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Revision notes energetics - patterns/trends in enthalpies of combustion & bond enthalpy & bond lengths - for Advanced Level Theoretical-Physical Chemistry:

Part 1 ΔH Enthalpy Changes The thermochemistry of enthalpies of reaction, formation, combustion and neutralisation

Part 1.4 Enthalpy data patterns (a) combustion of alkanes & alcohols, (b) examples of bond enthalpy and bond length patterns

Doc Brown's A Level Chemistry - Advanced Level Theoretical Physical Chemistry Revision Notes - Basic Thermodynamics

GCE A Level Thermodynamicsthermochemistry subindex links below

This page describes patterns of enthalpy values for some homologous series of organic compounds e.g. the enthalpies of combustion of alkanes, enthalpy of combustion of alcohols. A second section describes and explains the data patterns for series of bond enthalpies and bond lengths e.g. group 7 hydrides and other sets of 'XH' bonds and further consideration, single, double and triple carboncarbon or nitrogennitrogen bonds.

Sub-index for this page

1.4a The combustion of linear alkanes and linear aliphatic alcohols

1.4b Some patterns in bond enthalpies, bond Length and bond order

1.4b(i) Examples of single versus multiple bond trends

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

1.4b(iii) The effect of bond polarity, electronic situations and a problems in using average bond enthalpies
 

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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. alkane formula Mr ΔHcomb

kJ/mol

ΔHcomb

kJ/g alkane

ΔHcomb kJ/g CO2 produced alcohol formula ΔHcomb

kJ/mol

1 methane CH4 16 890 -55.6 -20.2 methanol CH3OH 726
2 ethane C2H6 30 1560 -52.0 -17.7 ethanol CH3CH2OH 1367
3 propane C3H8 44 2219 -50.4 -16.8 propan1ol CH3(CH2)2OH 2021
4 butane C4H10 58 2877 -49.6 -16.3 butan1ol CH3(CH2)3OH 2676
5 pentane C5H12 72 3509 -48.7 -16.0 pentan1ol CH3(CH2)4OH 3329
6 hexane C6H14 86 4163 -48.4 -15.8 hexan1ol CH3(CH2)5OH 3984
7 heptane C7H16 100 4817 -48.2 -15.6 heptan1ol CH3(CH2)6OH 4638
8 octane C8H18 114 5470 -48.0 -15.5 octan1ol CH3(CH2)7OH 5294
20 n-eicosane C20H42 282.6 -13316 -47.1 -15.1      

Note for reference:

For burning pure carbon the energy release figures are 32.75 kJ/g of carbon and 8.93 kJ/g of CO2 emitted.

See note on global warming and carbon dioxide emissions

 

General formula of these homologous series: Alkanes CnH2n+2 and aliphatic alcohols H(CH2)nOH

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

alkanes: CnH2n+2(g/l) + (11/2n + 1/2)O2(g) ===>  nCO2(g) + (n + 1)H2O(l)

alcohols: H(CH2)nOH(l) + 11/2nO2(g) ===> nCO2(g) + (n + 1)H2O(l)

Graph interpretation and comments

The graph of ΔHcomb versus the number of carbon atoms shows an almost linear relationship as the combustion of each extra CH2 unit usually contributes an extra 632670kJ to the molar enthalpy of combustion. The first incremental rise in ΔHc 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 ΔHvap(C5H12) is +36 kJ mol1. 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 653658 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 653656 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.

 

Note on global warming and carbon dioxide emissions

In the debate on fossil fuels its often quoted that natural gas (mainly methane) is 'greener' than heavier fuel oils, so I thought I'd put a data input to justify the statement or otherwise.

 

(a) In the table of alkane combustion data I've worked out the energy released per gram of pure alkane fuel.

This ranges from 55.6 kJ/g for methane down to 47.1 kJ/g for a long chain hydrocarbon (equates to a heating oil etc.).

Therefore a heavy fuel oil - central heating oil gives about 85% of the energy per unit mass compared to methane from natural gas.

So on this a basis there a case for methane being 'greener' on heat released per unit mass of fuel.

 

(b) Also, in the table of data, I've worked out the energy released per gram of carbon dioxide formed.

This ranges from 22.2 kJ/g CO2 for methane down to 15.1 kJ/g CO2 for a long chain hydrocarbon (equates to a heating oil etc.).

So a heavy fuel oil - central heating oil gives about 68% of the energy per unit mass of carbon dioxide emitted compared to methane from natural gas.

So on this a basis, there is an even greater case for methane being 'greener' on heat released per unit of carbon dioxide released into the environment.

 

I'm not using these figures to argue the case for continuing to use large quantities of fossil fuels for power generation or heating, but methane is definitely 'greener' than other hydrocarbon fuels.

