How to Use This Section

This is the last section of the chapter, meant to be read the night before the paper and again in the queue outside the hall.

Nothing new is taught here. Every card compresses something Sections 1 to 13 worked through properly, in the same notation and with the same numbers. If a line surprises you, go back and reread that section instead of memorising the line.

Eight cards, one mistake checklist, one 60-second panic list. Screenshot the three figures.

Card Topic Sections it compresses Who needs it most
1 The classification timeline — Dobereiner to Seaborg, and Mendeleev's predictions 1, 2 Board, NEET
2 Structure of the long form — periods, groups, lanthanoids and actinoids, the period/group/block finder 2, 3, 4 Everyone
3 IUPAC digit roots and the names of elements 101 to 118 2 Board, NEET
4 The four blocks, their configurations and properties; metals, non-metals, metalloids 4 Everyone
5 Atomic and ionic radius — data, rules, isoelectronic species 5 Everyone
6 Ionization enthalpy — trends, factors, anomalies, successive values 6, 10 Everyone
7 Electron gain enthalpy and electronegativity — data tables and anomalies 7, 10 Everyone
8 Chemical trends — valence, hydrides and oxides, second-period anomalies, diagonal pairs, reactivity, oxide character 8, 12 Everyone

Key Point: The whole chapter is one idea. Properties of elements are periodic functions of their atomic numbers, because atomic number fixes the electronic configuration, and the outer configuration repeats after every 2, 8, 8, 18, 18, 32 elements. Every trend below — radius, ionization enthalpy, electron gain enthalpy, electronegativity, valence, oxide character — is the outer configuration plus two competing effects: nuclear charge pulling in and shielding by inner electrons pushing out. Across a period nuclear charge wins; down a group shielding and the new shell win. Hold on to that and the anomalies become footnotes instead of a separate list.


Card 1 — The Classification Timeline and Mendeleev's Predictions

Who did what, and where it broke

Year Scientist The idea Where it failed or what it lacked
1829 Dobereiner (Germany) Triads: groups of three similar elements in which the middle atomic weight is roughly the mean of the other two — Li (7), Na (23), K (39): mean (7+39)/2=23(7 + 39)/2 = 23; Ca (40), Sr (88), Ba (137): mean 88.588.5; Cl (35.5), Br (80), I (127): mean 81.2581.25 Worked for only a handful of elements; dismissed as coincidence
1862 de Chancourtois (France) Elements in order of increasing atomic weight on a cylinder (telluric helix); similar elements fell on vertical lines Little attention; awkward to use
1865 Newlands (England) Law of octaves: arranged by atomic weight, every eighth element resembles the first, like the notes of music Held only up to calcium; ridiculed at the time, Davy Medal only in 1887
1869 Lothar Meyer (Germany) Plotted physical properties (atomic volume, melting and boiling points) against atomic weight and saw a repeating pattern; his 1868 table resembled Mendeleev's Published after Mendeleev, with less bold predictions
1869 Mendeleev (Russia) Periodic law: properties of elements are a periodic function of their atomic weights. Arranged 63 elements in rows and columns by weight, but gave similar properties priority over weight — so he swapped iodine (higher weight) after tellurium, and left gaps for undiscovered elements Positions of Ar/K, Co/Ni, Te/I could not be explained by weight; isotopes had no place; hydrogen had no fixed home
1913 Moseley (England) X-ray spectra: ν\sqrt{\nu} of the characteristic X-ray line is a straight line against atomic number ZZ, not against atomic weight; so ZZ is the fundamental property. Modern periodic law: physical and chemical properties of elements are periodic functions of their atomic numbers Fixed every Mendeleev anomaly at once: Ar (18) before K (19), Co (27) before Ni (28), Te (52) before I (53)
1940s onward Glenn Seaborg (USA) Discovered the transuranium elements from plutonium (94) to 102 and placed the actinoids as a second f-series below the lanthanoids; element 106 named seaborgium in his honour —

Key Point (Definition): Mendeleev's periodic law — the physical and chemical properties of the elements are a periodic function of their atomic weights. Modern periodic law — the physical and chemical properties of the elements are periodic functions of their atomic numbers. Write the correct noun; that is the one-mark difference.

Mendeleev's predictions

Property Eka-aluminium (predicted) Gallium (found, 1875) Eka-silicon (predicted) Germanium (found, 1886)
Atomic weight 68 70 72 72.6
Density / g cm−3^{-3} 5.9 5.94 5.5 5.36
Melting point / K Low 302.93 High 1231
Formula of oxide E2O3\mathrm{E_2O_3} Ga2O3\mathrm{Ga_2O_3} EO2\mathrm{EO_2} GeO2\mathrm{GeO_2}
Formula of chloride ECl3\mathrm{ECl_3} GaCl3\mathrm{GaCl_3} ECl4\mathrm{ECl_4} GeCl4\mathrm{GeCl_4}

"Eka" is Sanskrit for one: eka-aluminium means "one place below aluminium" in the same group (group 13). Eka-boron was scandium, eka-manganese was technetium.

Element counts: about 31 known in 1800, 63 by 1865 (Mendeleev's table), 114 with official names when your textbook was printed and 118 today. Classification became necessary because nobody can remember 100-plus elements one at a time.

[NEET] Why Mendeleev is remembered and Newlands is not: Mendeleev trusted the pattern more than the data — he left gaps, predicted the properties of the missing elements, and even suggested that some atomic weights had been measured wrongly. Newlands forced every element into an octave whether it fit or not.


Card 2 — Structure of the Long Form of the Periodic Table

Revision card: long-form table skeleton with blocks, period lengths and group numbers

Periods — how long, and why

Key Point: The period number equals the principal quantum number nn of the valence shell, and the number of elements in a period is twice the number of orbitals being filled (one orbital, two electrons).

