Why atoms combine
Apart from the noble gases, no element exists in nature as an independent atom under ordinary conditions. Atoms instead group together as molecules, held by an attractive force called a chemical bond. The question Kossel and Lewis set out to answer in 1916 was deceptively simple: why do atoms combine at all, and why only in certain ratios. Their shared insight was that bonding is nature's way of lowering the energy of a system, and that the special stability of the noble gases points to the configuration every other atom is trying to imitate.
G. N. Lewis pictured an atom as a positively charged kernel (the nucleus plus the inner electrons) wrapped in an outer shell that can hold at most eight electrons. He imagined these eight occupying the corners of a cube around the kernel. Sodium, with one outer electron, fills a single corner; a noble gas fills all eight. This octet represents a particularly stable arrangement, and Lewis postulated that atoms reach it when they are joined by chemical bonds.
Every system tends to be more stable, and bonding is nature's way of lowering the energy of the system to attain stability. Only the outer-shell electrons — the valence electrons — take part in this process; the inner electrons are well protected and stay out of the combination.
Kossel's electron-transfer view
Kossel approached the same problem from the geography of the periodic table. He noted that the highly electronegative halogens and the highly electropositive alkali metals are separated by the noble gases. A halogen forms a negative ion by gaining an electron; an alkali metal forms a positive ion by losing one. Each ion then attains the stable octet (or, for the helium end, the duplet) of the nearest noble gas, and the oppositely charged ions are held together by electrostatic attraction.
The bond arising from this attraction Kossel called the electrovalent bond. The electrovalence equals the number of unit charges carried by the ion. The formation of sodium chloride is the canonical illustration:
$$\ce{Na ->[\text{$-e^-$}] Na^+}\qquad \ce{Cl + e^- -> Cl^-}\qquad \ce{Na^+ + Cl^- -> NaCl}$$In electron-configuration terms, $\ce{Na}$ ($\mathrm{[Ne]\,3s^1}$) sheds its lone outer electron to become $\ce{Na+}$ ($\mathrm{[Ne]}$), while $\ce{Cl}$ ($\mathrm{[Ne]\,3s^2 3p^5}$) accepts it to reach $\mathrm{[Ar]}$. The same logic, applied to a metal that loses two electrons, gives calcium fluoride:
$$\ce{Ca -> Ca^{2+} + 2e^-}\qquad \ce{2F + 2e^- -> 2F^-}\qquad \ce{Ca^{2+} + 2F^- -> CaF2}$$Kossel's postulates remain the basis of the modern picture of ion formation by electron transfer and of the lattice structure of ionic crystals. He himself recognised, however, that a large class of compounds — those bonded by sharing rather than transfer — would not fit this scheme, which is where Lewis's covalent picture enters.
Lewis symbols and the octet rule
A Lewis symbol is the chemical symbol of an element surrounded by dots, one dot per valence electron. The number of dots gives the valence-electron count and, with it, the common valence of the element — which is generally either equal to the number of dots, or to eight minus that number. The second-period elements illustrate the pattern.
The unifying statement of Kossel and Lewis is the octet rule: atoms combine by transferring, gaining, or sharing valence electrons so as to acquire eight electrons in their valence shell, matching the $\mathrm{ns^2 np^6}$ configuration of a noble gas. Where transfer produces ions, sharing produces a covalent bond — a refinement Langmuir added in 1919 when he abandoned Lewis's static cube and introduced the term covalent bond. In $\ce{Cl2}$, each $\ce{Cl}$ atom ($\mathrm{[Ne]\,3s^2 3p^5}$) is one electron short of argon, so the two atoms share one pair, each contributing one electron, and both reach the argon octet.
