Introduction & Kossel-Lewis Approach to Chemical Bonding

Why Do Atoms Combine At All?

Let's start with a simple observation: in nature, atoms are very often found in combined form. Hydrogen is commonly found as $H_2$, not as free $H$. Oxygen is found as $O_2$. Table salt is $NaCl$. The graphite in your pencil is a giant network of carbon atoms. The only atoms that commonly exist as single atoms are the noble gases — helium, neon, argon and similar elements — which are chemically very unreactive.

Think of it this way: that one difference is the biggest clue in all of chemical bonding. The noble gases are the only atoms with completely filled outermost shells ($ns^2np^6$, i.e. 8 electrons — except He which has 2). Every other atom tends to combine with other atoms to reach a more stable noble-gas arrangement.

Definition: A chemical bond is the attractive force that holds two or more atoms (or ions) together in a molecule or compound.

The central principle of the whole chapter is the drive towards stability: atoms combine because the combined system has lower energy than the separate atoms. Lower energy means greater stability. Whenever a bond forms, energy is released; to break that bond, energy must be supplied.

[JEE Tip] Bond formation is generally exothermic and bond breaking is generally endothermic. This single idea explains lattice enthalpy, bond enthalpy and the Born-Haber cycle later in the chapter.

The Kossel-Lewis Approach (1916)

In 1916, two scientists working independently — Walther Kossel and Gilbert N. Lewis — gave the first successful explanation of bond formation in terms of electrons.

Lewis's picture: Lewis imagined the atom as a positively charged kernel (the nucleus plus all the inner electrons) surrounded by the outer-shell electrons placed at the corners of a cube. The eight corners of the cube could hold a maximum of 8 electrons — this is where the magic number 'eight' first appears. He proposed that atoms achieve stability by completing this octet, either by sharing electrons (covalent bond) or by transferring them.

Kossel's picture: Kossel focused on electron transfer. He noted that across the periodic table, highly electropositive metals and highly electronegative non-metals lie on opposite sides, with noble gases in between. He proposed that a metal atom loses electrons to become a positive ion (cation) and a non-metal atom gains them to become a negative ion (anion); the two oppositely charged ions are then held together by electrostatic attraction.

The Octet Rule: Atoms tend to gain, lose, or share electrons so as to acquire eight electrons in their valence shell — the stable electronic configuration of the nearest noble gas.

For hydrogen, lithium and beryllium the target is the duplet (2 electrons, like helium), not the octet.

Lewis Dot Symbols

Before we draw bonds, we need a quick shorthand for the valence electrons — the electrons in the outermost shell that actually participate in bonding. Lewis gave us electron-dot symbols: the chemical symbol of the element, surrounded by dots, one dot per valence electron.

How to write them:

1. Find the group number (for main-group elements, the units digit of the group number = number of valence electrons).
2. Place the dots one at a time on the four sides of the symbol; pair them up only after each side has one dot (Hund-like spreading).

Examples (valence electrons in brackets):

• Sodium $Na$ [1]: one dot
• Magnesium $Mg$ [2]: two dots
• Carbon $C$ [4]: four single dots
• Nitrogen $N$ [5]: one lone pair + three single dots
• Oxygen $O$ [6]: two lone pairs + two single dots
• Chlorine $Cl$ [7]: three lone pairs + one single dot
• Neon $Ne$ [8]: four lone pairs (complete octet)

Why this matters: Lewis symbols make the significance of the valence shell visual. The number of unpaired dots usually tells you the valence (combining capacity) of the element — carbon has 4 unpaired dots and forms 4 bonds; oxygen has 2 and forms 2.

[NEET Important] The number of dots equals the number of valence electrons, not the group number directly for transition metals. Stick to s- and p-block elements for Lewis symbols.

The Founding Examples: NaCl and Cl$_2$

Kossel and Lewis explained two contrasting bond types with two classic examples.

Electron transfer — sodium chloride ($NaCl$)

Sodium ($2,8,1$) has one electron too many for a neat octet; chlorine ($2,8,7$) has one too few. The neat solution: sodium donates its lone valence electron to chlorine.

$$Na \rightarrow Na^+ + e^- \qquad (\text{now } 2,8 \text{ - neon core})$$ $$Cl + e^- \rightarrow Cl^- \qquad (\text{now } 2,8,8 \text{ - argon config})$$

The resulting $Na^+$ and $Cl^-$ ions attract each other electrostatically — this is the electrovalent (ionic) bond. The number of electrons an atom loses or gains is its electrovalence (here, 1 for both).