Period Orbitals filled (in order) Number of orbitals Elements From To
1 1s1s 1 2 H (1) He (2)
2 2s2s, 2p2p 1 + 3 = 4 8 Li (3) Ne (10)
3 3s3s, 3p3p 4 8 Na (11) Ar (18)
4 4s4s, 3d3d, 4p4p 1 + 5 + 3 = 9 18 K (19) Kr (36)
5 5s5s, 4d4d, 5p5p 9 18 Rb (37) Xe (54)
6 6s6s, 4f4f, 5d5d, 6p6p 1 + 7 + 5 + 3 = 16 32 Cs (55) Rn (86)
7 7s7s, 5f5f, 6d6d, 7p7p 16 32 Fr (87) Og (118)

The third period has 8, not 18, because after 3p3p the next orbital in energy is 4s4s, not 3d3d (the n+ln + l rule, 4s4s: 4+0=44 + 0 = 4 versus 3d3d: 3+2=53 + 2 = 5). So 3d3d is filled in the fourth period (Sc to Zn, the first transition series), 4d4d in the fifth (Y to Cd), 5d5d in the sixth (La, Hf to Hg) and 6d6d in the seventh.

Groups

Group (1 to 18) Old notation Family name Outer configuration
1 IA alkali metals ns1ns^1
2 IIA alkaline earth metals ns2ns^2
3 to 12 IIIB, IVB, VB, VIB, VIIB, VIII (8, 9, 10), IB, IIB transition metals (n−1)d1−10 ns0−2(n-1)d^{1-10}\,ns^{0-2}
13 IIIA boron family ns2np1ns^2 np^1
14 IVA carbon family ns2np2ns^2 np^2
15 VA pnictogens (nitrogen family) ns2np3ns^2 np^3
16 VIA chalcogens (oxygen family) ns2np4ns^2 np^4
17 VIIA halogens ns2np5ns^2 np^5
18 0 (or VIIIA) noble gases ns2np6ns^2 np^6 (He: 1s21s^2)

Elements of one group have the same number of valence electrons in the same type of orbital, which is why they behave alike: the alkali metals Li, Na, K, Rb, Cs, Fr are all ns1ns^1 with n=2,3,4,5,6,7n = 2, 3, 4, 5, 6, 7.

Lanthanoids and actinoids

Series Elements Orbital being filled Period Where they sit
Lanthanoids (4f inner transition) Ce (58) to Lu (71) 4f4f 6 separate panel below the table, belonging to group 3 after La
Actinoids (5f inner transition) Th (90) to Lr (103) 5f5f 7 separate panel below the lanthanoids, after Ac

They are printed separately only to keep the table from becoming 32 columns wide. Elements after uranium (92) are the transuranium elements, all man-made.

The period, group and block finder

To find Rule
Period the highest principal quantum number nn in the configuration
Block the subshell that received the last electron: ss, pp, dd or ff
Group, s-block number of nsns electrons: ns1ns^1 is group 1, ns2ns^2 is group 2
Group, p-block 10+10 + number of valence electrons =12+= 12 + number of npnp electrons: ns2np4ns^2 np^4 is group 16
Group, d-block number of (n−1)d(n-1)d electrons ++ number of nsns electrons: 3d64s23d^6 4s^2 is group 8
Group, f-block always group 3, period 6 (4f) or 7 (5f)
Given Work Answer
Z=117Z = 117 [Rn] 5f146d107s27p5[\mathrm{Rn}]\,5f^{14} 6d^{10} 7s^2 7p^5 period 7, group 17, p-block, halogen
Z=120Z = 120 [Og] 8s2[\mathrm{Og}]\,8s^2 period 8, group 2, s-block, alkaline earth metal
Z=114Z = 114 [Rn] 5f146d107s27p2[\mathrm{Rn}]\,5f^{14} 6d^{10} 7s^2 7p^2 period 7, group 14, p-block
ns2np4ns^2 np^4, n=3n = 3 S period 3, group 16, p-block
(n−1)d2ns2(n-1)d^2 ns^2, n=4n = 4 Ti period 4, group 4, d-block
(n−2)f7(n−1)d1ns2(n-2)f^7 (n-1)d^1 ns^2, n=6n = 6 Gd period 6, group 3, f-block (lanthanoid)

[Board] The 100th element (fermium) is in period 7. The fifth period has 18 elements because n=5n = 5 allows 5s5s (1), 4d4d (5) and 5p5p (3) orbitals to fill before 6s6s: 9 orbitals, 18 electrons.


Card 3 — IUPAC Nomenclature for Elements With Z > 100

Why it exists

Both American and Soviet groups claimed element 104 (rutherfordium versus kurchatovium). To avoid such fights, IUPAC gives every new element a temporary systematic name built from the digits of its atomic number until the discovery is confirmed and an official name is agreed.

The digit roots

Digit 0 1 2 3 4 5 6 7 8 9
Root nil un bi tri quad pent hex sept oct enn
Letter n u b t q p h s o e

Key Point: Roots are joined in order of the digits, the name ends in -ium, and the symbol is the first letter of each root (three letters). Two spelling rules: a final "i" of bi or tri is dropped before "ium" (so 102 is unnilbium, not unnilbiium), and a double "nn" from enn + nil is written with a single "n" (so 190 would be unennilium).

Elements 101 to 118 — compact

ZZ Systematic name (symbol) Official name (symbol) ZZ Systematic name (symbol) Official name (symbol)
101 Unnilunium (Unu) Mendelevium (Md) 110 Ununnilium (Uun) Darmstadtium (Ds)
102 Unnilbium (Unb) Nobelium (No) 111 Unununium (Uuu) Roentgenium (Rg)
103 Unniltrium (Unt) Lawrencium (Lr) 112 Ununbium (Uub) Copernicium (Cn)
104 Unnilquadium (Unq) Rutherfordium (Rf) 113 Ununtrium (Uut) Nihonium (Nh)
105 Unnilpentium (Unp) Dubnium (Db) 114 Ununquadium (Uuq) Flerovium (Fl)
106 Unnilhexium (Unh) Seaborgium (Sg) 115 Ununpentium (Uup) Moscovium (Mc)
107 Unnilseptium (Uns) Bohrium (Bh) 116 Ununhexium (Uuh) Livermorium (Lv)
108 Unniloctium (Uno) Hassium (Hs) 117 Ununseptium (Uus) Tennessine (Ts)
109 Unnilennium (Une) Meitnerium (Mt) 118 Ununoctium (Uuo) Oganesson (Og)

Practice the mechanism on unfamiliar numbers, because that is what is asked: Z=120Z = 120 is unbinilium (Ubn), Z=121Z = 121 is unbiunium (Ubu), Z=130Z = 130 is untrinilium (Utn), Z=150Z = 150 is unpentnilium (Upn).