| Shared pairs | Bond type | Example | Lewis sense |
|---|---|---|---|
| One pair | Single bond | $\ce{H2}$, $\ce{Cl2}$, $\ce{H2O}$ | 2 shared electrons between the atoms |
| Two pairs | Double bond | $\ce{CO2}$, $\ce{C2H4}$ | 4 shared electrons between the atoms |
| Three pairs | Triple bond | $\ce{N2}$, $\ce{C2H2}$ | 6 shared electrons between the atoms |
Drawing Lewis dot structures
A Lewis dot structure pictures bonding in terms of shared pairs and lone pairs, and although it does not capture shape or energy, it is a reliable map of where the valence electrons sit. NCERT lays out a fixed procedure:
| Step | What to do |
|---|---|
| 1 | Add the valence electrons of all combining atoms. For anions add one electron per negative charge; for cations subtract one per positive charge. |
| 2 | Place the least electronegative atom at the centre (e.g. N in $\ce{NF3}$, C in $\ce{CO3^2-}$); terminal atoms surround it. |
| 3 | Connect the central atom to each terminal atom with a single bond (one shared pair). |
| 4 | Distribute the remaining electrons as lone pairs; where an octet is still incomplete, convert lone pairs into multiple bonds until every bonded atom has eight electrons. |
The carbon monoxide molecule is a clean test of the method. Carbon ($\mathrm{2s^2 2p^2}$) and oxygen ($\mathrm{2s^2 2p^4}$) together bring $4 + 6 = 10$ valence electrons. A single $\ce{C-O}$ bond plus completed octet on oxygen leaves carbon short, so a triple bond is forced, satisfying both octets:
$$\ce{:C#O:}$$For polyatomic anions the count grows by the charge. In the nitrite ion the nitrogen ($\mathrm{2s^2 2p^3}$), two oxygens, and one extra electron from the negative charge give $5 + (2\times 6) + 1 = 18$ electrons, which resolve into one $\ce{N-O}$ single bond, one $\ce{N=O}$ double bond, and lone pairs completing every octet.
Once shared pairs are clear, the next step is bond strength and geometry — see Covalent Bond for how shared-pair bonding develops into single, double and triple bonds.
Formal charge
Lewis structures do not show real charge separation, but it is useful to assign a formal charge to each atom — the difference between the valence electrons of the free atom and the electrons assigned to it in the structure. The counting assumes each atom owns one electron of every shared pair and both electrons of every lone pair:
$$\text{F.C.} = (\text{valence electrons in free atom}) - (\text{lone-pair electrons}) - \tfrac{1}{2}(\text{bonding electrons})$$Assign formal charges to the three oxygen atoms in ozone, $\ce{O3}$, drawn with one $\ce{O=O}$ double bond and one $\ce{O-O}$ single bond from the central atom.
Central O (atom 1): one lone pair, one single bond and one double bond, i.e. 2 lone-pair electrons and 6 bonding electrons. $\text{F.C.} = 6 - 2 - \tfrac{1}{2}(6) = 6 - 2 - 3 = +1$.
Double-bonded end O (atom 2): two lone pairs and one double bond, i.e. 4 lone-pair electrons and 4 bonding electrons. $\text{F.C.} = 6 - 4 - \tfrac{1}{2}(4) = 6 - 4 - 2 = 0$.
Single-bonded end O (atom 3): three lone pairs and one single bond, i.e. 6 lone-pair electrons and 2 bonding electrons. $\text{F.C.} = 6 - 6 - \tfrac{1}{2}(2) = 6 - 6 - 1 = -1$.
Ozone is therefore written with a $+1$ on the central atom and a $-1$ on one terminal atom; the molecule as a whole stays neutral.
Formal charge earns its place because it lets us choose between competing Lewis structures: the lowest-energy structure is generally the one carrying the smallest formal charges on its atoms. It is, however, a bookkeeping tool built on a purely covalent view of equal sharing — it does not report the actual distribution of charge inside the molecule.
Formal charge is not oxidation number, and not real charge
A common error is to treat the formal charge as the genuine charge on an atom or to confuse it with oxidation state. Formal charge assumes equal sharing of every bonding pair; oxidation number assumes the more electronegative atom takes both electrons. The two coincide only by accident.
Use formal charge only to rank Lewis structures — pick the one with the smallest formal charges spread over the atoms.
