Periodic Properties: Detailed Notes

Periodic Properties

Atomic Size

Definition: The size of an atom is the distance of the outermost electron or the most probable distance of the outermost electron from the nucleus.
General Variation:
- Down a Group: Atomic size increases due to the addition of more electron shells.
 - Example:
 - H < Li < Na < K < Rb < Cs
- Across a Period (Left to Right): Atomic size decreases because the number of shells remains the same, but the effective nuclear charge increases, leading to size contraction.
 - Example (2nd period):
 - Li > Be > B > C > N > O > F

Effective Nuclear Charge ( $Z_{eff}$ )

Formula: $Z_{eff} = Z - \sigma$
- $Z$ = atomic number
- $\sigma$ = shielding constant / screening constant

Shielding Effect

Definition: The phenomenon where inner electrons (lower principal quantum number, $n$ ) reduce the force of attraction of the nucleus on outer electrons (higher $n$ ).
Explanation: An electron closer to the nucleus diminishes the attractive pull of the nucleus on more distant electrons.
Influence of Orbital Shape:
- The shape of the orbital determines its shielding effect.
- Order of shielding effect: s > p > d > f
- The s orbital, being spherically symmetrical, has the highest shielding effect.
Penetration:
- Definition: The ability of an electron to get close to the nucleus.
- For a given quantum number $n$ , the s orbital has maximum shielding effect, hence it would be lying closest to the nucleus with maximum penetrating power.

Force of Attraction

Single-electron system (e.g., Li $^{2+}$ ):
- $F = k \frac{Ze^2}{r^2}$
Multiple-electron system ( $\geq$ 2) (e.g., Li $^{3+}$ ):
- F < k \frac{Ze^2}{r^2}
- Reason: Inner electrons shield the outer electrons from the full nuclear charge.

General Exceptions to the Above Trend

D-Block Contraction

The size of Ga (Gallium) is found to be smaller than that of Al (Aluminum) because Ga has 31 protons exerting an attractive force on the 4th shell.
There are 10 electrons in the d orbital which have a very poor shielding effect.
The attractive force on the 4th shell in Ga becomes very high, resulting in size contraction, also known as d-block contraction.

Lanthanide Contraction

The size of 4d series elements is larger than 3d series elements.
The size of 5d series & 4d series elements from group 4 are almost similar.
Zr & Hf are even referred to as twin elements due to similarity in their properties.
In groups 1, 2, and 3 the size variation is normal (increases on moving down the group).

F Block

Analogy:
- d block: 31 protons, attractive force on 4th shell, 10 electrons in d orbital.
- f block: 72 protons, attractive force on 6th shell, 14 electrons in f orbital.
Lanthanide Contraction:
- In Hf (Z=72), the valence shell configuration is $6s^2 4f^{14} 5d^2$ .
- The force of 72 protons on the 6th shell is very high.
- There are 14 electrons in the f subshell which have a very poor shielding effect, resulting in size contraction.
- Thus, Hf is equal in size to Zr.
- This continues until group 12 (Zn family); the elements are almost the same size.
Effect on Group 13: The size of Tl is not as large as In as expected.
Exceptions Among Lanthanides:
- On moving from left to right, the size generally decreases, but Eu & Yb have exceptionally large sizes, making them the largest and second largest elements, respectively, in the 4f series.
- Eu is the largest element among 3d, 4d, 5d, and 4f series.
Actinides: Among the actinides, the size variation is regular as we move from left to right (it decreases).

