Classification of Elements and Periodicity in Properties

CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES

NEED FOR CLASSIFICATION OF ELEMENTS

**Why Classification is Essential:**

In 1800, only 31 elements were known. By 1865, this increased to 63 elements. Currently, 118 elements are known (94 naturally occurring + 24 man-made).

Studying 118+ elements individually and their millions of compounds is impractical and time-consuming.

Classification provides a systematic organization that:

Rationalizes known chemical facts about elements

Predicts properties of undiscovered elements

Facilitates understanding of periodic trends and relationships

Simplifies chemical knowledge management

**Exam Relevance:** Students must understand that periodic classification emerged from necessity to organize chemical knowledge, not from abstract theory.

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HISTORICAL DEVELOPMENT OF THE PERIODIC TABLE

Dobereiner's Triads (1829)

**Concept:** German chemist Johann Dobereiner identified that certain elements could be grouped in sets of three (triads) based on atomic weight and chemical properties.

**The Law of Triads:**

The middle element of each triad had an atomic weight approximately midway between the other two elements

The chemical and physical properties of the middle element were intermediate to the other two

**Examples of Dobereiner's Triads:**

Li (7), Na (23), K (39) - where 23 ≈ (7+39)/2 ≈ 23

Ca (40), Sr (88), Ba (137) - where 88 ≈ (40+137)/2 ≈ 88.5

Cl (35.5), Br (80), I (127) - where 80 ≈ (35.5+127)/2 ≈ 81.25

**Limitation:** This relationship worked only for a few elements and was dismissed as mere coincidence. The principle was too limited to classify all known elements.

Chancourtois's Helical Arrangement (1862)

French geologist A.E.B. de Chancourtois arranged elements in order of increasing atomic weight on a cylindrical surface

Observed periodic recurrence of properties

Limited acceptance due to poor predictive power and visualization difficulty

Newlands's Law of Octaves (1865)

**Concept:** English chemist John Alexander Newlands discovered that if elements were arranged in order of increasing atomic weights, every eighth element possessed properties similar to the first element.

**The Law of Octaves:**

Musical analogy: Every eighth note in an octave resembles the first note

Elements repeated their properties at regular intervals of 8 elements

Valid only up to calcium (atomic weight 40)

**Example Pattern:**

Li, Be, B, C, N, O, F, Ne (1st octave)

Na, Mg, Al, Si, P, S, Cl, Ar (2nd octave - Na resembles Li, Mg resembles Be, etc.)

**Limitation:** The pattern broke down for heavier elements. Law not universally applicable because periodic intervals were not constant. Despite its limitations, Newlands received the Davy Medal in 1887 for this work.

Lothar Meyer's Contribution (1868-1870)

German chemist Lothar Meyer developed a table closely resembling the Modern Periodic Table

Plotted physical properties (atomic volume, melting point, boiling point) against atomic weight

Observed periodic patterns with changing wavelengths of repetition

Work published after Mendeleev's, thus less credited

More sophisticated than Newlands as it recognized varying periodic intervals

Mendeleev's Periodic Table (1869)

**Dmitri Mendeleev's Periodic Law:**

"The properties of the elements are a periodic function of their atomic weights."

**Key Innovations:**

1. **Systematic Organization:**

Arranged elements horizontally (rows = series, now called periods) and vertically (columns = groups)

Elements with similar properties placed in same vertical column

Used broader range of chemical and physical properties for classification

Relied on empirical formulas of compounds formed by elements

2. **Bold Departure from Atomic Weight Order:**

Ignored strict atomic weight order when necessary to group similar elements

Example: Placed iodine (I, atomic weight 127) before tellurium (Te, atomic weight 128) in Group VII with Cl and Br because I's properties matched Group VII, not Group VI

This showed that chemical properties, not just atomic weight, determined grouping

3. **Prediction of Unknown Elements:**

Left gaps in the table for undiscovered elements

Predicted existence of Eka-aluminium (Gallium) and Eka-silicon (Germanium)

Predicted their properties with remarkable accuracy

**Mendeleev's Predictions vs. Actual Properties:**

For **Eka-Aluminium (Gallium)**:

Predicted atomic weight 68, found 70

Predicted density 5.9 g/cm³, found 5.94 g/cm³

Predicted melting point low, found 302.93 K

Predicted oxide formula E₂O₃, found Ga₂O₃

Predicted chloride formula ECl₃, found GaCl₃

For **Eka-Silicon (Germanium)**:

Predicted atomic weight 72, found 72.6

Predicted density 5.5 g/cm³, found 5.36 g/cm³

Predicted high melting point, found 1231 K

Predicted oxide formula EO₂, found GeO₂

Predicted chloride formula ECl₄, found GeCl₄

**Success Factor:** The accuracy of these predictions validated Mendeleev's system and made him famous. His table was published in 1905 in the form shown in Fig. 3.1.