Limitations of the octet rule
The octet rule is useful — it works for most organic compounds and most second-period elements — but it is not universal. NCERT identifies three classes of exception, summarised below before each is examined.
| Exception | What happens at the central atom | Examples |
|---|---|---|
| Incomplete octet | Fewer than 8 electrons; typical of elements with under four valence electrons (Li, Be, B) | $\ce{LiCl}$, $\ce{BeH2}$, $\ce{BeCl2}$, $\ce{BCl3}$, $\ce{BF3}$, $\ce{AlCl3}$ |
| Expanded octet | More than 8 electrons; third-period and heavier atoms use available 3d orbitals | $\ce{PF5}$, $\ce{PCl5}$, $\ce{SF6}$, $\ce{H2SO4}$ |
| Odd-electron molecules | An odd electron count means not every atom can complete its octet | $\ce{NO}$, $\ce{NO2}$ |
Incomplete octet
When the central atom has fewer than four valence electrons, it may bond without ever reaching eight. Beryllium in $\ce{BeCl2}$ has only four electrons around it; boron in $\ce{BF3}$ has six. These are electron-deficient molecules, and their hunger for electrons drives much of their chemistry. NEET frames this directly: $\ce{BF3}$ is planar and electron-deficient, with $\ce{B}$ surrounded by just six electrons.
Expanded octet
Elements in the third period and beyond have 3d orbitals available alongside 3s and 3p, so their central atoms can accommodate more than eight valence electrons. Phosphorus in $\ce{PCl5}$ carries ten; sulphur in $\ce{SF6}$ carries twelve. This is the expanded octet, and it is the reason the rule fails for $\ce{PF5}$, $\ce{H2SO4}$ and a great many coordination compounds. Sulphur is instructive precisely because it is inconsistent: in $\ce{SF6}$ it expands its octet, yet in $\ce{SCl2}$ it keeps a normal octet of eight.
Odd-electron molecules and other gaps
A molecule with an odd total number of valence electrons cannot pair them all, so at least one atom is left short of an octet. Nitric oxide $\ce{NO}$ and nitrogen dioxide $\ce{NO2}$ are the standard examples. Beyond these three structural exceptions, the rule has deeper gaps NCERT flags explicitly.
| Other drawback | Why it matters |
|---|---|
| Noble gases react | The rule rests on noble-gas inertness, yet $\ce{XeF2}$, $\ce{KrF2}$ and $\ce{XeOF2}$ exist. |
| Silent on shape | The octet rule says nothing about molecular geometry — that needs VSEPR theory. |
| Silent on stability | It gives no account of bond energy or the relative stability of molecules. |
Counting electrons "around the central atom"
A frequent NEET item asks how many species in a list do not have eight electrons around the central atom. The reliable check: $\ce{NH3}$ (8, N), $\ce{CCl4}$ (8, C) obey the rule; $\ce{AlCl3}$ and $\ce{BeCl2}$ are incomplete (6 and 4 respectively) — though $\ce{BeCl2}$ as written with two single bonds gives only 4 — and $\ce{PCl5}$ is expanded (10). Count bonds, not formulae.
Incomplete = Be, B, Al centres; expanded = period-3+ centres with five or more bonds.
Kossel-Lewis approach at a glance
- Kossel and Lewis (1916) tied bonding to noble-gas stability: atoms transfer or share valence electrons to reach an octet.
- Kossel's electron transfer gives the electrovalent (ionic) bond; Lewis's sharing gives the covalent bond, with the octet rule as the common statement.
- Lewis symbols show valence electrons as dots; Lewis structures are built by counting electrons, centring the least electronegative atom, then adding bonds and lone pairs to complete every octet.
- Formal charge $= V - L - \tfrac{1}{2}B$ selects the best Lewis structure (smallest charges) but is not a real charge.
- Three octet exceptions — incomplete ($\ce{BeCl2}$, $\ce{BF3}$), expanded ($\ce{PCl5}$, $\ce{SF6}$), odd-electron ($\ce{NO}$, $\ce{NO2}$) — plus its silence on shape, stability, and reactive noble gases.