Ionic Size

Depends on electron density, which depends on the $\frac{Z}{e}$ ratio.
For isoelectronic ions, greater is the $\frac{Z}{e}$ value, smaller would be the size.
- Z = atomic number
- e = number of electrons
Cations: electron number decreases -> $\frac{Z}{e}$ increases -> size decreases.
Anions: electron number increases -> $\frac{Z}{e}$ decreases -> size increases.
- Example: O^{+2} < O^{+} < O < O^{-} < O^{-2}
Isoelectronic Series:
- Mg^{2+} < Na^+ < F^- < O^{-2} < N^{-3}
- Number of electrons: 10 for all
- Atomic numbers: 12, 11, 9, 8, 7
Variation trend is same as elements: increases down group, decreases across period
- Li^+ < Na^+ < K^+ < Rb^+ < Cs^+ < Fr^+
- Be^{+2} < Mg^{+2} < Ca^{+2} < Sr^{+2} < Ba^{+2} < Ra^{+2}
- O^{-2} < S^{-2} < Se^{-2} < Te^{-2}

Cross-Group Comparison of s-Block Elements

Size Comparison:
- Li < Mg (152 pm < 160 pm)
- Na < Ca (186 pm < 197 pm)
- K > Ba (227 pm > 222 pm)
Ionic Size Comparison:
- Li^+ > Mg^{+2} (76 pm > 72 pm)
- Na^+ > Ca^{+2} (102 pm > 100 pm)
- K^+ > Ba^{+2} (138 pm > 135 pm)
Group 13 elements: Size increases smoothly down the group for +3 ions:
- Al^{+3} < Ga^{+3} < In^{+3}
Hydrogen Anion Size:
- Hydrogen has minimum Z/e value and has an exceptionally large size such that among the mono anions: F^- < Cl^- < Br^- < H^- < I^-

Covalent and Metallic Radii

Atoms are typically measured in bonded form as they can't be easily isolated
Types reported:
- Covalent radius
- Metallic radius
- Van der Waals radius

Covalent Radius

Size when atoms are covalently bonded, considering only single-bonded molecules/forms.
- Examples: H-H in H2, O-O in $H2O2$ (HO-OH), N-N in $N2H4$ ( $H2N-NH2$ ).
- Also called Single Bond Covalent Radii (SBCR).
Definition: Half of the distance between the nuclei in a single covalent bond.
For Homoatomic molecules (e.g., $A_2$ ):
- $rA = \frac{d{A-A}}{2}$
- $d_{A-A}$ = distance between nuclei of A

Metallic Radius

Definition: Half the distance between the nuclei in a metallic bond.
In element A:
- $rA = \frac{d{A-A}}{2}$
- $d_{A-A}$ = distance between nuclei in metallic bond.

Van der Waals Radius

Definition: Distance between the nuclei of two nearest non-bonded neighbors, generally measured in the solid state.

Radius Comparison

r{Vander Waals} > r{SBCR}
Based upon bond strength, radius data is observed which is just opposite to the bond strength trend.
Bond Strength: Covalent bond > Metallic bond > Van der Waals force
Size: Covalent radius < Metallic radius < Van der Waals radius
Noble Gases:
- Do not form compounds (except Krypton & Xenon).
- Only Van der Waals radius is reported, making them appear largest in their respective period.

Heteroatomic Molecules

For heteroatomic molecules like AB:
- $d{A-B} = rA + r_B - 0.009 |\Delta x|$
 - where atomic radii are in angstroms.
- $d{A-B} = rA + r_B - 9 |\Delta x|$
 - where atomic radii are in picometers.
- $\Delta x$ = difference in electronegativity of A & B.

Ionization Energy (I.E.)

