Why Carbon Dioxide Has Polar Bonds but No Overall Dipole

A single sodium atom or chlorine atom is unstable and reactive. Together they form common salt, which sits calmly in your kitchen. Atoms bond because the bonded arrangement has lower energy than the separate atoms.

This part covers Lewis structures and formal charge, ionic bonding and lattice enthalpy, bond parameters and resonance, and dipole moments with Fajans' rules.

**In the Kossel-Lewis approach, atoms reach a stable noble-gas-like octet by transferring electrons (ionic bonds) or sharing them (covalent bonds); a Lewis structure shows all valence electrons, and formal charge $=V-L-\frac{1}{2}B$ helps pick the most acceptable structure.**

Here $V$ is the valence electrons of the free atom, $L$ the non-bonding electrons and $B$ the bonding electrons on that atom.

Worked example 1 — ozone, $18$ valence electrons, O=O–O:

- Central O: $6-2-\frac{1}{2}(6)=+1$
- Double-bonded end O: $6-4-\frac{1}{2}(4)=0$
- Single-bonded end O: $6-6-\frac{1}{2}(2)=-1$

**Worked example 2 — choosing for CO${}_2$.** O=C=O gives every atom a formal charge of $0$, while O$\equiv$C–O gives $+1$, $0$ and $-1$. The structure with smaller formal charges is preferred.

An everyday example. Handing your whole tiffin to a friend is like electron transfer; sharing it at the same bench is like a covalent bond.

The substance. Formal charges are bookkeeping, not real charges on the atoms.

An ionic bond forms when an atom with low ionisation enthalpy transfers electrons to one with a large negative electron gain enthalpy, and the resulting ions pack into a crystal; lattice enthalpy, the energy needed to separate one mole of the solid into gaseous ions, is so large that it makes the whole process favourable.

Worked example — sodium chloride.

- Removing an electron from Na: $+496$ kJ/mol
- Adding an electron to Cl: $-349$ kJ/mol
- Net so far: $496-349=+147$ kJ/mol — energy must be supplied

Forming the crystal releases the lattice enthalpy, $788$ kJ/mol:

$$147-788=-641\text{ kJ/mol}$$

Ignoring the smaller steps of vaporising sodium and splitting chlorine molecules, the energy released by the lattice turns an uphill electron transfer into a strongly downhill process.

Trends. Smaller ions and higher charges give larger lattice enthalpies — MgO, with $2+$ and $2-$ ions, has a lattice enthalpy several times that of NaCl, and a much higher melting point.

An everyday example. Table salt does not melt on a kitchen gas stove, because breaking its strongly bonded ionic lattice needs a very high temperature.

The substance. Ionic compounds are stable because of lattice enthalpy, not simply because the ions have octets.

Bond length is the distance between bonded nuclei, bond angle the angle between bonds at an atom, bond enthalpy the energy to break one mole of a bond, and bond order the number of bonds between two atoms; a higher bond order means a shorter, stronger bond, and resonance is used when one Lewis structure cannot explain the measured bond lengths.

Worked example 1 — carbon-carbon bonds.

- C–C (order $1$): $154$ pm, about $348$ kJ/mol
- C=C (order $2$): $134$ pm, about $614$ kJ/mol
- **C$\equiv$C** (order $3$): $120$ pm, about $839$ kJ/mol

Worked example 2 — ozone. Measured O–O bond lengths are **both $128$ pm**, between a single bond ($148$ pm) and a double bond ($121$ pm). No single structure fits, so ozone is a resonance hybrid of O=O–O and O–O=O.

Worked example 3 — carbonate ion. CO${}_3^{2-}$ has three resonance structures, each with one C=O and two C–O bonds, giving every C–O bond an order of

$$\frac{1+1+2}{3}=\frac{4}{3}\approx 1.33$$

An everyday example. A masala blend is one real mixture with its own taste, not a spice that keeps switching between cumin and coriander — just as a resonance hybrid is one real structure.

The substance. Resonance structures do not exist separately or flip back and forth; the hybrid is more stable than any one of them.

A bond between atoms of different electronegativity is polar, but a molecule's overall dipole moment is the vector sum of its bond dipoles, so symmetric molecules can be non-polar; Fajans' rules say ionic bonds gain covalent character when the cation is small and highly charged and the anion is large.

Dipole moment is $\mu =q\times d$, measured in debye (D), where $1$ D $=3.336\times 10^{-30}$ C m.

Worked example 1 — ionic character of HCl. If HCl were fully ionic with a bond length of $127$ pm:

$$\mu =1.602\times 10^{-19}\times 1.27\times 10^{-10}\approx 2.03\times 10^{-29}\text{ C m}\approx 6.1\text{ D}$$

Its measured $1.03$ D means about $\frac{1.03}{6.1}\approx 17\%$ ionic character.

Worked example 2 — shape decides. CO${}_2$ (linear), BF${}_3$ (trigonal planar) and CH${}_4$ (tetrahedral) have zero dipole moment, while bent H${}_2$O has about $1.85$ D. NH${}_3$ ($1.47$ D) is more polar than NF${}_3$ ($0.23$ D), because in NH${}_3$ the lone-pair dipole adds to the bond dipoles, while in NF${}_3$ it opposes them.

Fajans' rules — more covalent character with: smaller cation (LiCl over NaCl), higher cation charge (AlCl${}_3$ over NaCl), larger anion (LiI over LiCl), and cations without a noble gas core (CuCl over NaCl).

An everyday example. Salt dissolves in water but not in coconut oil, because polar water molecules can surround and pull apart the ions.

The substance. Polar bonds do not guarantee a polar molecule — CO${}_2$ has two polar bonds that cancel exactly.