[NEET] Three one-liner facts: element 106 is named after Seaborg (the only element named after a living person at the time); 117 tennessine and 118 oganesson are the newest halogen and noble gas; the temporary symbol always has three letters, the official one has one or two.


Card 4 — The Four Blocks; Metals, Non-metals and Metalloids

The four blocks in one table

Block Groups Outer configuration Members Key properties
s 1, 2 (plus He) ns1−2ns^{1-2} alkali and alkaline earth metals soft, low IE, highly reactive, reactivity increases down the group; +1 and +2 oxidation states; mostly ionic compounds (Li and Be are the exceptions); never found free in nature
p 13 to 18 ns2np1−6ns^2 np^{1-6} metals, metalloids, non-metals, halogens (17), chalcogens (16), noble gases (18) s + p together are the representative (main-group) elements; non-metallic character rises across the block; halogens and chalcogens have very negative ΔegH\Delta_{eg} H; noble gases are closed-shell and inert
d 3 to 12 (n−1)d1−10 ns0−2(n-1)d^{1-10}\,ns^{0-2} transition metals (Sc to Zn, Y to Cd, La and Hf to Hg, Ac and Rf to Cn) all metals, coloured ions, variable oxidation states, paramagnetism, catalysts; a bridge between the very reactive s-block metals and the less reactive metals of groups 13 and 14
f inside group 3 (n−2)f1−14 (n−1)d0−1 ns2(n-2)f^{1-14}\,(n-1)d^{0-1}\,ns^2 lanthanoids Ce to Lu, actinoids Th to Lr inner transition elements, all metals, all similar to each other; actinoids radioactive, elements after U synthetic (transuranium)

The exceptions to remember

Case Rule it bends The fact
Helium placed in group 18 although it is 1s21s^2 (s-block by configuration) its shell is complete, so it behaves as a noble gas — the property wins over the block label
Hydrogen has one electron like the alkali metals, but needs only one more to fill its shell like the halogens placed separately at the top of the table; it is not a metal, not an alkali metal
Zn, Cd, Hg group 12, (n−1)d10 ns2(n-1)d^{10}\,ns^2 dd-subshell completely filled in the element and in its common ions, so they show none of the typical transition properties (colourless ions, no variable oxidation state); they are in the d-block but are not transition elements in the strict sense
Pd (Z=46Z = 46) the ns0ns^{0} case configuration [Kr] 4d10 5s0[\mathrm{Kr}]\,4d^{10}\,5s^0; this is why the general d-block configuration is written ns0−2ns^{0-2}, not ns1−2ns^{1-2}
Cr, Cu ns1ns^1 cases [Ar] 3d54s1[\mathrm{Ar}]\,3d^5 4s^1 and [Ar] 3d104s1[\mathrm{Ar}]\,3d^{10} 4s^1 — half-filled and fully filled dd

Metals, non-metals and metalloids

Class Where How many Properties
Metals left and centre; more than 78% of all elements about 91 solid at room temperature (Hg is the exception, and Cs and Ga melt in the hand), high melting and boiling points, good conductors, malleable and ductile
Non-metals top right corner about 20 mostly gases or brittle solids (Br is a liquid), low melting points, poor conductors
Metalloids (semi-metals) on the zig-zag line separating the two B, Si, Ge, As, Sb, Te, (Po, At) in-between properties; semiconductors

Metallic character increases down a group (Be to Ba, C to Pb) and decreases across a period (Na to Cl); non-metallic character does the opposite. The most metallic elements are at the bottom left (Cs, Fr), the most non-metallic at the top right (F, O).

[JEE/NEET] Because the change is gradual, Sn and Pb are metals, Ge and Si are metalloids, and C is a non-metal — all in the same group 14. Do not call boron a metal even though it heads group 13.


Card 5 — Atomic Radius and Ionic Radius

The definitions

Key Point (Definition): Atomic size cannot be measured directly (the electron cloud has no sharp edge), so it is defined from bond lengths. Covalent radius = half the distance between the nuclei of two bonded atoms of the same element in a molecule: the Cl-Cl distance in Cl2\mathrm{Cl_2} is 198 pm, so r(Cl)=99r(\mathrm{Cl}) = 99 pm. Metallic radius = half the internuclear distance between neighbouring atoms in a metal crystal: the Cu-Cu distance is 256 pm, so r(Cu)=128r(\mathrm{Cu}) = 128 pm. Noble gases have only a van der Waals radius (from non-bonded contact), which is why their large values are not compared with the others in a period.

The data

Period 2 Li Be B C N O F
Atomic radius / pm 152 111 88 77 74 66 64
Period 3 Na Mg Al Si P S Cl
Atomic radius / pm 186 160 143 117 110 104 99
Group 1 Li Na K Rb Cs
Atomic radius / pm 152 186 231 244 262
Group 17 F Cl Br I At
Atomic radius / pm 64 99 114 133 140

The two rules and why

Direction Trend Reason
Across a period (left to right) radius decreases electrons enter the same shell; each extra proton raises the nuclear charge but the same-shell electrons shield each other poorly, so the effective nuclear charge rises and the cloud is pulled in
Down a group radius increases each step adds a new shell (nn rises), and the inner shells shield the outer electrons from the nucleus; the shell effect beats the extra protons

Ionic radius

Ion type Size relative to the atom Reason Example
Cation smaller electrons are removed, often an entire outer shell disappears; the remaining electrons feel a larger net pull Na 186 pm, Na+\mathrm{Na^+} 95 pm
Anion larger electrons are added to the same shell; more repulsion, same nuclear charge, so the cloud expands F 64 pm, F−\mathrm{F^-} 136 pm

Same element, different charge: the higher the positive charge, the smaller the ion — Fe>Fe2+>Fe3+\mathrm{Fe} > \mathrm{Fe^{2+}} > \mathrm{Fe^{3+}}; O2−>O−>O\mathrm{O^{2-}} > \mathrm{O^-} > \mathrm{O}.

Isoelectronic species — the one rule

Key Point: Isoelectronic species have the same number of electrons. Among them, the one with the largest nuclear charge is the smallest, because the same cloud is pulled by more protons.

