcal mol-1
E_H-F = 134.6 kcal mol^-1,
X_H = 2.1 

Sol.
Using Pauling's equation relating bond energies,

Example 14 (repeat of Ex.7 in input). The electron affinity of chlorine is 3.7 eV. How much energy in kcal is released when 2 g of chlorine is completely converted to Cl- ion in a gaseous state? (1 eV = 23.06 kcal mol-1)

Sol.

35.5 3.7 × 23.06 kcal

∴ Energy released for conversion of 2 g gaseous chlorine into Cl- ions

 × 2 = 4.8 kcal

Example 15 (Pauling repeat). Calculate electronegativity of fluorine from: E_H-H = 104.2 kcal mol-1, 
E_F-F = 36.6 kcal mol-1, 
E_H-F = 134.6 kcal mol-1, 
X_H = 2.05.

Sol.

From (i)

 = = 1.5534

x_F = x_H + 1.4434 = 2.05 + 1.5534 = 3.6034

METALLIC PROPERTY

Metals tend to lose electrons to form cations; this electropositive tendency defines their metallic character. Trends in metallic character follow ionisation energy and atomic size: metallic character increases where ionisation energy is low and size is large.

Oxides

Oxygen reacts with most elements (exceptions: noble gases and some noble metals like Au, Pd, Pt under ordinary conditions) to form oxides. Oxides vary in bonding and properties according to the element:

• Metallic oxides (e.g., most Group 1 and 2 oxides) are ionic (O2-) and are basic; many dissolve in water to form hydroxides.
• Peroxides (contain O2²-, e.g., Na2O2) and superoxides (contain O²-, e.g., KO2) are formed by heavier alkali metals under certain conditions.
• Oxides of non-metals are usually covalent and acidic (e.g., CO2, SO3, P4O10), producing acids on reaction with water.

The tendency of Group 1 (alkali) metals to form oxygen-rich compounds (peroxides, superoxides) increases down the group due to increasing cation radius and decreasing charge density. In Group 2, heavier members (Ca, Sr, Ba) form peroxides under appropriate conditions (Be does not).

Oxides of IA and IIA dissolve in water forming basic solution where as other oxides do not dissolve in water.

Oxygen combines with many non-metals to form covalent oxides such as CO, CO₂, SO₂, P₄O₁₀, Cl₂O₇ etc.

Examples of nonmetal oxide hydrolysis:

P₄O₁₀ + 6H₂O → 4H₃ PO4 ;
SO₃ + H₂O → H₂SO₄ : Cl₂O₇ + H₂O → 2HClO₄

• Across a period the nature of oxides changes from basic (left) → amphoteric (middle) → acidic (right).
• Down a group oxides become more basic (or less acidic).
• Metalloids often form amphoteric oxides (e.g., Al2O3, ZnO, SnO)

 Strongly acidic CO, N₂O, NO and H₂O are neutral oxides.

Periodic Trends in Chemical Properties of Elements

Oxidation State (Valency)

Oxidation state (or valency in simple contexts) is the formal charge that an atom would have if all bonds were considered completely ionic. It can be inferred from electronic configuration or by counting electrons in the valence shell.

• Valence electrons are those in the outermost shell and largely determine typical valency.
• For s- and p-block elements, valency is often equal to the number of valence electrons or 8 minus that number (in simple compounds).
• For d- and f-block elements, valency involves outer s and inner d (and sometimes f) electrons; common oxidation states are +2 and +3 for many transition metals.

Variation of Oxidation State within a Period

Across a period left to right the number of valence electrons increases from 1 to 8. When elements combine with hydrogen or oxygen, oxidation states vary; for example, in Na2O oxygen is -2 and Na is +1, whereas in F2O oxygen is +2 and fluorine is -1 because fluorine is more electronegative than oxygen.

Variation of Oxidation State within a Group

Down a group the number of valence electrons remains the same so elements of a group commonly show similar valences (e.g., alkali metals are typically +1, alkaline earths +2).

Guidelines for Assigning Oxidation States

• Oxidation state of an element in its elemental form (H2, O2, N2, P4, S8, Fe(s), etc.) is zero.
• Oxygen is usually -2; in peroxides (e.g., H2O2, Na2O2) oxygen is -1; in superoxides O2- per oxygen average is -½ per O atom.
• Hydrogen is usually +1 but is -1 in metal hydrides (e.g., NaH, LiH).
• Halogens are usually -1 when combined with less electronegative elements, except when bonded to oxygen or other halogens where higher positive oxidation states are possible.
• Alkali metals are +1; alkaline earth metals are +2 in their common compounds.

Anomalous Periodic Properties of Second Period Elements

The elements of the second period (Li, Be, B, C, N, O, F) show several anomalous properties compared with the heavier elements of the same groups. These anomalies arise mainly from small size, high electronegativity and absence of inner d/f orbitals.

Observed anomalies and reasons:

• Small atomic/ionic sizes, leading to higher polarising power and stronger covalent bonding tendencies (e.g., Li and Be form covalent compounds more readily than heavier group mates).
• High electronegativity compared with heavier congeners.
• Large charge/radius ratio (high polarising ability) causes greater covalency and formation of compounds with significant covalent character.
• Limited availability of orbitals for bonding: second-period elements use only 2s and 2p orbitals (four valence orbitals), whereas third-period elements can utilize 3d in addition to 3s and 3p, allowing higher coordination numbers and higher oxidation states (e.g., Al vs B in fluoride complexes: [BF4]- vs [AlF6]3-).
• Diagonal relationships: second-period elements may resemble the next heavier element of the next group (e.g., Li ≈ Mg, Be ≈ Al) in some properties because of compensating effects of charge/radius and electronegativity.