PYQ explainedUnit 2 · Chemical bonding14 November 2026

Fajans' rules: why AlCl₃ sublimes and AgCl does not dissolve in water

Q: What are Fajans' rules?

Fajans' rules say how much covalent character an ionic bond has. Covalent character increases when the cation is small and highly charged (high ionic potential z/r), when the anion is large and highly charged (easily polarised), and when the cation has an 18-electron (pseudo-noble-gas) shell such as Ag+, Cu+ or Zn2+ instead of an 8-electron noble-gas shell.

Q: Why does AlCl3 sublime at about 180 °C while NaCl melts at 801 °C?

Al3+ is small and triply charged (z/r = 5.61 per 100 pm against 0.98 for Na+), so it polarises chloride strongly and AlCl3 is largely covalent. In the vapour it exists as Al2Cl6 molecules held by weak intermolecular forces, so little energy is needed to vaporise it. NaCl is a three-dimensional ionic lattice.

Q: Why is AgCl insoluble in water when NaCl is soluble, though Ag+ and Na+ are of similar size?

Ag+ has a [Kr]4d10 18-electron shell. The d electrons shield the nuclear charge poorly, so Ag+ has a higher effective nuclear charge and strongly polarises Cl−. The Ag–Cl bond becomes partly covalent, the lattice is held more strongly than the ionic model predicts, and hydration cannot pay for breaking it. Ksp of AgCl is only 1.8 × 10−10.

Q: Which is more covalent, NaBr or MgBr2?

MgBr2. Mg2+ (72 pm, charge +2) has a much higher polarising power than Na+ (102 pm, +1), so it distorts the large Br− ion more. This was asked in UPSC Civil Services 2019, Chemistry Paper I, Q1(a)(i), for 10 marks.

Q: Why does the 18-electron rule matter in Fajans' rules?

For two cations of the same size and charge, the one with d10 electrons in its outer shell is more polarising, because d electrons shield the nucleus less well than s and p electrons. That is why CuCl is more covalent than NaCl and AgCl, AgBr and AgI are far less soluble than the sodium halides.

Q: How often does UPSC ask Fajans' rules?

In Mains, polarisation and covalent character came 4 times for 33 marks in Civil Services and IFoS from 2019 to 2024. The Geo-Scientist Prelims Chemistry paper has asked a Fajans' rules or polarisation question in every paper from 2021 to 2026.

By Vimal Swarnkar (VKC) · UPSC Chemistry · Civil Services, Combined Geo-Scientist and IFoS

Na⁺ and Ag⁺ are almost the same size, yet one chloride dissolves by the kilogram and the other hardly at all. Size alone cannot explain it; the electrons behind the size can. In this post I will show you how often UPSC asks polarisation, which book to use, how I plan the answer, and how it should look in your booklet.

Day 08 question (Daily Answer Writing, 11 November 2026), 10 marks

State Fajans' rules. Use them to explain: (i) the melting points NaCl 801 °C, MgCl₂ 714 °C, while AlCl₃ sublimes at about 180 °C; (ii) AgCl is sparingly soluble in water whereas NaCl is very soluble, although Ag⁺ (115 pm) and Na⁺ (102 pm) are of nearly the same size.

Built on UPSC Civil Services (Main) 2019, Chemistry Paper I, Q1(a)(i), 10 marks: “In which of the following compounds do the bonds have greater covalent character: NaBr or MgBr₂? Give reasons.”

Short answer

A cation polarises the anion's electron cloud; more polarisation means more covalent character. Covalent character rises for a small, highly charged cation, a large, highly charged anion, and a cation with an 18-electron shell. (i) z/r rises Na⁺ 0.98 < Mg²⁺ 2.78 < Al³⁺ 5.61 (×100 pm⁻¹), so NaCl (801 °C) > MgCl₂ (714 °C) > AlCl₃, which exists as Al₂Cl₆ molecules and sublimes at about 180 °C. (ii) Ag⁺ is [Kr]4d¹⁰; d electrons shield poorly, so Ag⁺ polarises Cl⁻ strongly, Ag–Cl is partly covalent and K_sp(AgCl) = 1.8 × 10⁻¹⁰, while NaCl dissolves to about 6 mol kg⁻¹.

Watch the video

Day 08 of my Daily Answer Writing series on YouTube: I write this 10-mark answer the way it should go into your booklet, with the polarisation sketch and the z/r table.