N3−>O2−>F−>Ne>Na+>Mg2+>Al3+(10 electrons; Z=7,8,9,10,11,12,13)\mathrm{N^{3-}} > \mathrm{O^{2-}} > \mathrm{F^-} > \mathrm{Ne} > \mathrm{Na^+} > \mathrm{Mg^{2+}} > \mathrm{Al^{3+}} \qquad (\text{10 electrons; } Z = 7, 8, 9, 10, 11, 12, 13)

Other sets to recognise on sight: S2−>Cl−>Ar>K+>Ca2+\mathrm{S^{2-}} > \mathrm{Cl^-} > \mathrm{Ar} > \mathrm{K^+} > \mathrm{Ca^{2+}} (18 electrons); H−\mathrm{H^-}, He, Li+\mathrm{Li^+}, Be2+\mathrm{Be^{2+}} (2 electrons); Br−\mathrm{Br^-}, Kr, Rb+\mathrm{Rb^+}, Sr2+\mathrm{Sr^{2+}} (36 electrons).

[NEET] Ordering traps: (1) K+\mathrm{K^+} (18 electrons, n=3n = 3 outer shell) is larger than Na+\mathrm{Na^+} (10 electrons, n=2n = 2) — a new shell beats charge. (2) Al3+<Mg2+<Na+\mathrm{Al^{3+}} < \mathrm{Mg^{2+}} < \mathrm{Na^+} — same shell, rising charge. (3) The largest atom in any period is the alkali metal, and the largest bonded atom overall is Cs (262 pm) or Fr — leave the noble gases out of size comparisons unless the question says van der Waals radius.


Card 6 — Ionization Enthalpy

The definition and its three conditions

Key Point (Definition): The first ionization enthalpy ΔiH\Delta_i H is the enthalpy change when the most loosely bound electron is removed from an isolated gaseous atom in its ground state: X(g)⟶X+(g)+e−,ΔiH1\mathrm{X(g)} \longrightarrow \mathrm{X^+(g)} + e^-, \qquad \Delta_i H_1 The second, ΔiH2\Delta_i H_2, removes the next electron from X+(g)\mathrm{X^+(g)}. Units kJ mol−1\mathrm{kJ\ mol^{-1}}. Every ionization enthalpy is positive (energy is always needed to pull an electron away from a positive nucleus), and ΔiH1<ΔiH2<ΔiH3\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3 always, because each electron leaves a more positive ion.

Three words that carry marks: isolated (no neighbouring atoms), gaseous (no lattice or solvent energy), ground state (not excited).

The periodicity graph, Z=1Z = 1 to 60

Maxima at the noble gases (He highest of all, 2372 kJ mol−1\mathrm{kJ\ mol^{-1}}), minima at the alkali metals (Cs lowest, then Rb, K). Each period starts at a minimum (Li, Na, K, Rb, Cs) and climbs to a maximum (Ne, Ar, Kr, Xe), with two dips on the way in periods 2 and 3.

Direction Trend Reason
Across a period ΔiH\Delta_i H increases same shell, rising effective nuclear charge, shrinking radius
Down a group ΔiH\Delta_i H decreases outer electron in a higher shell, farther away and shielded by more inner electrons; the extra nuclear charge is more than cancelled

The factors on which it depends

Factor Effect on ΔiH\Delta_i H
Atomic size (radius) larger atom, lower ΔiH\Delta_i H
Nuclear charge / effective nuclear charge higher ZeffZ_{eff}, higher ΔiH\Delta_i H
Shielding by inner shells more shielding, lower ΔiH\Delta_i H
Penetration of the subshell s>p>d>fs > p > d > f; an ss electron is closer to the nucleus, so it is harder to remove than a pp electron of the same shell
Half-filled or fully filled subshells extra stability, higher ΔiH\Delta_i H (p3p^3, d5d^5, p6p^6, d10d^{10})

The two classic anomalies

Anomaly Values / kJ mol−1\mathrm{kJ\ mol^{-1}} Reason
Be > B (also Mg > Al) Be 899, B 801; Mg 737, Al 577 B removes a 2p2p electron, Be a 2s2s electron; 2p2p is higher in energy, less penetrating and better shielded by the 2s22s^2 pair, so it comes off more easily
N > O (also P > S) N 1402, O 1314; P 1012, S 1000 N is 2p32p^3: three electrons in three separate orbitals (half-filled, extra stable). O is 2p42p^4: the fourth electron is paired in an orbital and is pushed out by repulsion

The order in period 2 is Li<B<Be<C<O<N<F<Ne\mathrm{Li} < \mathrm{B} < \mathrm{Be} < \mathrm{C} < \mathrm{O} < \mathrm{N} < \mathrm{F} < \mathrm{Ne}, and in period 3 Na<Al<Mg<Si<S<P<Cl<Ar\mathrm{Na} < \mathrm{Al} < \mathrm{Mg} < \mathrm{Si} < \mathrm{S} < \mathrm{P} < \mathrm{Cl} < \mathrm{Ar}. Predicting aluminium from its neighbours — Na 496, Mg 737, Si 786 — gives "between 496 and 786 but below Mg", and the value is 577.

The group 13 irregularity

Element B Al Ga In Tl
ΔiH1\Delta_i H_1 / kJ mol−1\mathrm{kJ\ mol^{-1}} 801 577 579 558 589

Ga is slightly above Al because the ten 3d3d electrons between Al and Ga shield poorly, so Ga's outer electron feels a larger effective nuclear charge than the size increase would suggest. Tl is above In for the same reason with the 4f4f electrons added (lanthanoid contraction).

Successive ionization enthalpies — the jump rule

Key Point: A sudden big jump between ΔiHn\Delta_i H_n and ΔiHn+1\Delta_i H_{n+1} means the (n+1)(n+1)th electron comes from a noble-gas core. The element has nn valence electrons, sits in group nn (s-block) or 10+n10 + n (p-block), and its stable valence is nn.

