Advanced Level Chemistry: More on covalent bonding - bond lengths & bond enthalpies

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More on covalent bonding - single, double and triple bond, their length and strength, dative covalent bonds and bond enthalpy trends

Extra Notes on Covalent Bonding and Covalent Compounds

Doc Brown's A level Chemistry Revision

Extra Notes on chemical bonding for advanced A level chemistry students

All the advanced A level 'basics' with lots of examples of dot and cross diagrams of ionic bonding, Lewis diagrams, properties of covalent compounds etc. is on a separate page.

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All my structure and bonding notes

Part 6. Extra advanced level chemical bonding notes

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The formation of a covalent bond

In covalent bonds there is a balance between the repulsive forces between the positive nuclei and the attractive forces between the nuclei and the negative electrons between them. The covalent bond is mutual attraction between the nuclei of two atoms and the electrons in between them (+) -- (+). The bond length is determined by the two atoms adopting the position of minimum potential energy.

One or more atomic orbitals from each atom overlap so the bonding pairs of electrons are shared between the nuclei.

In more advanced theory you consider the overlapping orbitals form common molecular orbitals - but that's for university level chemistry.

The 'dot and cross' (Lewis) electron diagrams only tell part of the story


Dative covalent bond (co-ordinate bond)

A dative covalent is formed when the pair of electrons forming the bond are donated by one atom only. This contrasts with the usual covalent bond by each atom of the bond contributing one electron.

Examples of dative bond formation

1. Formation of the oxonium ion H3O+    (also known as hydroxonium ion, hydronium ion)

H2O(l) + H+(aq)  [H3O]+, a pair of electrons (a lone pair) from the oxygen atom of the water is donated to a proton to form an oxygen-hydrogen dative (co-ordinate) covalent bond in the oxonium ion.

This reaction happens whenever you dissolve a soluble acidic substance in water, but the proton can also come from another water molecule in a self-ionisation process 2H2O(l) H3O+  + OH-(aq).

H2O: + H+  [H2OH]+    where the arrow indicates and 'accentuates' the dative (co-ordinate) covalent bond between the oxygen and the hydrogen. BUT, note that all 3 O-H bonds in the oxonium ion are identical.


2. Formation of the ammonium ion NH4+

NH3(aq)  +  H+(aq)    NH4+(aq),  the lone pair of electrons on the nitrogen atom is donated to the proton to form a nitrogen-hydrogen dative (co-ordinate) covalent bond in the ammonium ion.

This reaction happens when you dissolve ammonia gas in water (the proton comes from the water) or when you react aqueous ammonia solution with any acid.

H3N: + H+  [H3NH]+    where the arrow indicates and 'accentuates' the dative covalent bond between the nitrogen and the hydrogen. BUT, note that all 4 N-H bonds in the ammonium ion are identical.


3. Transition metal complexes - dative covalent bonds with ligands

The ligands surrounding the central ion of a complex ion donate pairs of electrons to form the ligand-metal ion bond

octahedral complexes with 6 dative (co-ordinate) bonds

tetrahedral complexes with 4 dative (co-ordinate) bonds

Single and multiple covalent bonds - representations

(a) A molecule with all single covalent bonds (known as a σ bond, sigma bond, C-H and C-C in this case)

alkanes structure and naming (c) doc b ethane


(b) Double covalent bond = (σ bonds C-H, and a delocalised pi bond, the C=C bond is a σ bond plus a π bond)



(c) The C=C bond is a σ bond plus π bonding)

O=O oxygen


(d) Double covalent bond = (σ bond and delocalised π bond)



(e) Triple covalent bond (σ bond and a double π bond)

Alkynes are unsaturated hydrocarbons with a Calkene (c) doc bC carbon-carbon triple bond

Examples: C2H2, alkene (c) doc b ethyne

C3H4, alkene (c) doc b propyne

All the C-H bonds are single σ bonds.


(f) The nitrogen molecule also has a triple bond  :NN:

triple bond, all the rest have all single σ bonds C-H, C-C, C-Cl, C-O and O-H.

Relating single, double and triple bonds to average bond enthalpies and bond length

The average bond enthalpy is the 'typical' energy required to break 1 mole of a covalent chemical bond (but only involving gaseous species). Bond enthalpy is a measure of the bond strength.