**Significance:** Mendeleev's willingness to leave gaps and predict unknown elements demonstrated that the periodic law was based on deep chemical principles, not mere numerical coincidence.

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MODERN PERIODIC LAW AND STRUCTURE

The Problem with Mendeleev's Original Law

Mendeleev formulated his law based on atomic weights, developed in the 1800s before knowledge of atomic structure

Several anomalies existed: some elements with higher atomic weights had properties fitting earlier groups

Example: Ar (40) comes before K (39) in atomic weight, but K belongs to Group I and Ar to Group 0 (noble gases)

Henry Moseley's Revolutionary Discovery (1913)

**Background:** English physicist Henry Moseley studied characteristic X-ray spectra of elements.

**Key Finding:**

Plotted √ν (where ν = frequency of X-rays emitted) against atomic number (Z)

Obtained a straight-line relationship, NOT with atomic weight

Demonstrated that **atomic number is more fundamental than atomic weight**

**Mathematical Relationship:** Moseley's Law

√ν = R(Z - σ)

where R = Rydberg constant, σ = screening constant

Modern Periodic Law (Post-1913)

**Statement:** "The physical and chemical properties of the elements are periodic functions of their atomic numbers."

**Advantages over Mendeleev's Law:**

Based on atomic number (number of protons), which is invariant

Atomic weights can be variable (isotopes have different masses)

Atomic number directly relates to nuclear charge and electron number

Removes all anomalies of atomic weight ordering

Provides theoretical basis for periodicity

**Connection to Electronic Configuration:**

Atomic number determines number of electrons

Electronic configuration (arrangement of electrons) determines chemical properties

Periodic variation in electronic configuration causes periodic variation in properties

This is the fundamental reason for periodicity

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IUPAC NOMENCLATURE OF ELEMENTS WITH Z > 100

Historical Problem

Naming of new elements traditionally was privilege of discoverer(s)

Led to controversial claims (Example: Element 104 claimed by both USA as Rutherfordium and USSR as Kurchatovium)

Multiple claims arose because highly unstable elements synthesized in minute quantities difficult to characterize

IUPAC Systematic Nomenclature System

To provide temporary systematic names until official discovery is confirmed, IUPAC adopted nomenclature derived directly from atomic number.