Values / kJ mol−1\mathrm{kJ\ mol^{-1}} Reading
520, 7300 jump after 1: one valence electron, group 1 (Li), covalent MX possible for such a small ion
738, 1451, then 7733 jump after 2: two valence electrons, group 2 (Mg), forms MX2\mathrm{MX_2}
578, 1817, 2745, then 11 577 jump after 3: group 13 (Al)
2372, 5251 huge first value: noble gas (He), least reactive

The Na/Mg puzzle

ΔiH1\Delta_i H_1 ΔiH2\Delta_i H_2
Na 496 about 4562
Mg 737 1451

First ionization: Na (loses its lone 3s3s electron) is lower than Mg (two 3s3s electrons, higher nuclear charge, smaller atom). Second ionization: Na is now Na+\mathrm{Na^+} with the stable neon core 2s22p62s^2 2p^6, so the next electron is torn from a closed shell in a lower level — enormous cost. Mg+\mathrm{Mg^+} still has one 3s3s electron to give. So ΔiH1(Na)<ΔiH1(Mg)\Delta_i H_1(\mathrm{Na}) < \Delta_i H_1(\mathrm{Mg}) but ΔiH2(Na)≫ΔiH2(Mg)\Delta_i H_2(\mathrm{Na}) \gg \Delta_i H_2(\mathrm{Mg}).

[JEE Main] Hydrogen's ionization enthalpy in J per atom is 2.18×10−182.18 \times 10^{-18} J; multiply by Avogadro's number and you get 1312 kJ mol−11312\ \mathrm{kJ\ mol^{-1}}, or 1.312×106 J mol−11.312 \times 10^6\ \mathrm{J\ mol^{-1}} if the question asks in those units.


Card 7 — Electron Gain Enthalpy and Electronegativity

Revision card: four periodic trends with arrows on a table outline

Electron gain enthalpy — definition and sign

Key Point (Definition): Electron gain enthalpy ΔegH\Delta_{eg} H is the enthalpy change when an electron is added to an isolated gaseous atom to form a gaseous anion: X(g)+e−⟶X−(g),ΔegH\mathrm{X(g)} + e^- \longrightarrow \mathrm{X^-(g)}, \qquad \Delta_{eg} H It is negative (exothermic) for most elements because a neutral atom usually attracts an electron; it is positive (endothermic) for the noble gases (the electron must enter the next higher shell) and for a few ns2ns^2 elements (Be, Mg) and np3np^3 elements (N) with stable configurations.

Sign convention: electron affinity (EA) is the energy released, so a positive EA means a negative ΔegH\Delta_{eg} H of roughly the same size: EA of Cl =+349= +349 means ΔegH(Cl)=−349 kJ mol−1\Delta_{eg} H(\mathrm{Cl}) = -349\ \mathrm{kJ\ mol^{-1}}. (Strictly ΔegH=−EA−52RT\Delta_{eg} H = -\mathrm{EA} - \tfrac{5}{2}RT; ignore the small term unless asked.)

The data

Group 1 H Li Na K Rb Cs
ΔegH\Delta_{eg} H / kJ mol−1\mathrm{kJ\ mol^{-1}} −73-73 −60-60 −53-53 −48-48 −47-47 −46-46
Group 16 O S Se Te Po
ΔegH\Delta_{eg} H / kJ mol−1\mathrm{kJ\ mol^{-1}} −141-141 −200-200 −195-195 −190-190 −174-174
Group 17 F Cl Br I At
ΔegH\Delta_{eg} H / kJ mol−1\mathrm{kJ\ mol^{-1}} −328-328 −349-349 −325-325 −295-295 −270-270
Group 18 He Ne Ar Kr Xe Rn
ΔegH\Delta_{eg} H / kJ mol−1\mathrm{kJ\ mol^{-1}} +48+48 +116+116 +96+96 +96+96 +77+77 +68+68

Trends and the two anomalies

Direction Trend Reason
Across a period ΔegH\Delta_{eg} H becomes more negative smaller atom, higher effective nuclear charge; the added electron enters the same shell close to the nucleus
Down a group ΔegH\Delta_{eg} H becomes less negative the added electron enters a shell farther from the nucleus
O and F are less negative than S and Cl O −141-141 versus S −200-200; F −328-328 versus Cl −349-349 O and F are so small that the 2p2p subshell is already crowded; the incoming electron feels strong repulsion from the electrons already there. In S and Cl the 3p3p subshell is larger, so the repulsion is smaller

So chlorine has the most negative electron gain enthalpy of all elements (−349-349), not fluorine. Among the halogens the order is Cl>F>Br>I\mathrm{Cl} > \mathrm{F} > \mathrm{Br} > \mathrm{I} (most to least negative). Fluorine is still the most electronegative element and the most reactive non-metal; those are different properties.

Electronegativity — the Pauling scale

Key Point (Definition): Electronegativity is the ability of an atom in a chemical compound to attract the shared electrons of a bond to itself. It is not a measurable quantity and has no units; it is a number on an arbitrary scale. On Pauling's scale fluorine is assigned 4.0 and every other element is placed relative to it. It depends on the bonding partner and the oxidation state, so it is a property of an atom in a molecule, not of an isolated atom.

Period 2 Li Be B C N O F
Electronegativity 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Period 3 Na Mg Al Si P S Cl
Electronegativity 0.9 1.2 1.5 1.8 2.1 2.5 3.0
Group 1 Li Na K Rb Cs Group 17 F Cl Br I At
Electronegativity 1.0 0.9 0.8 0.8 0.7 4.0 3.0 2.8 2.5 2.2

Trend: increases across a period (Li 1.0 to F 4.0), decreases down a group (F 4.0 to At 2.2; Li 1.0 to Cs 0.7). It moves with ionization enthalpy and non-metallic character and against atomic radius and metallic character — smaller atom, higher ZeffZ_{eff}, stronger pull on bond electrons. The most electronegative element is F, the least is Cs (Fr).

Three properties that students mix up

Property What is measured Isolated atom? Units Sign
Ionization enthalpy energy to remove an electron yes, gaseous kJ mol−1\mathrm{kJ\ mol^{-1}} always positive
Electron gain enthalpy enthalpy change on adding an electron yes, gaseous kJ mol−1\mathrm{kJ\ mol^{-1}} usually negative, positive for noble gases
Electronegativity tendency to attract shared electrons in a bond no, atom in a compound none relative number, 0.7 to 4.0

[JEE Main] The Mulliken scale is χM=(IE+EA)/2\chi_M = (IE + EA)/2 in eV; divide by 2.8 to get a Pauling-like value. The second electron gain enthalpy of O and S (O−→O2−\mathrm{O^-} \rightarrow \mathrm{O^{2-}}) is strongly positive because a negative ion is being asked to accept another electron.