Video coming soon. It goes up on the VKC YouTube channel and is announced first on Telegram.

A word from me

Every student can recite “small cation, large anion”. Very few write the third rule, the one about the 18-electron shell, and that is exactly the rule part (ii) of this question is testing. If you explain AgCl by size, you have explained nothing, because the question itself tells you Ag⁺ and Na⁺ are almost the same size. The examiner gives this question to see who reads the data.

So learn the rules as a set of three, and always attach one number to each: z/r for the first, the anion series F⁻ → I⁻ for the second, and the [Kr]4d¹⁰ configuration for the third. Then the same three lines answer melting points, solubility, colour of silver halides and lattice energies that come out “too high”. If something does not add up, write to me on Telegram or at [email protected].

Every Geo-Scientist Prelims paper, and Mains every few years

In Mains, polarisation and covalent character came 4 times, for 33 marks, in Civil Services Paper I and IFoS Paper I from 2019 to 2024: Civil Services 2019 Q1(a)(i) (NaBr or MgBr₂, 10 marks), Civil Services 2022 Q4(e) (percentage ionic character of Br–Cl, 10 marks), Civil Services 2024 Q1(a)(ii) (lattice energies of NaBr and NaI above the calculated values, 5 marks) and IFoS 2024 Q5(a) (solubility of LiF, LiI, CsF and CsI, 8 marks).

The Geo-Scientist Prelims Chemistry paper asks it every year: a Fajans' rules, polarising power or ionic-character question appears in each paper from 2021 to 2026 (2021 Q11 and Q13, 2022 Q20, 2023 Q22, 2024 Q20 and Q21, 2025 Q20, 2026 Q20). If you are writing Geo-Scientist, this is a sure mark every year.

Syllabus and books

In Civil Services it is Paper I, Unit 2, Chemical bonding. IFoS asks it in Paper I, and the Geo-Scientist Prelims Chemistry paper under chemical bonding. The Civil Services syllabus reads:

“Ionic bond, characteristics of ionic compounds, lattice energy, Born-Haber cycle; covalent bond and its general characteristics, polarities of bonds in molecules and their dipole moments …”

IFoS adds the words factors affecting stability of ionic compounds. Covalent character inside an ionic compound is exactly the bridge between the two halves of that line.

You do not need all of these books. Any one of them is enough for this question.

Book 1: J. D. Lee, Concise Inorganic Chemistry (5th edition), the chapter “The ionic bond”, the part on covalency in ionic compounds and Fajans' rules. Short and exam-ready; if you have this book, this is the one I would use.
Book 2: Huheey, Keiter and Keiter, Inorganic Chemistry (4th edition), the chapter on ionic compounds, the section on covalent character in predominantly ionic bonds. Best for the 18-electron argument and lattice energy data.
Book 3: Puri, Sharma and Kalia, Principles of Inorganic Chemistry, the chapter on the ionic bond, Fajans' rules. Good if you prefer an Indian textbook.

How to build the answer

Read the tree from left to right. Every leaf is a point to write, in that order. The highlighted words are the ones the examiner looks for.

Fajans' rules → falling m.p. NaCl, MgCl₂, AlCl₃; AgCl insoluble, NaCl soluble

Introduction

Given

r: Na⁺ 102, Mg²⁺ 72, Al³⁺ 53.5, Ag⁺ 115 pm

Key idea

cation polarises anion's e⁻ cloud
more polarisation = more covalent character

Three rules

small, high-charge cation (z/r)
large, high-charge anion
18-e⁻ shell cation

Body

Diagram

polarised anion sketch

(i) Trend

z/r: 0.98 < 2.78 < 5.61
3D ionic → layer → Al₂Cl₆
weak forces → sublimes 180 °C

(ii) AgCl

Na⁺ [Ne] vs Ag⁺ [Kr]4d¹⁰
d e⁻ shield poorly → high Z_eff
K_sp = 1.8 × 10⁻¹⁰

Conclusion

Principle

high z/r + 18-e⁻ shell → strong polariser
covalent → m.p. ↓, solubility ↓

Application

AgCl, AgBr: gravimetric Cl⁻, Br⁻
AgF soluble; AgCl > AgBr > AgI

Final answer

two orders, double underlined

Pictures that earn marks

Figure 1. Fajans' picture. A small, highly charged cation pulls the electron cloud of a large anion towards itself. The electron density shared between the two is the covalent part of the bond.