**Numerical Roots for IUPAC Nomenclature:**

| Digit | Name | Abbreviation |

|-------|------|--------------|

| 0 | Nil | n |

| 1 | Un | u |

| 2 | Bi | b |

| 3 | Tri | t |

| 4 | Quad | q |

| 5 | Pent | p |

| 6 | Hex | h |

| 7 | Sept | s |

| 8 | Oct | o |

| 9 | Enn | e |

**Procedure:**

1. Write atomic number

2. Identify each digit separately

3. Use corresponding root name for each digit

4. Combine roots in order of digits (left to right)

5. Add suffix "-ium" at the end

6. Use three-letter symbol from first letter of each root

**Example (Problem 3.1):** Element with Z = 120

Atomic number 120: digits are 1, 2, 0

Roots: 1 = un, 2 = bi, 0 = nil

Name: **Unbinilium**

Symbol: **Ubn**

**Examples of Actual Elements (Z > 100):**

| Z | Temporary IUPAC Name | Symbol | Official Name | Symbol |

|---|---|---|---|---|

| 101 | Unnilunium | Unu | Mendelevium | Md |

| 102 | Unnilbium | Unb | Nobelium | No |

| 103 | Unniltrium | Unt | Lawrencium | Lr |

| 104 | Unnilquadium | Unq | Rutherfordium | Rf |

| 105 | Unnilpentium | Unp | Dubnium | Db |

| 106 | Unnilhexium | Unh | Seaborgium | Sg |

| 107 | Unnilseptium | Uns | Bohrium | Bh |

| 108 | Unniloctium | Uno | Hassium | Hs |

| 109 | Unnilennium | Une | Meitnerium | Mt |

| 110 | Ununnillium | Uun | Darmstadtium | Ds |

| 111 | Unununnium | Uuu | Rontgenium | Rg |

| 112 | Ununbium | Uub | Copernicium | Cn |

| 113 | Ununtrium | Uut | Nihonium | Nh |

| 114 | Ununquadium | Uuq | Flerovium | Fl |

| 115 | Ununpentium | Uup | Moscovium | Mc |

| 116 | Ununhexium | Uuh | Livermorium | Lv |

| 117 | Ununseptium | Uus | Tennessine | Ts |

| 118 | Ununoctium | Uuo | Oganesson | Og |

**Official Recognition Process:**

Element first assigned temporary IUPAC name and three-letter symbol

After reliable characterization, permanent name voted by IUPAC representatives from each country

Permanent names often honor:

Country or state of discovery (Francium, Polonium, Californium, Americium)

Notable scientists (Mendelevium after Dmitri Mendeleev, Nobelium after Alfred Nobel, Seaborgium after Glenn Seaborg)

Mythological names (Thorium after Thor, Uranium after Uranus)

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ELECTRONIC CONFIGURATIONS AND THE PERIODIC TABLE

Connection Between Configuration and Position

**Fundamental Principle:** An element's position in the Periodic Table reflects the quantum numbers of the last orbital filled (valence electrons).

**Key Relationship:**

**Period number** = highest principal quantum number (n) of the valence shell

**Group number** = number of valence electrons

**Block** = orbital type being filled (s, p, d, or f)

Electronic Configurations in Periods

**Period 1 (n = 1): 2 elements**

Filling: 1s orbital

H: 1s¹

He: 1s²

First shell complete with 2 maximum electrons (2 × 1² = 2)

**Period 2 (n = 2): 8 elements**

Filling: 2s and 2p orbitals

Li: 1s²2s¹ (start 2s)

Be: 1s²2s²

B to Ne: 2p orbitals filled (B: 2p¹, C: 2p², ..., Ne: 2p⁶)

Total: 8 elements (2 from 2s + 6 from 2p = 8)

**Period 3 (n = 3): 8 elements**

Filling: 3s and 3p orbitals

Na: 1s²2s²2p⁶3s¹ (start 3s)

Mg: 1s²2s²2p⁶3s²

Al to Ar: 3p filled (Al: 3p¹, ..., Ar: 3p⁶)

Total: 8 elements

**Period 4 (n = 4): 18 elements**

Sequence: 4s filling → 3d filling → 4p filling

K: 1s²2s²2p⁶3s²3p⁶4s¹ (start 4s)

Ca: 1s²2s²2p⁶3s²3p⁶4s²

Sc to Zn: 3d orbitals fill (transition metals)

Sc (Z=21): [Ar]3d¹4s²

Zn (Z=30): [Ar]3d¹⁰4s²

Ga to Kr: 4p orbitals fill (Ga: 4p¹, ..., Kr: 4p⁶)

Total: 18 elements (2 from 4s + 10 from 3d + 6 from 4p = 18)

**Why 3d fills after 4s:**

After 4s orbital is filled, the 3d orbital becomes lower in energy than 4p

Electrons prefer lower energy orbitals (Aufbau principle)

This creates the transition series

**Period 5 (n = 5): 18 elements**

Similar to Period 4 with 4d transition series

Rb: [Kr]5s¹ (start 5s)

Y: [Kr]4d¹5s² (start 4d filling at Z=39)

Zr to Cd: 4d series (Cd: [Kr]4d¹⁰5s²)

In to Xe: 5p orbitals filled

**Period 6 (n = 6): 32 elements**

Sequence: 6s → 4f → 5d → 6p

Cs: [Xe]6s¹

Ba: [Xe]6s²

La: [Xe]4f⁰5d¹6s² (marks beginning of 4f-series)

Ce to Lu: 4f orbitals fill (lanthanoid series = elements 58-71)

Ce (Z=58): [Xe]4f¹5d⁰6s²

Lu (Z=71): [Xe]4f¹⁴5d¹6s²

Hf to Hg: 5d orbitals fill

Tl to Rn: 6p orbitals fill

Total: 32 elements (2 + 14 + 10 + 6 = 32)

**Period 7 (n = 7): 32 elements (theoretical)**

Similar to Period 6 with 5f inner transition series

Fr: [Rn]7s¹

Ra: [Rn]7s²

Ac: [Rn]5f⁰6d¹7s² (marks beginning of 5f-series)

Th to Lr: 5f orbitals fill (actinoid series = elements 90-103)