Card 8 — Chemical Trends: Valence, Hydrides and Oxides, Second-Period Anomalies, Reactivity and Oxide Character

Revision card: anomalies, diagonal pairs and oxide character map

Valence of the representative elements

Key Point: Valence == number of valence (outermost) electrons, or 8−8 - that number. Groups 1, 2, 13, 14 use the first; groups 15, 16, 17 mostly the second (with respect to hydrogen).

Group 1 2 13 14 15 16 17 18
Valence electrons 1 2 3 4 5 6 7 8
Valence 1 2 3 4 3, 5 2, 6 1, 7 0, 8
Hydride LiH, NaH, KH CaH2\mathrm{CaH_2} B2H6\mathrm{B_2H_6}, AlH3\mathrm{AlH_3} CH4\mathrm{CH_4}, SiH4\mathrm{SiH_4}, GeH4\mathrm{GeH_4}, SnH4\mathrm{SnH_4} NH3\mathrm{NH_3}, PH3\mathrm{PH_3}, AsH3\mathrm{AsH_3} H2O\mathrm{H_2O}, H2S\mathrm{H_2S}, H2Se\mathrm{H_2Se}, H2Te\mathrm{H_2Te} HF, HCl, HBr, HI —
Oxide Li2O\mathrm{Li_2O}, Na2O\mathrm{Na_2O}, K2O\mathrm{K_2O} MgO, CaO, SrO, BaO B2O3\mathrm{B_2O_3}, Al2O3\mathrm{Al_2O_3}, Ga2O3\mathrm{Ga_2O_3}, In2O3\mathrm{In_2O_3} CO2\mathrm{CO_2}, SiO2\mathrm{SiO_2}, GeO2\mathrm{GeO_2}, SnO2\mathrm{SnO_2}, PbO2\mathrm{PbO_2} N2O3\mathrm{N_2O_3}, N2O5\mathrm{N_2O_5}; P4O6\mathrm{P_4O_6}, P4O10\mathrm{P_4O_{10}}; As2O3\mathrm{As_2O_3}, As2O5\mathrm{As_2O_5}; Sb2O3\mathrm{Sb_2O_3}, Sb2O5\mathrm{Sb_2O_5}; Bi2O3\mathrm{Bi_2O_3} SO3\mathrm{SO_3}, SeO3\mathrm{SeO_3}, TeO3\mathrm{TeO_3} Cl2O7\mathrm{Cl_2O_7} —

Oxidation state follows electronegativity: in OF2\mathrm{OF_2} oxygen is +2+2 (F is more electronegative), in Na2O\mathrm{Na_2O} oxygen is −2-2. Transition elements and actinoids show variable valence. In [AlCl(H2O)5]2+[\mathrm{AlCl(H_2O)_5}]^{2+} the oxidation state of Al is +3+3 but its covalency is 6 (six bonds) — oxidation state and covalency are not the same number.

Anomalous behaviour of the second-period elements (Li, Be, B, C, N, O, F)

Cause Consequence
Very small size and high charge/radius ratio Li 152 pm versus Na 186 pm; Li+\mathrm{Li^+} 76 pm versus Na+\mathrm{Na^+} 102 pm; Be2+\mathrm{Be^{2+}} 31 pm versus Mg2+\mathrm{Mg^{2+}} 72 pm — so Li and Be form covalent compounds where their group-mates form ionic ones
High electronegativity polarising, more covalent
Only four valence orbitals (2s2s, 2px2p_x, 2py2p_y, 2pz2p_z) versus nine for period 3 (3s3s, 3p3p, 3d3d) maximum covalency 4: boron gives BF4−\mathrm{BF_4^-}, aluminium gives AlF63−\mathrm{AlF_6^{3-}}; nitrogen cannot form NF5\mathrm{NF_5} while phosphorus forms PF5\mathrm{PF_5}
Small atoms come close enough for sideways pp overlap strong pπp\pi-pπp\pi multiple bonds: C=C\mathrm{C{=}C}, C≡C\mathrm{C{\equiv}C}, N≡N\mathrm{N{\equiv}N}, C=O\mathrm{C{=}O}, N=O\mathrm{N{=}O}; the heavier members prefer single bonds

Diagonal relationship

Key Point: The first element of a group often resembles the second element of the next group because their sizes and charge/radius ratios are similar: Li and Mg, Be and Al, B and Si.

Pair Shared behaviour
Li / Mg both form nitrides directly with N2\mathrm{N_2}, carbonates that decompose on heating, and covalent-ish compounds
Be / Al both form amphoteric oxides and hydroxides, covalent chlorides that fume in air
B / Si both non-metals with acidic oxides and covalent hydrides

Chemical reactivity — the ends-of-period rule

Position Behaviour Reason
Extreme left (group 1) most reactive metals; reactivity increases down the group (Li < Na < K < Rb < Cs) lowest ΔiH\Delta_i H; lose an electron easily
Extreme right (group 17) most reactive non-metals; reactivity decreases down the group (F > Cl > Br > I) most negative ΔegH\Delta_{eg} H, highest electronegativity; gain an electron easily
Centre (groups 13, 14, transition) least reactive middling ΔiH\Delta_i H and ΔegH\Delta_{eg} H; the noble gases at the far right are inert for a different reason (closed shells)

Metallic character and reactivity of metals go down and left; non-metallic character and reactivity of non-metals go up and right. The elements change from electropositive (electron losers) at the left to electronegative (electron gainers) at the right.