Definition: The energy required to remove an electron from an isolated gaseous atom in its ground state.
Successive Ionization Energies:
- First I.E.: Energy to remove the first electron.
- Second I.E.: Energy to remove the second electron.
- Third I.E.: Energy to remove the third electron, and so on.
Equations:
- $A(g) \rightarrow A^+(g) + e^-; \Delta H = x \text{ kJ/mol } (IE_1 \text{ of A})$
- $A^+(g) \rightarrow A^{2+}(g) + e^-; \Delta H = y \text{ kJ/mol } (IE_2 \text{ of A})$
- $A^{2+}(g) \rightarrow A^{3+}(g) + e^-; \Delta H = z \text{ kJ/mol } (IE_3 \text{ of A})$
- $A(g) \rightarrow A^{3+}(g) + 3e^-; \Delta H = (x + y + z) \text{ kJ/mol}$
Positive $\Delta H$ signifies an endothermic process (energy is consumed).
Total Ionization Energy: The sum of successive ionization energies required to form a particular cation.
- Example: (x + y + z) is the total ionization energy required for A to make $A^{3+}$ cation.
General Observation:
- If the difference between two successive I.E.s is less than or equal to 11 eV, the higher oxidation number is more stable.
- If the difference between two successive I.E.s is greater than 16 eV, the lower oxidation state is more stable.
Successive Ionization Energy Trend: IE1 < IE2 < IE3< IE4 < IE5, indicating that as more electrons are removed from an atom, the energy required to remove the next electron increases due to the increasing positive charge of the ion.
I.E. is generally an endothermic process for neutral atoms & cations.

Factors Affecting I.E.

Atomic Size

Larger atomic size implies a greater distance between valence electrons and the nucleus, resulting in smaller I.E.
Size $\uparrow$ , I.E. $\downarrow$
Down the group: I.E. decreases as size increases.
Across a period (left to right): I.E. increases as size decreases.
Exceptions to this due to d-block and lanthanide contraction.

General Exceptions to the Trend:

Group 1: Difference of 1st I.E. between Cs & Fr is minimal.
- Cs = 376 kJ/mol
- Fr = 375 kJ/mol
Ra > Ba This is because of the involvement of 14 electrons in the f subshell, which has poor shielding effect, increasing the nucleus' hold on valence electrons, thus increasing the I.E.
Lithium's 1st I.E. is higher than only Ba and Ra in group 2, while Na has its 1st I.E. lower than all elements of group 2.
The order of 1st I.E of group 13 elements becomes even more random due to size contraction.
- Order of 1st I.E: B > Tl > Ga > Al > In
- 2nd I.E: B > Ga > Tl > In > Al
- 3rd I.E: B > Ga > Tl > Al > In
In d block elements, the variation of size from left to right does not decrease regularly, rather it decreases till the configuration of d5.
But as soon as the electron starts getting paired in the d subshell, i.e from d6 the inter electronic repulsion develops which counters the effect of increased nuclear charge and in the configuration of d9 and d10 the size is found to increase.
eg. Zn is the 3rd largest element in the 3d series
Sc>Ti>Mn=Zn>V>Cr>Cu>Fe>Co=Ni

Type of Orbital

It is harder to remove electrons from s orbitals than from other orbitals because s orbitals have a high penetration power, placing the electrons close to the nucleus.
Example: Grp 2 (ns2 ) > Grp 13 (ns2 np1 ).

Electronic Configuration

Half-filled and fully-filled subshells are highly stable, so removing electrons from them requires more energy.
Noble gases have the highest 1st I.E. in their respective periods due to their $ns^2 np^6$ configuration.
In 3d series 1st I. E of Zn is highest, also it is higher than Boron & all the elements of group 14 except carbon. This is because electrons in Zn have to be removed from the s subshell, which is poorly shielded by the inner d-electrons.

I.E. in d-Block Elements

Variation of size from left to right does not decrease regularly; it decreases until $d^5$ .
After $d^5$ , electron pairing causes inter-electronic repulsion, countering the effect of increased nuclear charge, causing an increase in size at $d^9$ & $d^{10}$ .
- Example: Zn is the 3rd largest element in the 3d series.
- Size order in 3d series: Sc < Ti < Mn = Zn > V > Cr > Cu > Fe > Co < Ni
Example for 1st I.E.:
- Cr > Mn where (IE $\downarrow$ , Size $\uparrow$ )
- Mn: 4s2 3d5
- Cr: 4s1 3d5
- Even though Mn is larger than Cr, if 1 electron is removed from Cr, it gets a stable half-filled d5, hence removal of this electron becomes easier making this I.E very low
- For 2nd I.E: Cr > Fe > Mn
- For 3rd I.E: Mn > Cr > Fe
Also the 1st IE of Zn is highest in 3d series whereas 2nd I. E of Cu is highest in 3d series.
Similarly 3rd IE of zinc would again be highest in 3d series.
In p block, 1st I. E of group 15 elements ( $ns^2 np^3$ ) is greater than those of group 16 elements ( $ns^2 np^4$ ) because in group 15 a stable half-filled p subshell has to be disturbed.
* 2nd I.E. of group 16 becomes higher than group 17 when removing of one electron gives a half-filled/stable configuration.
First I. E of group 1 elements is very low, whereas the 2nd I. E is very high (highest in their respective period) because the electron has to be removed from a full filled noble gas configuration.