Electron sharing — chlorine molecule ($Cl_2$)

Two chlorine atoms each need one more electron. Neither will give one up (both are non-metals), so instead they share a pair:

$$\overset{..}{\underset{..}{Cl}} \, : \, \overset{..}{\underset{..}{Cl}}$$

Each $Cl$ now 'counts' 8 electrons around it. The shared pair is a covalent bond, and the number of shared pairs is the covalence (here, 1). When the shared electrons are donated entirely by one atom, the bond is called a coordinate (dative) bond — we'll meet this in $NH_4^+$ and $O_3$ later.

Key Point: Ionic bonding = transfer of electrons; covalent bonding = sharing. Both serve the same master goal — completing the octet.

Solved Examples

Example 1: Why don't noble gases form bonds easily?

Explain, using the octet rule, why helium and neon are chemically inert.

Solution:

1. Look at the configuration: $He = 1s^2$ (duplet complete); $Ne = 1s^2 2s^2 2p^6$ (octet complete).
2. Apply the principle: Atoms bond to reach a noble-gas configuration. Noble gases already have it.
3. Conclusion: With a filled valence shell, there is no energetic gain from gaining, losing or sharing electrons, so they remain unreactive (inert).

Takeaway: Stability of the filled octet/duplet is the reference point for the entire chapter.

Example 2: Writing a Lewis dot symbol

Write the Lewis dot symbol for phosphorus ($Z = 15$).

Solution:

1. Electronic configuration: $1s^2 2s^2 2p^6 3s^2 3p^3$.
2. Count valence electrons: outermost shell $3s^2 3p^3$ → $2 + 3 = 5$ valence electrons (Group 15).
3. Place the dots: one lone pair (from $3s^2$) and three single dots (from $3p^3$) around the symbol $P$.
4. Result: $\cdot\overset{\textstyle ..}{P}\cdot$ with three unpaired dots → phosphorus is trivalent and can form five bonds in expanded-octet compounds.

Takeaway: Three unpaired electrons → typical valence of 3 (as in $PCl_3$).

Example 3: Electrovalence of magnesium

What is the electrovalence of magnesium when it forms $MgCl_2$?

Solution:

1. Configuration of Mg: $2,8,2$. To reach the neon octet it must lose 2 electrons.
2. Ion formed: $Mg \rightarrow Mg^{2+} + 2e^-$.
3. Electrovalence = number of electrons lost = 2. Each chlorine accepts one electron, so two $Cl^-$ ions balance the charge, giving $MgCl_2$.

Takeaway: Electrovalence equals the magnitude of the charge on the ion formed.

Example 4: Covalence of nitrogen in N$_2$

How many electron pairs are shared between the two nitrogen atoms in $N_2$, and what is the covalence of nitrogen?

Solution:

1. Valence electrons: each $N$ has 5; each needs 3 more for an octet.
2. Sharing: the two atoms share three pairs of electrons (a triple bond): $:N \equiv N:$.
3. Covalence = number of shared pairs = 3. Each nitrogen now counts 8 electrons (2 lone-pair + 6 shared).

Takeaway: Covalence = number of covalent bonds (shared pairs) an atom forms.

Example 5: Predicting a formula from the octet rule

Use the octet rule to predict the formula of the compound formed between aluminium ($Z=13$) and oxygen ($Z=8$).

Solution:

1. Al ($2,8,3$) loses 3 electrons → $Al^{3+}$.
2. O ($2,6$) gains 2 electrons → $O^{2-}$.
3. Balance the charges: lowest common multiple of 3 and 2 is 6. Need 2 $Al^{3+}$ (total $+6$) and 3 $O^{2-}$ (total $-6$).
4. Formula: $Al_2O_3$.

Takeaway: Cross-over the charges: $Al^{3+}, O^{2-} \Rightarrow Al_2O_3$.

Example 6: Identifying lone pairs and bond pairs

In the water molecule $H_2O$, how many bond pairs and lone pairs are around the oxygen atom?

