1.4 Some enthalpy data patterns

1.4a The combustion of linear alkanes and linear aliphatic alcohols

The standard enthalpies of complete combustion (at 298K, 1 atm = 101kPa) are listed below (4 sf)

C no. n	name	alkane	ΔHcomb		name	alcohol	ΔHcomb	other names in common use e.g. in US etc.
1	methane	CH4	-890		methanol	CH3OH	-726
2	ethane	C2H6	-1560		ethanol	CH3CH2OH	-1367
3	propane	C3H8	-2219		propan-1-ol	CH3(CH2)2OH	-2021	1-propanol
4	butane	C4H10	-2877		butan-1-ol	CH3(CH2)3OH	-2676	1-butanol
5	pentane	C5H12	-3509		pentan-1-ol	CH3(CH2)4OH	-3329	1-pentanol
6	hexane	C6H14	-4163		hexan-1-ol	CH3(CH2)5OH	-3984	1-hexanol
7	heptane	C7H16	-4817		heptan-1-ol	CH3(CH2)6OH	-4638	1-heptanol
8	octane	C8H18	-5470		octan-1-ol	CH3(CH2)7OH	-5294	1-octanol

General formula of these homologous series: Alkanes C_nH_2n+2 and aliphatic alcohols H(CH₂)_nOH

and the general equations for complete combustion can be represented as ... (n = 1, 2, 3 etc.)

alkanes: C_nH_2n+2(g/l) + (1¹/₂n + ¹/₂)O_2(g) ===>  nCO_2(g) + (n + 1)H₂O_(l)

alcohols: H(CH₂)_nOH_(l) + 1¹/₂nO_2(g) ===> nCO_2(g) + (n + 1)H₂O_(l)

Graph interpretation and comments

The graph of ΔH_comb versus the number of carbon atoms shows an almost linear relationship as the combustion of each extra -CH₂- unit usually contributes an extra 632-670kJ to the molar enthalpy of combustion. The first incremental rise in ΔH_c from C₁ to C₂ is slightly anomalous in both homologous series compared to the general trend.

For the first 8 alkanes, this incremental rise ranges from 632 kJ to 670 kJ. For methane ==> ethane the incremental rise is 670 kJ. The increment for butane ==> pentane is 632 kJ and this lesser incremental rise corresponds to a the first change in state involved i.e. some of the energy released on burning pentane must be used to vapourise it and evaporation is an endothermic process. In fact ΔH_vap(C₅H₁₂) is +36 kJ mol^-1. This absorbed energy is not required by methane ==> butane which are already in the gaseous state. Apart from these two small anomalies all the other incremental rises are 653-658 kJ.

In the case of the first 8 alcohols, all liquids at 298K 101kPa, apart from the incremental rise of 641 kJ from methanol to ethanol, all the other incremental rises up this homologous series are 653-656 kJ and these are completely consistent with incremental rises for most alkane.

For the same carbon number (n) the values for alcohols are slightly smaller than those for alkanes because the alcohols are already partially oxidised i.e. the presence of a single oxygen atom in each alcohol molecule.

 

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1.4b Some patterns in Bond Enthalpies and Bond Length

1.4b(i) Examples of single versus multiple bond

For a pair of atoms (similar/dissimilar) the bond length shortens and the bond enthalpy increases in going from a single to double to triple bond (1, 2 and 3 electron pairs involved). This is a rule in chemistry which is always true! The reason is quite simple. A covalent bond results from the sharing of electrons, which is actually the mutual attraction of two positive nuclei for the negative electrons between them. The greater the number of electrons between the two nuclei the stronger the attraction between them. Therefore the nuclei are drawn together more closely to give a shorter bond length and more energy is required to 'pull them apart' i.e. a greater bond enthalpy (bond dissociation energy). The number of bonding electrons for a particular bond divided by 2 is referred to as the bond order.

Bond	Bond order	Bond enthalpy/kJmol-1	Bond length/nm
single C-C	1	+347	0.154
double C=C	2	+612	0.134
triple CC	3	+838	0.120
single C-O	1	+358	0.143
double C=O (not CO2)	2	+743	0.122
O-O in peroxides	1	+146	0.148
O=O in oxygen	2	+496	0.121
single N-N	1	+163	0.146
double N=N	2	+409	0.120
triple NN	3	+944	0.110

Since reactions usually involve collision and initiated by bond fission you might think that single bonds would automatically be more reactive i.e. have a lower activation energy due to a smaller bond enthalpy.