Rf to Cn: 6d orbitals fill

Nh to Og: 7p orbitals fill

Period 7 incomplete; theoretically should have 32 but currently only confirmed up to 118 (Og)

Pattern in Number of Elements per Period

**Formula:** Number of elements in period with principal quantum number n = 2n²

| Period | n | Formula (2n²) | Actual Elements | Orbital Sequence |

|--------|---|---|---|---|

| 1 | 1 | 2(1²) = 2 | 2 | 1s |

| 2 | 2 | 2(2²) = 8 | 8 | 2s, 2p |

| 3 | 3 | 2(3²) = 18 | 8 | 3s, 3p (3d not filled) |

| 4 | 4 | 2(4²) = 32 | 18 | 4s, 3d, 4p |

| 5 | 5 | 2(5²) = 50 | 18 | 5s, 4d, 5p |

| 6 | 6 | 2(6²) = 72 | 32 | 6s, 4f, 5d, 6p |

| 7 | 7 | 2(7²) = 98 | 32 | 7s, 5f, 6d, 7p |

**Important Note:** Period 3 has only 8 elements (not 18) because:

The 3d orbital is much higher in energy than 3p

Before 3d can fill, the 4s orbital of the next period (Period 4) becomes lower in energy

This is why transition metals (3d series) appear in Period 4, not Period 3

Why 18 Elements Appear in Period 4 (Problem 3.2 Justification)

**Explanation:**

Period 4 involves filling of 4s, 3d, and 4p orbitals

4s can hold 2 electrons (s orbital = 1 subshell)

3d can hold 10 electrons (d orbital = 5 subshells, each holds 2 electrons)

4p can hold 6 electrons (p orbital = 3 subshells, each holds 2 electrons)

Total: 2 + 10 + 6 = **18 elements**

**Sequential Filling:**

1. K and Ca (4s filling) = 2 elements

2. Sc to Zn (3d filling) = 10 elements

3. Ga to Kr (4p filling) = 6 elements

**Total = 18 elements in Period 4**

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BLOCK CLASSIFICATION OF ELEMENTS

**Definition:** Elements are classified into blocks based on which orbital (s, p, d, or f) is being filled.

s-Block Elements

**Definition:** Elements whose last electron enters an s orbital (ns¹ or ns²)

**Groups:** Groups 1 and 2

**Characteristics:**

Highly reactive metals

Strong reducing agents

Form ionic compounds

Valence electrons in s orbital

**Group 1 (ns¹):**

Alkali metals (Li, Na, K, Rb, Cs, Fr)

Plus hydrogen (1s¹)

**Group 2 (ns²):**

Alkaline earth metals (Be, Mg, Ca, Sr, Ba, Ra)

p-Block Elements

**Definition:** Elements whose last electron enters a p orbital (np¹ to np⁶)

**Groups:** Groups 13 to 18 (IUPAC notation; old notation: IIIA to VIIIA/0)

**Subgroups:**

Group 13 (III A): p¹ - Boron family

Group 14 (IV A): p² - Carbon family

Group 15 (V A): p³ - Nitrogen family

Group 16 (VI A): p⁴ - Oxygen family

Group 17 (VII A): p⁵ - Halogen family

Group 18 (VIII A / 0): p⁶ - Noble gases

**Characteristics:**

Variable metallic character (metals, metalloids, nonmetals)

Include most nonmetals

Variable oxidation states

Form both ionic and covalent compounds

d-Block Elements (Transition Metals)

**Definition:** Elements whose last electron enters a d orbital (d¹ to d¹⁰)

**Groups:** Groups 3 to 12 (IUPAC notation; old notation: IIIB to IIB)

**Electronic Configuration:** [noble gas] (n-1)d^x ns²

**Characteristics:**

All are metals

High melting and boiling points (except Hg - liquid at room temperature)

Variable oxidation states

Form colored compounds

Exhibit catalytic properties

Paramagnetic (except Zn)

Can form multiple stable ions

**Examples:**

Fe, Mn, Cu - variable oxidation states (Fe²⁺/Fe³⁺, Mn²⁺/Mn⁷⁺, Cu⁺/Cu²⁺)

Cr - forms CrO₄²⁻ (yellow) and Cr₂O₇²⁻ (orange)

Platinum group metals - high reactivity and catalytic activity

f-Block Elements (Inner Transition Metals)

**Definition:** Elements whose last electron enters an f orbital (f¹ to f¹⁴)

**Characteristics:**

Lanthanoids (4f series): Ce to Lu (Z = 58 to 71)