Figure 2. Ionic potential z/r of Na⁺, Mg²⁺ and Al³⁺ (radii for coordination number 6). As polarising power rises, the chloride changes from a 3D ionic lattice to a layer lattice to separate Al₂Cl₆ molecules, and the melting point falls.

Figure 3. Al₂Cl₆: two AlCl₄ tetrahedra sharing an edge through two bridging chlorine atoms. Only weak forces act between these molecules, which is why AlCl₃ sublimes near 180 °C.

Figure 4. Na⁺ and Ag⁺ are nearly the same size, but Ag⁺ carries ten 4d electrons in its outer shell. d electrons shield the nucleus poorly, so Ag⁺ has a higher effective nuclear charge and polarises Cl⁻ far more strongly.

What gains marks

All three Fajans' rules, including the 18-electron (pseudo-noble-gas) rule (3 marks).
A sketch of the polarised anion, or the z/r values in a table (1 mark).
(i) The z/r trend Na⁺ < Mg²⁺ < Al³⁺, and Al₂Cl₆ molecules with weak intermolecular forces to explain sublimation (3 marks).
(ii) Ag⁺ = [Kr]4d¹⁰, poor shielding by d electrons, strong polarisation, partly covalent lattice; K_sp quoted (3 marks).
One line of application: AgF soluble but AgCl > AgBr > AgI in solubility; silver halides in gravimetric analysis.

Match the length to the marks

For 5 marks, as in Civil Services 2024 Q1(a)(ii), state the rule that applies and write one comparison, about half a page. For 10 marks, as in Civil Services 2019 Q1(a)(i) and this question, write all three rules, the sketch, the table and both parts: the two pages below. For 15 marks, add the lattice energy against hydration enthalpy argument with a Born–Haber line and the full AgF → AgI series with colours.

How it looks in the booklet

This is the full answer in the order of the tree above. Page 1 states the rules and builds the table for part (i); page 2 explains AlCl₃, then AgCl, and closes with the principle and one application.

Page 1 of 2 · Rules and part (i)Fajans' rules, sketch, z/r table

Q.)State Fajans' rules. Explain (i) m.p. NaCl 801 °C, MgCl₂ 714 °C, AlCl₃ sublimes ≈180 °C; (ii) AgCl sparingly soluble, NaCl very soluble, though Ag⁺ (115 pm) ≈ Na⁺ (102 pm). [Day 08], 10M

Ans.A cation polarises (distorts) the electron cloud of the anion; the more the distortion, the more the covalent character. Fajans' rules: covalent character increases when

i) the cation is small and highly charged (high ionic potential φ = z/r);
ii) the anion is large and highly charged (easily polarised);
iii) the cation has an 18-electron (ns²np⁶nd¹⁰) shell, not an 8-electron shell.

(i) NaCl → MgCl₂ → AlCl₃ (radii for CN 6):

Cation	r / pm	z/r (×100 pm⁻¹)	Chloride	m.p. / °C
Na⁺	102	0.98	3D ionic	801
Mg²⁺	72	2.78	layer lattice	714
Al³⁺	53.5	5.61	Al₂Cl₆	≈180 (subl.)

Page 2 of 2 · Part (ii) and conclusionAl₂Cl₆, AgCl vs NaCl, principle, application

So polarising power rises Na⁺ < Mg²⁺ < Al³⁺, and so does covalent character. AlCl₃ is largely covalent: in the vapour it is Al₂Cl₆ molecules held by weak intermolecular forces, so it sublimes at ≈180 °C.

(ii) AgCl vs NaCl: Na⁺ = [Ne] (8 e⁻); Ag⁺ = [Kr]4d¹⁰ (18 e⁻). The 4d electrons shield poorly, so Ag⁺ has a higher Z_eff and strongly polarises the large Cl⁻. Ag–Cl gains covalent character; the lattice is held more strongly than the ionic model predicts, and hydration cannot pay for breaking it.

K_sp(AgCl) = 1.8 × 10⁻¹⁰; s ≈ 1.3 × 10⁻⁵ mol L⁻¹

against about 6 mol kg⁻¹ for NaCl. Same trend: AgF soluble; solubility AgCl > AgBr > AgI, colour deepens.

Conclusion: high z/r and an 18-e⁻ shell make a cation strongly polarising; covalent character lowers m.p. and water solubility. Application: insoluble AgCl, AgBr in gravimetric estimation of Cl⁻, Br⁻.