Solution:

1. Oxygen valence electrons: 6. It forms 2 O–H bonds (sharing 2 pairs).
2. Bond pairs: 2 (one per O–H bond).
3. Remaining electrons: $6 - 2 = 4$ electrons → 2 lone pairs.
4. Total around O: $2\ bp + 2\ lp = 4$ electron pairs (octet complete).

Takeaway: Bond pairs are shared; lone pairs belong to one atom only — this distinction drives VSEPR shapes later.

Example 7: Why MgO has a higher melting point than NaCl

Both are ionic. Using the octet/charge idea, explain qualitatively why $MgO$ melts much higher than $NaCl$.

Solution:

1. Charges: $NaCl$ has $+1, -1$ ions; $MgO$ has $+2, -2$ ions.
2. Electrostatic force is proportional to $q_1q_2$ and inversely proportional to the square of the distance between the ions.
3. Conclusion: Stronger electrostatic attraction in $MgO$ → larger lattice enthalpy → much higher melting point ($MgO \approx 2850\,^{\circ}C$ vs $NaCl \approx 801\,^{\circ}C$).

Takeaway: Higher ionic charge (and smaller size) → stronger ionic bonding. We'll quantify this in Section 2.

Example 8: Coordinate bond recognition

In the ammonium ion $NH_4^+$, all four N–H bonds are identical, yet one is said to 'originate' as a coordinate bond. Explain.

Solution:

1. Start with $NH_3$: nitrogen has 3 bond pairs and 1 lone pair.
2. Add $H^+$: the bare proton has no electrons. Nitrogen's lone pair is donated to form the fourth N–H bond — a coordinate (dative) bond.
3. After formation: all four bonds become indistinguishable because electrons are shared and the bonds are equivalent.

Takeaway: A coordinate bond differs only in origin (both electrons from one atom); once formed it is an ordinary covalent bond.

Example 9: Duplet vs octet

Why does hydrogen aim for 2 electrons while carbon aims for 8?

Solution:

1. Nearest noble gas to H is helium ($1s^2$) — only 2 electrons fill the first shell. So H needs a duplet.
2. Nearest noble gas to C is neon ($2,8$) — 8 electrons in the valence shell. So C needs an octet.
3. Conclusion: The 'target number' is whatever fills the valence shell of the nearest noble gas: 2 for H, Li, Be; 8 for second-period onwards.

Takeaway: Octet rule is really a 'nearest noble-gas configuration' rule.

Example 10: Counting shared and unshared electrons

In the $Cl_2$ molecule, how many electrons around each chlorine are shared and how many are unshared?

Solution:

1. Each Cl has 7 valence electrons. One pair is shared between the two atoms.
2. Shared electrons (counted by each Cl): 2 (the single bond).
3. Unshared (lone-pair) electrons on each Cl: $7 - 1 = 6$ → 3 lone pairs.
4. Octet check: $6\ (lone) + 2\ (shared) = 8$. ✓

Takeaway: When counting an octet, a shared pair is counted in full by both bonded atoms.

Example 11: Lewis symbol of a polyatomic — the carbonate skeleton

How many total valence electrons must a Lewis structure of the carbonate ion $CO_3^{2-}$ account for?

Solution:

1. Carbon: 4 electrons. Three oxygens: $3 \times 6 = 18$. Subtotal: $4 + 18 = 22$.
2. Add charge: the $2-$ charge means 2 extra electrons → $22 + 2 = 24$ valence electrons.
3. Pairs to place: $24 / 2 = 12$ electron pairs in the final Lewis structure.

Takeaway: For ions, add one electron per negative charge and subtract one per positive charge before drawing. This is the first step of every Lewis-structure problem (Section 3).

Example 12: Limitation preview — does the octet always hold?

Boron in $BF_3$ has only 6 electrons around it. Does this violate the octet rule?

Solution:

1. Count around B: three B–F single bonds → 3 shared pairs → only 6 electrons around boron.
2. Yes — it is an exception: $BF_3$ is an incomplete octet (electron-deficient) molecule.
3. Consequence: the electron-deficient boron readily accepts a lone pair (e.g. from $NH_3$) to complete its octet, acting as a Lewis acid.

Takeaway: The octet rule is a powerful guideline, not an unbreakable law — Section 4 catalogues the exceptions.