Actinoids (5f series): Th to Lr (Z = 90 to 103)

All are metals

Highly reactive (lanthanoids moderately, actinoids very highly)

Variable oxidation states

Lanthanoids have similar chemical properties (difficult to separate)

Actinoids mostly radioactive

Form complex compounds easily

**Why Separated:**

Maintain structure of main periodic table

Preserve principle of similar properties in same group

Lanthanoid/actinoid series would disrupt table symmetry if inserted in period

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PERIODIC TRENDS IN PHYSICAL AND CHEMICAL PROPERTIES

Atomic Radius (Atomic Size)

**Definition:** Effective distance from nucleus to outermost electron

**Trend Across a Period (Left to Right):**

**Decreases** (Example: Na > Mg > Al > Si > P > S > Cl)

Reason:

Electrons added to same shell (same n)

Increased nuclear charge (Z increases)

Greater nuclear attraction pulls electrons closer

Increased effective nuclear charge (Zeff)

**Trend Down a Group:**

**Increases** (Example: Li < Na < K < Rb < Cs)

Reason:

New electron shell added (n increases)

Outermost electrons farther from nucleus

Increased shielding by inner electrons outweighs increased nuclear charge

**Exam Important Points:**

Non-metallic radius (covalent radius) for nonmetals

Metallic radius for metals

Ionic radius differs from atomic radius

Atomic radius = ½ bond distance (X-X)

Ionic Radius

**Definition:** Effective nuclear radius of an ion

**Cation Formation (X → X^n+):**

Ionic radius **decreases**

Reason:

Loss of electrons reduces electron-electron repulsion

Same nuclear charge acts on fewer electrons

Increased Zeff

Example: Na⁺ (102 pm) < Na (186 pm)

**Anion Formation (X → X^n-):**

Ionic radius **increases**

Reason:

Gain of electrons increases electron-electron repulsion

Nuclear charge distributed among more electrons

Decreased Zeff

Example: Cl⁻ (181 pm) > Cl (99 pm)

**Isoelectronic Series (Same Number of Electrons):**

Ionic radius decreases with increasing atomic number

Example: O²⁻ > F⁻ > Ne > Na⁺ > Mg²⁺

All have 10 electrons but different nuclear charges

Higher Z means smaller radius

Ionization Enthalpy (Ionization Energy)

**Definition:** Minimum energy required to remove one electron from a neutral gaseous atom in its ground state (X(g) → X⁺(g) + e⁻)

**First Ionization Enthalpy (IE₁):**

Energy to remove the easiest-to-remove electron

**Second Ionization Enthalpy (IE₂):**

Energy to remove second electron from X⁺ (more difficult)

IE₂ > IE₁ due to increased nuclear attraction

**General Trends:**

**Across a Period (Left to Right):**

**Generally increases**

Example: Li < Be < B < C < N < O < F < Ne

Reason:

Increased nuclear charge (higher Z)

Electrons in same shell

Increased Zeff

Electrons more tightly bound

**Exception:**

B (1st p-orbital) < Be (2s² complete): Half-filled p orbital (2p¹) less stable

O (p⁴) < N (p³): Half-filled p³ highly stable; removing from p⁴ means breaking stable configuration

Down a Group:**

**Decreases** (Example: Li > Na > K > Rb > Cs)

Reason:

New shell added (n increases)

Outermost electron farther from nucleus

Increased shielding by inner electrons

Valence electron less tightly bound

**Factors Affecting Ionization Enthalpy:**

Size of atom (smaller = higher IE)

Nuclear charge (higher Z = higher IE)

Electronic configuration (filled/half-filled orbitals more stable)

Shielding effect (inner electrons reduce effective nuclear charge)

**Relative Values of Successive Ionization Enthalpies:**

Large jump occurs when removing core electrons

Example: Al: IE₁ = 578 kJ/mol, IE₂ = 1817 kJ/mol, IE₃ = 2745 kJ/mol (huge jump from removing core electron from 1s²)

This jump indicates electron configuration boundaries

Electron Gain Enthalpy (Electron Affinity)

**Definition:** Energy change when an electron is added to a neutral gaseous atom (X(g) + e⁻ → X⁻(g))

**Sign Convention:**

**Negative value:** Energy is released (exothermic) - favorable

**Positive value:** Energy is required (endothermic) - unfavorable

**Trend Across a Period (Left to Right):**

**Generally becomes more negative** (more favorable)

Example: Li > Be > B > C > N > O > F (in magnitude)

