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MHT-CET Chemistry · Formula sheet

Transition and Inner Transition Elements formulas

8 formulas, 3 reference tables and 12 common traps for MHT-CET Chemistry Transition and Inner Transition Elements, grouped by subtopic.

Full notes with worked examples

The d-Block: Position, d-Electron Counts and General Properties

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Counting d Electrons in Atoms and Ions

d electrons in a 3d ion

nd=Z−18−q;unpaired={ndnd≤510−ndnd>5n_d = Z - 18 - q;\qquad \text{unpaired} = \begin{cases} n_d & n_d \le 5 \\ 10 - n_d & n_d > 5 \end{cases}

Hard Metals, Soft Exceptions and First Ionisation Enthalpy

3d first ionisation enthalpy (ends)

Sc (633)<…<Fe (762)<Zn (906) kJ mol−1\text{Sc } (633) < \ldots < \text{Fe } (762) < \text{Zn } (906)\ \text{kJ mol}^{-1}

Four Transition Series in Groups 3 to 12

SeriesPeriodElementsExample
3d4Sc (21) – Zn (30)Co, Cr, Mn, Fe
4d5Y (39) – Cd (48)Mo, Ag
5d6La (57), Hf (72) – Hg (80)Pt, Au, Hg
The lanthanoids Ce–Lu sit inside this row but are f-block.
6d7Ac (89), Rf (104) onward—
Series number = period − 1; ten elements a series.

Common traps

Using the period number as the series number

Cobalt is in period 4 but is a 3d element; the d subshell being filled is one shell below the valence shell, (n − 1)d.

Removing the 3d electrons first

4s fills before 3d but empties first too. Fe²⁺ is 3d⁶, not 3d⁴ 4s²; Ti²⁺ is 3d², not 3d⁰ 4s².

Expecting a steady rise across the series

Cr (653) is barely above Sc (633) and below Fe (762); Zn's filled shell makes it the outlier. Learn the two ends and Fe, not a smooth trend.

Oxidation States of Transition Elements

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How Many Oxidation States, and the Highest One

Maximum oxidation state, Sc to Mn

max O.S.=n(4s)+n(3d): Sc +3, Ti +4, V +5, Cr +6, Mn +7\text{max O.S.} = n(4s) + n(3d):\ \text{Sc } {+3},\ \text{Ti } {+4},\ \text{V } {+5},\ \text{Cr } {+6},\ \text{Mn } {+7}

Common traps

Picking the element with most d electrons

Zinc and copper have the most d electrons but the fewest states — a full or nearly full d subshell does not give up electrons. The widest range belongs to the middle, Mn.

Colour and Magnetism of Transition Metal Ions

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Coloured and Colourless Ions

Colour condition

coloured  ⟺  1≤nd≤9;d0, d10⇒colourless\text{coloured} \iff 1 \le n_d \le 9;\quad d^0,\ d^{10} \Rightarrow \text{colourless}

Unpaired Electrons and the Spin-Only Magnetic Moment

Spin-only magnetic moment

μ=n(n+2) BM\mu = \sqrt{n(n+2)}\ \text{BM}

Common traps

Treating copper as always coloured

Cu²⁺ (d⁹) is blue, but Cu⁺ (d¹⁰) is colourless. Count the d electrons of the ION, not the element.

Counting all the d electrons as unpaired

Beyond d⁵ the electrons pair: Cu²⁺ (d⁹) has one unpaired electron, not nine, and Zn²⁺ (d¹⁰) has none.

Calling every paramagnetic metal ferromagnetic

Chromium has unpaired electrons and is paramagnetic, but only iron, cobalt and nickel are ferromagnetic — they stay magnetised when the field is removed.

Alloys, Ores and Catalysts of the Transition Metals

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Alloys, Ores and Catalysts to Know

MetalOresCatalyst use
CuChalcopyrite (copper pyrites) CuFeS₂; chalcocite Cu₂S—
ZnCalamine ZnCO₃; zincite ZnO; zinc blende ZnS—
FeSiderite FeCO₃; limonite; haematite Fe₂O₃; magnetite Fe₃O₄Haber process
V—V₂O₅ in the contact process
Co—Co–Th in the Fischer–Tropsch synthesis
Ni—Hydrogenation of oils; Ni–Cr is nichrome
Siderite, limonite and haematite are iron; calamine and zincite are zinc.

Common traps

Reading 'copper pyrites' as copper and sulphur only

Copper pyrites is CuFeS₂ — iron is in it too. And chalcocite (Cu₂S) is copper, while chalcopyrite is the mixed copper–iron sulphide.

Lanthanoids and Actinoids: Membership, 4f Configurations and the Lanthanoid Contraction

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4f Configurations and the +2 and +4 States

f electrons in Ln³⁺

nf(Ln3+)=Z−57;unpaired={nfnf≤714−nfnf>7n_f(\text{Ln}^{3+}) = Z - 57;\quad \text{unpaired} = \begin{cases} n_f & n_f \le 7 \\ 14 - n_f & n_f > 7 \end{cases}

The Lanthanoid Contraction: Size, Basicity and Ionisation Enthalpy

Trends along the lanthanoids

r(La3+)>…>r(Lu3+);La(OH)3>…>Lu(OH)3 (basicity)r(\text{La}^{3+}) > \ldots > r(\text{Lu}^{3+});\quad \text{La(OH)}_3 > \ldots > \text{Lu(OH)}_3\ \text{(basicity)}

Lanthanoid Compounds and General Properties

Common lanthanoid compounds

Ln3+: Ln(OH)3, Ln2O3, LnX3;Ln+2C→ΔLnC2\text{Ln}^{3+}:\ \text{Ln(OH)}_3,\ \text{Ln}_2\text{O}_3,\ \text{LnX}_3;\quad \text{Ln} + 2\text{C} \xrightarrow{\Delta} \text{LnC}_2

Which Element Is a Lanthanoid, Which an Actinoid

SeriesZMembers to recognise
Lanthanoids (4f)57–71La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Actinoids (5f)89–103Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
All actinoids are radioactive.
Tm, Pm, Sm are lanthanoids; Cm, Am, Np are actinoids — the look-alike pairs the options use.

Common traps

Matching by the ending of the name

Promethium, thulium and samarium are lanthanoids; americium, curium and neptunium are actinoids. The names do not sort them — the lists do.

Expecting f⁷ at +3 for europium

Eu is already 4f⁷ as an atom, so Eu³⁺ is f⁶; it is Eu²⁺ that keeps the half-filled shell. The f⁷ ion at +3 is Gd³⁺, and the f⁷ ion at +4 is Tb⁴⁺.

Picking Yb as the smallest ion

Yb is near the end but Lu is after it: when both appear, the smallest Ln³⁺ is Lu³⁺. Yb wins only the ionisation-enthalpy question.

Assuming every lanthanoid is stable

Promethium (Z = 61) has no stable isotope. 'All lanthanoids are non-radioactive' is the false statement the paper keys.

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