Oxide character

Type Where in the table Examples Reaction with water
Basic extreme left (group 1, 2 metals) Na2O\mathrm{Na_2O}, K2O\mathrm{K_2O}, MgO, CaO Na2O+H2O→2 NaOH\mathrm{Na_2O} + \mathrm{H_2O} \to 2\,\mathrm{NaOH} (strong base)
Amphoteric centre-left, near the zig-zag line Al2O3\mathrm{Al_2O_3}, As2O3\mathrm{As_2O_3}, ZnO, BeO, PbO react with both acids and bases: Al2O3+6 HCl→2 AlCl3+3 H2O\mathrm{Al_2O_3} + 6\,\mathrm{HCl} \to 2\,\mathrm{AlCl_3} + 3\,\mathrm{H_2O}; Al2O3+2 NaOH→2 NaAlO2+H2O\mathrm{Al_2O_3} + 2\,\mathrm{NaOH} \to 2\,\mathrm{NaAlO_2} + \mathrm{H_2O}
Neutral centre (non-metals in low oxidation states) CO, NO, N2O\mathrm{N_2O} neither acidic nor basic
Acidic extreme right (non-metals) Cl2O7\mathrm{Cl_2O_7}, SO3\mathrm{SO_3}, P4O10\mathrm{P_4O_{10}}, N2O5\mathrm{N_2O_5}, CO2\mathrm{CO_2} Cl2O7+H2O→2 HClO4\mathrm{Cl_2O_7} + \mathrm{H_2O} \to 2\,\mathrm{HClO_4} (strong acid); SO3+H2O→H2SO4\mathrm{SO_3} + \mathrm{H_2O} \to \mathrm{H_2SO_4}

Across period 3: Na2O\mathrm{Na_2O} (strongly basic), MgO (basic), Al2O3\mathrm{Al_2O_3} (amphoteric), SiO2\mathrm{SiO_2} (weakly acidic), P4O10\mathrm{P_4O_{10}} (acidic), SO3\mathrm{SO_3} (strongly acidic), Cl2O7\mathrm{Cl_2O_7} (most acidic). Down a group the oxides become more basic (N2O3\mathrm{N_2O_3} acidic, Bi2O3\mathrm{Bi_2O_3} basic). The higher the oxidation state of the same element, the more acidic the oxide (SO2<SO3\mathrm{SO_2} < \mathrm{SO_3}, Mn2O7\mathrm{Mn_2O_7} acidic while MnO is basic).

[Board] "Predict the formulas of the compounds between": silicon and bromine gives SiBr4\mathrm{SiBr_4} (valence 4 and 1); aluminium and sulphur gives Al2S3\mathrm{Al_2S_3} (3 and 2); element with Z=114Z = 114 and hydrogen gives FlH4\mathrm{FlH_4} (group 14). Read the group, read the valence, cross-multiply.


The Mistakes That Cost the Most Marks

Each of these was flagged somewhere in Sections 1 to 13, ordered roughly by how often they show up in answer scripts.

1. Saying fluorine has the most negative electron gain enthalpy. It is chlorine (−349 kJ mol−1-349\ \mathrm{kJ\ mol^{-1}}); F is −328-328. The small 2p2p subshell of F repels the incoming electron. F is the most electronegative (4.0) and the most reactive non-metal — three different properties, three different winners.

2. Ranking B above Be and O above N in ionization enthalpy. Be (2s22s^2) > B (2s22p12s^2 2p^1): the pp electron is less penetrating and better shielded. N (2p32p^3, half-filled) > O (2p42p^4, one pair repelling). Period 2 order: Li<B<Be<C<O<N<F<Ne\mathrm{Li} < \mathrm{B} < \mathrm{Be} < \mathrm{C} < \mathrm{O} < \mathrm{N} < \mathrm{F} < \mathrm{Ne}. Same shape in period 3 with Al/Mg and S/P.

3. Writing "atomic mass" in the modern periodic law, or "atomic number" in Mendeleev's. Mendeleev: periodic function of atomic weights. Modern (after Moseley, 1913): periodic function of atomic numbers. Moseley plotted ν\sqrt{\nu} against ZZ and got a straight line.

4. Calling helium s-block, or hydrogen an alkali metal. He is 1s21s^2 but sits in group 18 because its shell is complete. H is placed separately — one electron like group 1, one short of a full shell like group 17.

5. Comparing a noble-gas radius with the others in its period. Noble-gas radii are van der Waals radii (non-bonded), so they come out larger than the halogen before them. Leave them out of the "smallest atom in the period" answer — in period 2 it is F (64 pm), not Ne.

6. Ordering an isoelectronic series by size the wrong way. Same electrons, so more protons means smaller: O2−>F−>Na+>Mg2+>Al3+\mathrm{O^{2-}} > \mathrm{F^-} > \mathrm{Na^+} > \mathrm{Mg^{2+}} > \mathrm{Al^{3+}}. The anion with the lowest ZZ is the largest. For the same element, Fe>Fe2+>Fe3+\mathrm{Fe} > \mathrm{Fe^{2+}} > \mathrm{Fe^{3+}}.

7. Reading the p-block group number as the number of pp electrons. Group =10+= 10 + valence electrons for the p-block: ns2np4ns^2 np^4 is group 16, not 4 or 6. For the d-block, group == (n−1)d(n-1)d electrons ++ nsns electrons: 3d64s23d^6 4s^2 is group 8. Period == highest nn.

8. Treating electronegativity as a measurable energy with units. Electronegativity is a relative, unitless number on an arbitrary scale (Pauling: F =4.0= 4.0) for an atom in a compound. Ionization enthalpy and electron gain enthalpy are measured for isolated gaseous atoms in kJ mol−1\mathrm{kJ\ mol^{-1}}.

9. Getting the electron affinity sign backwards. Electron affinity is energy released, so a positive EA is a negative ΔegH\Delta_{eg} H: EA(Cl) =+349= +349, ΔegH(Cl)=−349 kJ mol−1\Delta_{eg} H(\mathrm{Cl}) = -349\ \mathrm{kJ\ mol^{-1}}. Noble gases have positive ΔegH\Delta_{eg} H (He +48+48, Ne +116+116).

10. Confusing the second ionization enthalpy of Na and Mg. ΔiH1\Delta_i H_1: Na (496) < Mg (737). ΔiH2\Delta_i H_2: Na (about 4562) ≫\gg Mg (1451), because Na+\mathrm{Na^+} has the neon core. The big jump in successive values tells you the number of valence electrons and hence the group.

11. Missing the group 13 irregularity. Ionization enthalpy does not fall smoothly: B 801, Al 577, Ga 579, In 558, Tl 589. Poor shielding by 3d3d (for Ga) and 4f4f (for Tl) electrons keeps the outer electron more tightly held.

12. Calling Al2O3\mathrm{Al_2O_3} acidic or basic, and CO acidic. Al2O3\mathrm{Al_2O_3} (and As2O3\mathrm{As_2O_3}, ZnO, BeO) is amphoteric — reacts with both acids and bases. CO, NO and N2O\mathrm{N_2O} are neutral. Acidic: Cl2O7\mathrm{Cl_2O_7}, SO3\mathrm{SO_3}, CO2\mathrm{CO_2}; basic: Na2O\mathrm{Na_2O}, MgO. Across a period oxides go basic to acidic; down a group they become more basic.

