Bond Length
Bond length is defined as the equilibrium distance between the nuclei of two bonded atoms in a molecule. It is measured experimentally by spectroscopic, X-ray diffraction and electron-diffraction techniques. Each atom of the bonded pair contributes to this distance, and in a covalent bond the contribution from each atom is called the covalent radius of that atom.
The covalent radius is measured approximately as the radius of an atom's core that is in contact with the core of an adjacent atom in a bonded situation; equivalently, it is half the distance between two like atoms joined by a covalent bond in the same molecule. This must not be confused with the van der Waals radius, which represents the overall size of the atom including its valence shell in a non-bonded situation — it is half the distance between two like atoms in separate molecules in a solid. For chlorine the covalent radius is $99\,\text{pm}$ while the van der Waals radius is $180\,\text{pm}$. For a bond $\ce{A-B}$ the bond length $R$ is simply the sum of the two covalent radii:
$$R = r_\text{A} + r_\text{B}$$
| Bond type | Covalent bond length (pm) |
|---|---|
O–H | 96 |
C–H | 107 |
N–O | 136 |
C–O | 143 |
C–N | 143 |
C–C | 154 |
C=O | 121 |
C=C | 133 |
C≡N | 116 |
C≡C | 120 |
Two patterns in this NCERT data (Table 4.2) are worth committing to memory. First, for the same pair of atoms the length contracts as the multiplicity rises: $\ce{C-C}$ at $154\,\text{pm}$ is longer than $\ce{C=C}$ at $133\,\text{pm}$, which is longer than $\ce{C#C}$ at $120\,\text{pm}$. Second, lengths in real molecules track these reference values closely, as Table 4.3 below shows for diatomics.
| Molecule | Bond length (pm) |
|---|---|
| $\ce{H2}$ (H–H) | 74 |
| $\ce{F2}$ (F–F) | 144 |
| $\ce{Cl2}$ (Cl–Cl) | 199 |
| $\ce{Br2}$ (Br–Br) | 228 |
| $\ce{I2}$ (I–I) | 267 |
| $\ce{N2}$ (N≡N) | 109 |
| $\ce{O2}$ (O=O) | 121 |
| $\ce{HF}$ (H–F) | 92 |
| $\ce{HCl}$ (H–Cl) | 127 |
| $\ce{HBr}$ (H–Br) | 141 |
| $\ce{HI}$ (H–I) | 160 |
Bond Angle
Bond angle is defined as the angle between the orbitals containing bonding electron pairs around the central atom in a molecule or complex ion. It is expressed in degrees and is determined experimentally by spectroscopic methods. The bond angle gives an idea of how the orbitals are distributed around the central atom, and hence it helps in determining the shape of the molecule.
A familiar example is the $\ce{H-O-H}$ bond angle in water, which is $104.5^\circ$. The same comparison appears in NEET stems: in moving from $\ce{CH4}$ to $\ce{NH3}$ to $\ce{H2O}$ the bond angle falls from $109.5^\circ$ to $107^\circ$ to $104.5^\circ$, because the number of lone pairs on the central atom increases and lone-pair repulsions squeeze the bonding pairs closer together. The mechanism behind these shapes belongs to a sibling topic, but the angles themselves are bond parameters.
Bond angles are predicted by counting electron pairs. See VSEPR Theory for how lone pairs distort the ideal geometry of $\ce{NH3}$ and $\ce{H2O}$.
Bond Enthalpy
Bond enthalpy is the amount of energy required to break one mole of bonds of a particular type between two atoms in the gaseous state. Its unit is $\text{kJ mol}^{-1}$. The larger the bond dissociation enthalpy, the stronger the bond. For the hydrogen molecule the H–H bond enthalpy is $435.8\,\text{kJ mol}^{-1}$:
$$\ce{H2(g) -> H(g) + H(g)} \qquad \Delta_a H = 435.8\ \text{kJ mol}^{-1}$$
Multiple bonds need correspondingly more energy. Breaking the double bond in dioxygen requires $498\,\text{kJ mol}^{-1}$, while the triple bond in dinitrogen requires $946.0\,\text{kJ mol}^{-1}$ — one of the highest bond enthalpies known for any diatomic molecule. A heteronuclear example is hydrogen chloride at $431.0\,\text{kJ mol}^{-1}$:
$$\ce{O2(g) -> 2O(g)} \qquad \Delta_a H = 498\ \text{kJ mol}^{-1}$$ $$\ce{N2(g) -> 2N(g)} \qquad \Delta_a H = 946.0\ \text{kJ mol}^{-1}$$
The same bond can need different energies
In a polyatomic molecule, breaking identical bonds one after another does not cost the same energy, because the chemical environment changes. In water, the first O–H bond requires $502\,\text{kJ mol}^{-1}$ but the second requires only $427\,\text{kJ mol}^{-1}$. Chemists therefore quote a mean (average) bond enthalpy, obtained by dividing the total dissociation enthalpy by the number of bonds broken.
For water: average O–H bond enthalpy $= \dfrac{502 + 427}{2} = 464.5\ \text{kJ mol}^{-1}$.