Reason:

Small atom with high nuclear charge attracts electrons strongly

Higher Zeff pulls electron toward nucleus

**Exception:**

O (more negative) > F (slightly less negative): Anomalous because F has lower electron capacity in p orbital before repulsion

**Trend Down a Group:**

**Generally becomes less negative** (less favorable)

Example: F >> Cl > Br > I (in magnitude)

Reason:

New shell added (electron farther from nucleus)

Increased shielding reduces effective nuclear attraction

Easier to remove added electron

**Special Cases:**

**Noble gases:** Positive electron gain enthalpy (repulsion of extra electron)

**Alkali metals:** Low negative value (one electron fills valence orbital)

**Halogens:** Very negative values (one electron completes octet)

**Group 15 (N, P, As, Sb):** Half-filled p³ configuration; adding electron begins pairing, increasing repulsion

**Exam Important:**

Don't confuse with ionization enthalpy (opposite direction)

More negative = more favorable

Halogens show highest negative values

Electronegativity

**Definition:** Ability of an atom to attract electron density toward itself in a chemical bond (Pauling scale: 0.7-4.0)

**Scale:** Pauling scale; Cl and F have highest values; Cs and Fr have lowest

**Trend Across a Period (Left to Right):**

**Increases**

Example: Na < Mg < Al < Si < P < S < Cl

Reason:

Increased nuclear charge

Smaller atomic size

Electrons held more tightly

Greater ability to attract electrons from bonds

**Trend Down a Group:**

**Decreases**

Example: F > Cl > Br > I

Reason:

Increased atomic size

Increased shielding

Valence electrons farther from nucleus

Weaker attraction for bonded electrons

**Relative Electronegativity Values:**

F: 4.0 (most electronegative)

Cl: 3.0

O: 3.5 (higher than Cl due to small size)

N: 3.0

H: 2.1

Cs: 0.7 (least electronegative)

**Applications:**

Predicts bond type:

ΔEN < 0.5: Nonpolar covalent

0.5 < ΔEN < 1.7: Polar covalent

ΔEN > 1.7: Ionic

Determines chemical reactivity and compound properties

Metallic Character

**Definition:** Tendency of an element to act as a metal (lose electrons and form cations)

**Trend Across a Period (Left to Right):**

**Decreases**

Example: Na > Mg > Al > Si > P > S > Cl

Reason:

Electronegativity increases

Ionization enthalpy increases

Tendency to form cations decreases

Element becomes more nonmetallic

**Trend Down a Group:**

**Increases**

Example: Li < Na < K < Rb < Cs

Reason:

Ionization enthalpy decreases

Atomic size increases

Valence electrons more easily lost

Stronger metallic character

**Relationship to Ionization Enthalpy:**

**High metallic character** correlates with **low ionization enthalpy**

Alkali metals (Group 1) show highest metallic character

Halogens show lowest metallic character

**Reactivity Correlations:**

Alkali metals (Group 1): Most reactive metals, strong reducing agents

Alkaline earth metals (Group 2): Reactive metals but less than Group 1

Transition metals: Variable reactivity

Nonmetals: Reactivity increases with electronegativity (F₂ most reactive nonmetal)

Noble gases: No metallic character, completely unreactive

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VALENCE OF ELEMENTS

**Definition:** Number of electrons in valence shell that determine combining capacity; also number of bonds an atom can form

**Relation to Group Number:**

For representative elements: **Valence = group number** (IUPAC Groups 1-18)

Example:

Group 1: Valence = 1 (Li⁺, Na⁺, K⁺)

Group 2: Valence = 2 (Be²⁺, Mg²⁺, Ca²⁺)

Group 13: Valence = 3 (B³⁺ or B forms 3 bonds in BCl₃)

Group 14: Valence = 4 (C forms 4 bonds in CH₄)

Group 15: Valence = 3 or 5 (N in NH₃ shows valence 3; N in HNO₃ shows valence 5)

Group 16: Valence = 2 or 6 (O in H₂O shows valence 2; S in H₂SO₄ shows valence 6)

Group 17: Valence = 1 or 7 (Cl in HCl shows valence 1; Cl in HClO₄ shows valence 7)

**Variable Valence:**

Transition metals exhibit multiple oxidation states

Example:

Mn: +2, +3, +4, +6, +7

Fe: +2, +3

Cu: +1, +2