Key Point: Two more that cost single marks: writing the IUPAC name with the roots in the wrong order or a four-letter symbol (105 is unnilpentium, Unp, official dubnium, Db), and forgetting that Zn, Cd and Hg are in the d-block but are not transition elements because their d10d^{10} subshell is full in the element and its ions.


The 60-Second Revision

The irreducible minimum, for the queue outside the hall.

History. Dobereiner 1829 triads (Li-Na-K, Ca-Sr-Ba, Cl-Br-I; middle weight is the mean). de Chancourtois 1862 cylinder. Newlands 1865 octaves, works only to Ca. Lothar Meyer atomic-volume curves. Mendeleev 1869: periodic law by atomic weight, 63 elements, swapped Te/I, gaps for eka-Al (Ga: 68 predicted, 70 found; E2O3\mathrm{E_2O_3}, ECl3\mathrm{ECl_3}) and eka-Si (Ge: 72 predicted, 72.6 found; EO2\mathrm{EO_2}, ECl4\mathrm{ECl_4}). Moseley 1913: ν∝Z\sqrt{\nu} \propto Z, modern periodic law by atomic number. Seaborg: actinoids, transuranium elements, seaborgium (106).

Table. 7 periods with 2, 8, 8, 18, 18, 32, 32 elements — twice the orbitals filled (1s1s; 2s2p2s2p; 3s3p3s3p; 4s3d4p4s3d4p; 5s4d5p5s4d5p; 6s4f5d6p6s4f5d6p; 7s5f6d7p7s5f6d7p). Period == highest nn. 18 groups: 1 alkali (ns1ns^1), 2 alkaline earth (ns2ns^2), 3 to 12 transition ((n−1)d1−10ns0−2(n-1)d^{1-10}ns^{0-2}), 13 to 18 p-block (ns2np1−6ns^2np^{1-6}); 15 pnictogens, 16 chalcogens, 17 halogens, 18 noble gases. Lanthanoids Ce to Lu (4f4f), actinoids Th to Lr (5f5f), group 3. p-block group =10+= 10 + valence electrons; d-block group =d+s= d + s electrons. He in group 18 (full shell); H alone. Zn, Cd, Hg: d-block, not transition. Metals 78%; metalloids B, Si, Ge, As, Sb, Te on the zig-zag.

IUPAC. nil un bi tri quad pent hex sept oct enn (0 to 9); roots in digit order + "ium"; three-letter symbol. 104 Unq/Rf, 106 Unh/Sg, 110 Uun/Ds, 114 Uuq/Fl, 117 Uus/Ts, 118 Uuo/Og, 120 Ubn.

Radius. Covalent (half of Cl-Cl 198 pm gives 99), metallic (half of Cu-Cu 256 gives 128), van der Waals for noble gases (do not compare). Decreases across (Li 152 to F 64; Na 186 to Cl 99), increases down (Li 152, Na 186, K 231, Rb 244, Cs 262; F 64, Cl 99, Br 114, I 133, At 140). Cation smaller (Na 186, Na+\mathrm{Na^+} 95), anion larger (F 64, F−\mathrm{F^-} 136). Isoelectronic: more protons, smaller — O2−>F−>Na+>Mg2+>Al3+\mathrm{O^{2-}} > \mathrm{F^-} > \mathrm{Na^+} > \mathrm{Mg^{2+}} > \mathrm{Al^{3+}}.

Ionization enthalpy. Isolated gaseous ground-state atom; always positive; ΔiH1<ΔiH2\Delta_i H_1 < \Delta_i H_2. Increases across, decreases down; max at noble gases (He 2372), min at alkali metals. Anomalies Be > B, N > O (Mg > Al, P > S). Period 2: Li < B < Be < C < O < N < F < Ne. Na 496, Mg 737, Al 577, Si 786; B 801, Al 577, Ga 579, In 558, Tl 589. Big jump in successive values reveals the group. ΔiH2\Delta_i H_2: Na ≫\gg Mg. H: 1312 kJ mol−11312\ \mathrm{kJ\ mol^{-1}}.

Electron gain enthalpy. X(g)+e−→X−(g)\mathrm{X(g)} + e^- \to \mathrm{X^-(g)}; more negative across, less negative down; noble gases positive (He +48, Ne +116, Ar +96). Cl −349-349 most negative of all; F −328-328; Br −325-325; I −295-295; O −141-141 < S −200-200. EA positive means ΔegH\Delta_{eg} H negative.

Electronegativity. Unitless, relative, atom in a bond, Pauling F = 4.0; Li 1.0, Be 1.5, B 2.0, C 2.5, N 3.0, O 3.5, F 4.0; Na 0.9 to Cl 3.0; Cs 0.7 lowest. Rises with ΔiH\Delta_i H and non-metallic character, falls with radius.

Chemistry. Valence = valence electrons or 8 minus them: hydrides LiH, CaH2\mathrm{CaH_2}, B2H6\mathrm{B_2H_6}, CH4\mathrm{CH_4}, NH3\mathrm{NH_3}, H2O\mathrm{H_2O}, HF; oxides Li2O\mathrm{Li_2O}, MgO, B2O3\mathrm{B_2O_3}, CO2\mathrm{CO_2}, N2O5\mathrm{N_2O_5}, SO3\mathrm{SO_3}, Cl2O7\mathrm{Cl_2O_7}. Second period anomalous: tiny size, high charge/radius, high electronegativity, only 4 valence orbitals (covalency 4: BF4−\mathrm{BF_4^-} versus AlF63−\mathrm{AlF_6^{3-}}), pπp\pi-pπp\pi bonds. Diagonal pairs Li/Mg, Be/Al, B/Si. Reactivity highest at both ends: metals down-left (Cs), non-metals up-right (F). Oxides: basic Na2O\mathrm{Na_2O} (to NaOH), amphoteric Al2O3\mathrm{Al_2O_3}, As2O3\mathrm{As_2O_3}, neutral CO, NO, N2O\mathrm{N_2O}, acidic Cl2O7\mathrm{Cl_2O_7} (to HClO4\mathrm{HClO_4}).

That is the whole chapter.