For more details see Bond Enthalpy (bond dissociation energy) calculations for Enthalpy of Reaction

Bond length is defined as the distance between the two nuclei of the two atoms bonded together.

You find general patterns of decreasing bond length with increasing bond enthalpy - shorter tends to be stronger because the bonding electrons between the nuclei are closer to the nuclei and consequently more strongly attracted.

Some examples and several important patterns to spot:

bond bond length (nm) bond enthalpy (kJ/mol) Comments
C-C 0.154 348 single carbon-carbon bond e.g. in alkanes
C=C 0.134 612 double carbon-carbon bond e.g. in alkenes
C≡C 0.120 837 triple carbon-carbon bond e.g. in alkynes

Note the decrease in bond length and increase in bond strength as shown by the increasing bond enthalpy - a shorter and stronger pattern when the element is the same e.g. carbon in this case.

bond length pattern: single > double > triple

bond strength pattern: triple > double >single

N-N 0.146 163 single nitrogen-nitrogen bond
N=N 0.120 409 double nitrogen-nitrogen bond
N≡N 0.110 944 triple bond in nitrogen molecule

Again, note the decrease in bond length and increase in bond strength as shown by the increasing bond enthalpy

H-F,  F-F 0.092, 0.142 562, 158 A very nice group trend. As you descend the group 7/17 halogens the atomic radius of halogen X gets larger.

Therefore down the group, where the other atom is the same e.g. HX, you get a steady increase in bond length.

You also get  steady decrease in bond enthalpy - bond gets shorter and weaker.

You get a similar pattern for the halogen molecules X2, down the group the bond length increases as the atomic radii increase and the bond enthalpy consequently decreases.

H-Cl,  Cl-Cl 0.128, 0.199 431, 242
H-Br,  Br-Br 0.141, 0.228 366, 193
H-I,  I-I 0.160, 0.267 299, 151
C-O 0.143 360 carbon-oxygen single bond e.g. in alcohols and ethers
C=O 0.122 743 carbon-oxygen double bond e.g. aldehyde & ketone carbonyl compounds, its 805 in O=C=O.

Again the double bond is shorter and stronger than the single bond.

Some Group VII (Group 7/17) Halogens trends in bond lengths and bond enthalpies

Halogen X fluorine chlorine bromine iodine
 molecule or bond bond length/nm bond enthalpy kJmol1 bond length/nm bond enthalpy kJmol1 bond length/nm bond enthalpy kJmol1 bond length/nm bond enthalpy kJmol1
XX, X2 0.142 +158 0.199 +242 0.228 +193 0.267 +151
HX, HX 0.092 +562 0.128 +431 0.141 +366 0.160 +299
CX, RX 0.138 +484 0.177 +338 0.193 +276 0.214 +238

Some general observations, most of which relate to smaller radii giving shorter stronger bonds:

Halogen molecules X2: From fluorine to iodine the bond length increases and, except for fluorine, the bond enthalpy decreases as the radius of the halogen atom increases with increasing number of filled inner electron shells. Fluorine is distinctly anomalous with a much lower than expected bond dissociation energy, though the bond length fits the general trend. This is explained by the close proximity of the small fluorine atoms causing repulsion between them due to the closeness of the outer electron orbitals.

Hydrogen halides HX: From hydrogen fluoride HF(g) to hydrogen iodide HI(g), there is clear trend in increasing bond length and decreasing bond enthalpy. One result is the increasing ease of aqueous ionisation from hydrofluoric acid to hydriodic acid so that the HX(aq) acids become stronger down the group. In fact, hydrofluoric acid HF(aq) is a relatively weak acid but hydrochloric, hydrobromic and hydriodic acids are all very strong. The latter three are so strong in aqueous media you don't really see the difference e.g. from pH readings, but in nonaqueous media the differences can be clearly measured.

Halogenoalkanes R3CX: Based on polarisation of the bond (Cδ+Xδ), you might expect the reactivity order with respect to nucleophiles (electron pair donors) attacking the δ+ carbon bond to be RF > RCl > RBr > RI as the electronegativity difference decreases from CF to CI. However, it is the decreasing bond enthalpies from CF to CI that override this polarisation trend giving the reactivity trend RI > RBr > RCl > RF.

See Nucleophilic substitution in halogenoalkanes


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