I.E. Summary

Trend in 1st I.E.

Li < Be < B < C < O < N < F < Ne \text{ (Exceptional)}

Na < Al < Mg < Si < S < P < Cl < Ar

K < Ga < Ca < Ge < As < Br < Kr

Rb < Sr < In < Sn < Sb < Te < I < Xe \text{ (Normal)}

Cs < Ba < Tl < Pb < Bi < Po < At < Rn \text{ (Normal)}

Application of I.E.

Prediction of Group Number

A sudden jump in ionization energy data suggests that a noble gas electronic configuration has been disturbed.
Example:
Element
IE1
IE2
IE3
IE4
Valence Electrons
Group No.
Na
5.13
47.28
71.68
98.91
1
1
Ge
11.26
26.38
47.44
77.43
4
14
Al
5.98
18.22
28.44
119.4
3
13

Element	IE1	IE2	IE3	IE4	Valence Electrons	Group No.
Na	5.13	47.28	71.68	98.91	1	1
Ge	11.26	26.38	47.44	77.43	4	14
Al	5.98	18.22	28.44	119.4	3	13

Metallic Nature

Elements with higher I.E. have lower metallic nature and vice versa.
- On moving down the group, metallic nature increases.
- On moving across a period from left to right, metallic nature decreases.

Reducing Nature

Lower I.E. means easy removal of electrons, which can then easily reduce other atoms.
- On moving down the group, the reducing power of elements increases.

Electron Gain Enthalpy / Electron Affinity

Definition: Energy released when an electron is added to an isolated gaseous atom.
- $A(g) + e^- \rightarrow A^-(g); \Delta H_{eg} = -x \text{ kJ/mol}$
Electron affinity (E.A.) is another term used for this process.
- $\Delta H_{eg} \approx -E.A.$
Addition of electrons, energy release is negative, EA would be taken as negative whereas, to remove an electron, EA would be taken as positive
Reason for emission of energy: when an electron is at a distance away from the nucleus and it suddenly enters in a zone where it can be attracted by the atom's nucleus, and then at a certain point, close enough to the atom, the electrons present already starts repelling the incoming electrons. which leads to rise in its P.E.
- $U = -k\frac{Ze^2}{r}$
- $U = k\frac{ne^2}{r}$
The total energy corresponding is liberated in the process, which is the electron gain enthalpy of the atom.
Successive electron affinities decrease in value (less negative).
- $O(g) + e^- \rightarrow O^-(g); \Delta H_{eg1} = -141 \text{ kJ/mol}$
- $O^-(g) + e^- \rightarrow O^{2-}(g); \Delta H_{eg2} = +844 \text{ kJ/mol}$
Adding an electron to an atom is exothermic, but adding an electron to an anion is always endothermic.

Factors Affecting E.A.

Size

Smaller atom size leads to the added electron being closer to the nucleus, hence greater energy released.
- Size $\downarrow$ , E.A. $\uparrow$
Down the group: EA decreases.
- Across the period: EA increases.

Exceptions

The EA of 2nd period elements in p block is lower than 3rd period elements.
- C > B
- Si > N
- P > O
- S > F
- Cl > F
- Chlorine (Cl) has the highest E. A. in the periodic table (not fluorine).
- Oxygen(O) has the lowest electron affinity in its group.