Bond Order
In the Lewis description of a covalent bond, the bond order is given by the number of bonds between the two atoms in a molecule. With one shared electron pair in $\ce{H2}$ the bond order is 1; with two shared pairs in $\ce{O2}$ it is 2; and with three shared pairs in $\ce{N2}$ it is 3. Carbon monoxide $\ce{CO}$ also has three shared electron pairs between carbon and oxygen, so its bond order is 3.
A useful shortcut for NEET is that isoelectronic molecules and ions have identical bond orders. Thus $\ce{F2}$ and the peroxide ion $\ce{O2^2-}$ both have bond order 1, while $\ce{N2}$, $\ce{CO}$ and $\ce{NO+}$ all have bond order 3. The fractional bond orders that appear in species such as $\ce{NO}$ (2.5) or $\ce{CN-}$ (3) come from molecular orbital counting, which is treated separately.
The Order–Length–Strength Rule
The three parameters above are not independent. The single most important correlation in this section, and a guaranteed source of statement-based questions, ties them together:
With an increase in bond order, bond enthalpy increases and bond length decreases.
More shared electron pairs pull the nuclei closer and bind them more tightly, so a higher-order bond is both shorter and stronger. The progression from $\ce{C-C}$ through $\ce{C=C}$ to $\ce{C#C}$ illustrates this cleanly, as does the carbon–carbon series across ethane, ethene and ethyne.
Resonance Structures
A single Lewis structure is often inadequate to represent a molecule in conformity with its experimentally determined parameters. The classic case is ozone, $\ce{O3}$, which can be drawn equally well as two structures, each containing one O–O single bond and one O=O double bond. The normal single-bond and double-bond lengths are $148\,\text{pm}$ and $121\,\text{pm}$, yet the experimentally measured oxygen–oxygen lengths in $\ce{O3}$ are both $128\,\text{pm}$ — intermediate between a single and a double bond, and equal to each other. Neither single Lewis structure can capture this.
The concept of resonance resolves the difficulty. Whenever a single Lewis structure cannot describe a molecule accurately, a number of structures with similar energy, the same positions of nuclei, and the same arrangement of bonding and non-bonding electron pairs are taken as the canonical (resonance) structures. The actual molecule is described by their resonance hybrid, and resonance is represented by a double-headed arrow.
The carbonate ion and carbon dioxide behave the same way. For $\ce{CO3^2-}$, a single Lewis structure with two single bonds and one double bond would imply unequal bonds, but experiment shows all three carbon–oxygen bonds are equivalent. The ion is therefore best described as a resonance hybrid of three canonical forms. For $\ce{CO2}$ the measured C–O length is $115\,\text{pm}$, lying between a $\ce{C=O}$ double bond ($121\,\text{pm}$) and a $\ce{C#O}$ triple bond ($110\,\text{pm}$); again three canonical forms are needed.
Canonical forms are not real and there is no equilibrium
The canonical forms have no real existence. The molecule does not spend part of its time in one form and part in another, and there is no equilibrium between them (unlike the keto–enol forms in tautomerism). The molecule has a single structure — the resonance hybrid — which cannot be drawn as one Lewis structure.
Resonance stabilises the molecule (the hybrid's energy is lower than any single canonical form) and averages the bond characteristics.
NEET 2024 turned exactly these facts into options: it is correct that three canonical forms can be drawn for the carbonate ion, whereas ozone has two canonical forms — a distinction worth memorising.
Polarity of Bonds and Dipole Moment
A hundred percent ionic or covalent bond is an ideal that no real bond reaches. When the bond joins two identical atoms, as in $\ce{H2}$, $\ce{O2}$, $\ce{Cl2}$, $\ce{N2}$ or $\ce{F2}$, the shared pair sits exactly between the two equal nuclei and the bond is a non-polar covalent bond. When the atoms differ, as in $\ce{HF}$, the shared pair is displaced towards the more electronegative atom (fluorine), producing a polar covalent bond with partial charges $\delta^+$ and $\delta^-$.
Polarisation gives the molecule a dipole moment, defined as the product of the magnitude of the charge and the distance between the centres of positive and negative charge. It is denoted $\mu$:
$$\mu = Q \times r$$
Dipole moment is usually expressed in Debye units (D), where $1\,\text{D} = 3.33564 \times 10^{-30}\ \text{C m}$. It is a vector quantity; by physical convention the arrow points from the negative to the positive centre, but in chemistry a crossed arrow is drawn on the Lewis structure with the cross on the positive end and the head on the negative end.