BUT, particularly in organic chemistry, the nature of the 'attacking' reagent is a major factor in the feasibility of a reaction. For example, unsaturated alkenes (>C=C< functional group) and alkynes (-CC- functional group) are much more reactive than saturated alkanes with only single C-C bonds. The pi electron clouds of the unsaturated hydrocarbons are very susceptible to attack by electrophilic (electron pair seeking) reagents like bromine Br₂, hydrogen bromide HBr etc. The polarised carbonyl group (>C^δ+=O^δ-) in aldehydes and ketones is susceptible to attack at the δ+ carbon by nucleophilic electron pair donors and much more so than the similarly polarised C^δ+-O^δ- bond in alcohols (C^δ+-O^δ--H) or ethers (C^δ+-O^δ--C).

However in the more inorganic situations the expected pattern is observed. Nitrogen, with its triple bond is extremely stable, hence the need for a catalyst and high temperature to make it combine with hydrogen in the Haber Synthesis of ammonia.

1.4b(ii) Some Group VII (Group 7/17) Halogens trends

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 bromine to iodine the bond length increases and 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 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 decrease 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.

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1.4b(iii) The effect of bond polarity and electronic situation

If the electronegativity difference between two atoms of a covalent bond increases then the polarity of the increases and the bond enthalpy increases with this increased 'ionic' character. I don't know how 'general' this rule is but  e.g.

Bond	Atomic covalent  radius nm	Electronegativity difference	Bond enthalpy	bond length
C-H	C = 0.077 nm	0.4	+413	0.109 nm
N-H	N = 0.074 nm	0.9	+388	0.101 nm
O-H	O = 0.074 nm	1.4	+463	0.096 nm
F-H	F = 0.072 nm	1.9	+562	0.092 nm

Note:

(a) this does also coincide with a decreasing covalent atomic radius across Period 2 which would contribute to the increase in bond enthalpy of X-H from left to right, so I'm not sure which has the greater influence on the trend?

(b) and for the ~non-polar C-H bond, the bond enthalpy is +413 which doesn't fit in with the trend at all, so this would suggest the increasing polarity of the bond does have some effect?

(c) If the polarity of the bond is 'shared out' the bond energy decreases e.g.

(i) P-Cl bond energy in gaseous PCl₃ is +319, but the P-Cl bond energy in gaseous PCl₅ is only +258 kJmol^-1.

Although both are covalent molecules in the gaseous state there is a significant electronic structure difference which results in quite different bond enthalpy values.

(ii) The three titanium chlorides show a similar pattern

The Ti-Cl bond enthalpy values are +502 in TiCl₂, +456 in TiCl₃ and + 427 kJmol^-1 in TiCl₄.

(d) These examples also illustrate the difficulties of using average bond enthalpies in theoretical calculations - like it or not, the actual bond enthalpy of an 'A-B' bond  is quite dependent on the particular 'electronic' situation even for a particular pair of covalently bonded atoms A and B.

This point can further be emphasised by considering the stepwise deprotonation of methane in which the enthalpy of each step corresponds to the particular C-H bond enthalpy of the homolytic fission of each individual C-H bond.

CH_4(g) ==> CH_3(g) + H_(g)  ΔH^θ₂₉₈(C-H bond) = +425 kJmol^-1

CH_3(g) ==> CH_2(g) + H_(g)  ΔH^θ₂₉₈(C-H bond) = +470 kJmol^-1

CH_2(g) ==> CH_(g) + H_(g)   ΔH^θ₂₉₈(C-H bond) = +416 kJmol^-1

CH_(g) ==> C_(g) + H_(g)       ΔH^θ₂₉₈(C-H bond) = +335 kJmol^-1

The average of these values is 411.5, but look at the variation!, one need say no more!

A Hess's law cycle thermochemical calculation gives an average C-H bond enthalpy of +415.5 kJmol^-1 for methane.

Other examples of electronically different situations for the same bond: For the O-H bond in water (HO-H) is +494, but for the O-H bond in the OH radical itself is +430 and the C=O bond enthalpy in carbon dioxide (OC=O) is +531 but, for the C=O bond in carbon monoxide itself, the bond enthalpy is +1075 kJmol^-1.

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A set of enthalpy calculation problems with worked out answers - based on enthalpies of reaction, formation, combustion and bond enthalpies

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