Type of Orbital

For a given shell, the addition of an electron is easiest in the s subshell and involves higher energy.

Electronic Configuration

Half-filled and full-filled subshells are exceptionally stable; disturbing them becomes an endothermic process.
- Noble gases have positive electron gain enthalpies.
  Ne(g) + e^- \rightarrow Ne^-(g); \Delta H > 0

General Trends

Electron affinity of group 15 elements is lower than group 14 elements.
- Nitrogen has positive EA.
- N less than C
- P less than Si
- As less than Ge
- Sb less than Sn
- Bi less than Pb
EA of group 2 elements is lower than group 1 elements due to filled s subshell, they are reluctant to electron addition.
- The EA of Be and Mg is positive.

Electronegativity

Defined separately by:
- Pauling
- Mulliken
- Allred-Rochow

Pauling's Definition

Tendency of an atom to pull shared electron pairs towards itself in a covalent bond.
- $\text{If energy is expressed in kJ/mol : } XA - XB = 0.102 \sqrt{\Delta_{A-B}}$
- $\text{If energy is expressed in kcal/mol : }XA - XB = 0.208 \sqrt{\Delta_{A-B}}$
 - $XA$ = electronegativity of A; $XB$ = electronegativity of B
- $\Delta{A-B} = E{A-B(observed)} - E_{A-B(calculated)}$
- $\Delta{A-B} = E{A-B(observed)} - \sqrt{E{A-A} \times E{B-B}}$

Metallic or Non-Metallic Behaviour

Less electronegative elements are metallic in nature.
- Down the group, metallic nature increases.
- Across the period, metallic nature decreases.
- Different oxides:

Non-metals are acidic, as number of oxygen per atom increases the order increases.

Basic oxides

Li, Na, K, Rb, Cs -> Increases down group.

Amphoteric oxides are which reacts with bases and acids to give salt.

Relationship between EA and IE

$ E.A \text{ of } Ax = I.E \text{ of } A{x-1} $
Example
$ O + e- \implies O^- \triangle H = -141 KJ mol O + e-\implies O - \triangle H 141 KJMol $

Muliken, over here the electronegativity is defined as average of ionization energy and electron affinity
Electronegativity factors affecting electronegativity are directly dependant on the atom
Only effects electronegativity, factors which affect size also effect electronegativity; smaller down the group and increasing across the group.
Metallic nature: is reduced which means increases down the group; decreasing the group, but reduces across the group
Down the group increases, increases across the period.
More electronegative is 1
Ionic Character is the tendency
$\%\text{ionic character}= 11\triangle ax1 + 35(ax1)^2$
Ionic chatacter = 1614x1 +3.5(1x)2 ; ax1 =diff in electronegativity of bond atoms
Metallic behaviour , less electronegativity -mettalic; more electronegativity->viceversa
*Down the group, increases, but increases across the period
Predicting nature of oxides, if decreases or increases the strength. But more form large number of oxides and it can effect the strength or increases by that said oxide.
*Those which gives based in water. Eg 20 when dissolved in water gives NAOH , nature of compounds and hydroxides are SAME
Amphoteric which gives salts and acids.
Neutral which do not change PM
Predicting bond nature breaking.
Hydration of ions.

When salt is dissolved into water the cations given by it are surrounded by the molecules of
The layer of the water can be more the water one. and as primary. secondary.
The strength layer determines can be more layer.
Is the strength how the water can be hold.
The shell radius holds on what the charger
Size increase on hydration.
Size charge decreases poor current capacity.
Which results how quickly get to the element.
*Diagonal Relationship in in their chemical properties from neighbourhood
*In these elents third property elents. Second propety properties
Equation
a(2b) a & b = constant
9What relationship of wave length of k line 26 & 21

Important Terms

Lothar Meyer elements based on classification

Observations

alkali metal, halogens and transition metals minimises

Periodic Properties: Detailed Notes