| Type | Example | µ / D | Geometry |
|---|---|---|---|
| AB | $\ce{HF}$ | 1.78 | linear |
| AB | $\ce{HCl}$ | 1.07 | linear |
| AB | $\ce{HBr}$ | 0.79 | linear |
| AB | $\ce{HI}$ | 0.38 | linear |
| AB | $\ce{H2}$ | 0 | linear |
| AB$_2$ | $\ce{H2O}$ | 1.85 | bent |
| AB$_2$ | $\ce{H2S}$ | 0.95 | bent |
| AB$_2$ | $\ce{CO2}$ | 0 | linear |
| AB$_3$ | $\ce{NH3}$ | 1.47 | trigonal pyramidal |
| AB$_3$ | $\ce{NF3}$ | 0.23 | trigonal pyramidal |
| AB$_3$ | $\ce{BF3}$ | 0 | trigonal planar |
| AB$_4$ | $\ce{CH4}$ | 0 | tetrahedral |
| AB$_4$ | $\ce{CHCl3}$ | 1.04 | tetrahedral |
| AB$_4$ | $\ce{CCl4}$ | 0 | tetrahedral |
In a polyatomic molecule the net dipole moment is the vector sum of the individual bond dipoles, so geometry decides the outcome. Water is bent, with its two O–H bonds at $104.5^\circ$; the bond dipoles do not cancel, giving a net $\mu = 1.85\,\text{D}$ ($6.17 \times 10^{-30}\ \text{C m}$). By contrast, $\ce{BeF2}$ is linear, so its two equal bond dipoles point in opposite directions and cancel to zero. In $\ce{BF3}$ the three B–F bonds lie $120^\circ$ apart and the resultant of any two is equal and opposite to the third, again giving zero.
Why μ(NH₃) > μ(NF₃)
Both $\ce{NH3}$ and $\ce{NF3}$ are pyramidal with a lone pair on nitrogen, and fluorine is more electronegative than nitrogen — yet $\ce{NH3}$ ($1.47\,\text{D}$) has a far larger dipole moment than $\ce{NF3}$ ($0.23\,\text{D}$). In $\ce{NH3}$ the orbital dipole from the lone pair points in the same direction as the resultant of the N–H bond dipoles, so they add. In $\ce{NF3}$ the lone-pair dipole points opposite to the resultant of the N–F bond dipoles, so they partly cancel.
Symmetric molecules ($\ce{CO2}$, $\ce{BeF2}$, $\ce{BF3}$, $\ce{CCl4}$, 1,4-dichlorobenzene) have $\mu = 0$ even with polar bonds.
Percent Ionic Character
Just as every covalent bond between unlike atoms carries some ionic character, every ionic bond carries some covalent character. The extent of the shift of the shared pair — and hence the magnitude of the ionic character — depends on the difference in electronegativity between the two bonded atoms. As a working rule from the NIOS text, an electronegativity difference of about $1.7$ corresponds to roughly $50\%$ ionic character; a smaller difference gives less, a larger difference gives more.
This is exactly why the hydrogen-halide dipole moments fall steadily from $\ce{HF}$ to $\ce{HI}$ as the electronegativity gap narrows: $\ce{HF}$ ($1.78\,\text{D}$) > $\ce{HCl}$ ($1.07\,\text{D}$) > $\ce{HBr}$ ($0.79\,\text{D}$) > $\ce{HI}$ ($0.38\,\text{D}$). The covalent character of an ionic bond is summarised by Fajans' rules: a smaller cation, a larger anion and a higher cationic charge all increase covalent character, and for cations of equal size and charge the transition-metal type (configuration $(n-1)d^n\,ns^0$) is more polarising than the noble-gas type ($ns^2np^6$).
Arrange $\ce{BeH2}$, $\ce{CaH2}$ and $\ce{BaH2}$ in order of increasing ionic character. (NEET 2018)
Down group 2 the size of the cation increases ($\ce{Be^2+} < \ce{Ca^2+} < \ce{Ba^2+}$). A larger cation has lower polarising power, so it distorts the hydride ion less; covalent character therefore decreases and ionic character increases down the group.
Order of ionic character: $\ce{BeH2} < \ce{CaH2} < \ce{BaH2}$.
Bond Parameters in one screen
- Bond length = equilibrium internuclear distance $= r_\text{A} + r_\text{B}$; covalent radius ≠ van der Waals radius (Cl: 99 pm vs 180 pm).
- Bond angle = angle between bonding orbitals at the central atom; $\ce{CH4}$ $109.5^\circ$ > $\ce{NH3}$ $107^\circ$ > $\ce{H2O}$ $104.5^\circ$.
- Bond enthalpy = energy to break 1 mol of bonds (kJ mol⁻¹); use the average value for polyatomic molecules (water: 464.5).
- Bond order = number of bonds between two atoms; isoelectronic species share bond order ($\ce{N2}$, $\ce{CO}$, $\ce{NO+}$ = 3).
- Master rule: higher bond order → higher bond enthalpy → shorter bond length.
- Resonance: hybrid of non-existent canonical forms (no equilibrium); $\ce{O3}$ has 2 forms, $\ce{CO3^2-}$ has 3; it stabilises and averages bonds.
- Dipole moment $\mu = Q \times r$ (vector sum); symmetric shapes ($\ce{CO2}$, $\ce{BeF2}$, $\ce{BF3}$, $\ce{CCl4}$) give $\mu = 0$; $\mu(\ce{NH3}) > \mu(\ce{NF3})$.
- Ionic character grows with electronegativity difference (≈ 1.7 → 50%); Fajans' rules govern covalent character of ionic bonds.