So, m.p. NaCl > MgCl₂ > AlCl₃; AgCl insoluble, NaCl soluble: both from rising polarisation

The same question in other exams

Civil Services 2019, Paper I, Q1(a)(i), 10 marks: NaBr or MgBr₂, which has more covalent character? MgBr₂: Mg²⁺ (72 pm, +2) polarises Br⁻ far more than Na⁺ (102 pm, +1). Rule 1 only.

Civil Services 2024, Paper I, Q1(a)(ii), 5 marks: NaBr and NaI have higher lattice energies than calculated. The Born–Landé value assumes pure ions; Br⁻ and I⁻ are large and easily polarised, so the real crystals gain extra covalent (and dispersion) bonding. Rule 2.

IFoS 2024, Paper I, Q5(a), 8 marks: LiF is less soluble than LiI; CsF or CsI? LiF has a very large lattice energy (small ions) that hydration cannot overcome; for big Cs⁺, the strong hydration of small F⁻ wins, so CsF is more soluble. Lattice energy against hydration, the same balance as part (ii).

Civil Services 2022, Paper I, Q4(e), 10 marks: percentage ionic character of BrCl from μ = 1.42 × 10⁻³⁰ C m and d = 214 pm: μ/(e·d) × 100 ≈ 4 %, so Br–Cl is a polar covalent bond. The other end of the ionic–covalent scale.

Geo-Scientist Prelims 2021, Q13: melting points BeCl₂ < MgCl₂ < CaCl₂ < NaCl, the same trend as part (i) with Group 2 cations.

Every version is one balance: how strongly the cation pulls on the anion's electrons (z/r, d¹⁰ shell) against how easily the anion gives way (size, charge). Decide which rule is being tested, give its number, and write the consequence for melting point, solubility or lattice energy.

Questions students ask

What are Fajans' rules?

Fajans' rules say how much covalent character an ionic bond has. Covalent character increases when the cation is small and highly charged (high ionic potential z/r), when the anion is large and highly charged (easily polarised), and when the cation has an 18-electron (pseudo-noble-gas) shell such as Ag+, Cu+ or Zn2+ instead of an 8-electron noble-gas shell.

Why does AlCl3 sublime at about 180 °C while NaCl melts at 801 °C?

Al3+ is small and triply charged (z/r = 5.61 per 100 pm against 0.98 for Na+), so it polarises chloride strongly and AlCl3 is largely covalent. In the vapour it exists as Al2Cl6 molecules held by weak intermolecular forces, so little energy is needed to vaporise it. NaCl is a three-dimensional ionic lattice.

Why is AgCl insoluble in water when NaCl is soluble, though Ag+ and Na+ are of similar size?

Ag+ has a [Kr]4d10 18-electron shell. The d electrons shield the nuclear charge poorly, so Ag+ has a higher effective nuclear charge and strongly polarises Cl−. The Ag–Cl bond becomes partly covalent, the lattice is held more strongly than the ionic model predicts, and hydration cannot pay for breaking it. Ksp of AgCl is only 1.8 × 10−10.

Which is more covalent, NaBr or MgBr2?

MgBr2. Mg2+ (72 pm, charge +2) has a much higher polarising power than Na+ (102 pm, +1), so it distorts the large Br− ion more. This was asked in UPSC Civil Services 2019, Chemistry Paper I, Q1(a)(i), for 10 marks.

Why does the 18-electron rule matter in Fajans' rules?

For two cations of the same size and charge, the one with d10 electrons in its outer shell is more polarising, because d electrons shield the nucleus less well than s and p electrons. That is why CuCl is more covalent than NaCl and AgCl, AgBr and AgI are far less soluble than the sodium halides.

How often does UPSC ask Fajans' rules?

In Mains, polarisation and covalent character came 4 times for 33 marks in Civil Services and IFoS from 2019 to 2024. The Geo-Scientist Prelims Chemistry paper has asked a Fajans' rules or polarisation question in every paper from 2021 to 2026.

Read the complete answers

CSE 2019 Q1(a)(i) solution CSE 2024 Q1(a)(ii) solution IFoS 2024 Q5(a) solution Notes: ionic bonding and Fajans' rules Day 08 question and model answer Join on Telegram

By VKC, your mentor. Integrated M.Sc. Chemistry, IIT Roorkee. CSIR NET Chemical Sciences, All India Rank 4. New posts are announced first on Telegram.