dative bond co-ordinate bond single double triple bonds coordinate covalent bond length patterns bond enthalpy trends advanced A level chemistry revision notes

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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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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)

ethene

O=O oxygen

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

O=C=O

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

Alkynes are unsaturated hydrocarbons with a CC carbon-carbon triple bond

Examples: C₂H₂, ethyne

C₃H₄, 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 kJmol^–1	bond length/nm	bond enthalpy kJmol^–1	bond length/nm	bond enthalpy kJmol^–1	bond length/nm	bond enthalpy kJmol^–1
X–X, X₂	0.142	+158	0.199	+242	0.228	+193	0.267	+151
H–X, HX	0.092	+562	0.128	+431	0.141	+366	0.160	+299
C–X, R–X	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 non–aqueous media the differences can be clearly measured.

Halogenoalkanes R₃C–X: Based on polarisation of the bond (C^δ+–X^δ–), you might expect the reactivity order with respect to nucleophiles (electron pair donors) attacking the δ+ carbon bond to be R–F > R–Cl > R–Br > R–I as the electronegativity difference decreases from C–F to C–I. However, it is the decreasing bond enthalpies from C–F to C–I that override this polarisation trend giving the reactivity trend R–I > R–Br > R–Cl > R–F.

See Nucleophilic substitution in halogenoalkanes

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