Methane is also much more 'greener' than coal, judging from my calculations in (c) below!

 

(c) Burning 'pure' coal i.e. burning pure carbon

C(s) + O2(g) ==> CO2(g)   ΔHθc = 393 kJmol1

Energy released in terms of molar mass in grams:

393/12 = 32.8 kJ/g of carbon fuel burned, 49% energy released compared to methane.

393/44 = 8.93 kJ/g of carbon dioxide emitted, 44% energy released compared to methane.

Apart from the greater pollution from burning coal, it does not release nearly as much energy per mass of fuel or CO2 emitted, compared to hydrocarbon fuels.

The difference is mainly due to the fact there is no hydrogen (and little in coal) to oxidise to water.

It should also be born in mind that coal is much less pure than processed natural gas, so more potentially more polluting and less energy releasing.

Burning coal doesn't produce water vapour, itself a greenhouse gas, but, unlike carbon dioxide, water can condense out until the equilibrium vapour pressure is achieved at the ambient temperature. On the other hand atmospheric carbon dioxide concentration can continue to build up and build up, and it is!

See Greenhouse effect, global warming, climate change, carbon footprint from fossil fuel burning

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1.4b Some patterns in bond enthalpies, bond Length and bond order

1.4b(i) Examples of single versus multiple bond

For the same 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 and the two positive nuclei of the bonded atoms.

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.

In other words bond order is the equivalent number of bond pairs involved between a bond between two atoms.

Bond order may not be needed for UK A level students but it is a useful and interesting concept.

e.g. look at the consistent pattern-trend for the five carbon-carbon bonds quoted.

Bond Bond order Bond enthalpy/kJmol1 Bond length/nm examples
single bond CC 1 +347 0.154 alkanes/diamond
CC 1.33 ? 0.142 graphite
CC 1.5 average +518 0.140 benzene
double bond C=C 2 +612 0.134 alkenes
triple bond CC 3 +838 0.120 alkynes
single bond CO 1 +358 0.143 alcohols/ethers
double C=O (not CO2) 2 +743 0.122 aldehydes/ketones
triple bond CO 3 +1077 0.113 carbon monoxide
single OO 1 +146 0.148 peroxides
double O=O 2 +496 0.121 oxygen
single bond NN 1 +163 0.146  
double bond N=N 2 +409 0.120  
triple NN 3 +944 0.110 nitrogen

Footnotes on bond order, bond enthalpy and bond length

(i) in CC the dots indicate the delocalised electrons (on average < 1) of the pi bond AND pm = nm x 1000.

(ii) In carbon dioxide, bond enthalpy of C=O is +805 kJ/mol, bond length is 0.116 nm

(iii) The triple bond of carbon monoxide comprises a double covalent bond plus a dative covalent bond.

(iv) Explaining the sequence for carbon-carbon bonds in increasing bond order for:

All arguments are based on carbon having four valency electrons, AND, all used in the various C-C bonding situations described below.

There is a consistent pattern-trend for the five carbon-carbon bonds quoted. 'On average', as the number of electrons each carbon atom contributes to the specified carbon-carbon bond increases, the bond length decreases and the bond strength (bond enthalpy) increases.

The more electrons between the two positive carbon nuclei, the greater the attractive force - the carbon atoms are more strongly attracted, shortening the bond length and more energy needed to 'pull them apart'.

 

Alkanes (bond order 1)

Saturated hydrocarbons with only single C-C bonds

or or alkanes structure and naming (c) doc b for the alkane ethane

(c) doc band its no different for propane alkanes structure and naming (c) doc b etc.

The C-C bond length is similar in diamond (an allotrope of the element carbon).

Each carbon atom, contributes one electron to each carbon-carbon bond.

 

Graphite (allotrope of carbon) (bond order 1.33)

(c) doc bIn graphite, three C-C bonds emanate from each carbon atom using three of carbon's four valency electrons. However, the fourth delocalised electron is shared between three C-C bonds, so the bond order is actually 1.33.

I have seen this quoted as 1.5 on the internet, but this is incorrect, and graphite's electronic structure is being confused with that of benzene (see below).

Each carbon atom, 'on average', contributes 1.33 (1 + 1/3) electrons to each carbon-carbon bond.

You can see why the bond order can't be 1 or 2, but intermediate, by drawing a sort of Kekule style structure (above right)  for a layer of graphite/graphene, so it looks a bit like conjoined benzene rings.

The more usual simplified structure (above left) seems to indicate three single bonds to each carbon atom. Three bond yes, but strictly speaking, not single bonds, since there is pi bonding involved due to delocalised electrons.

Unfortunately, for 'necessary simplicity', the 4th delocalised electron doesn't show up in the 'usual' diagrams for graphite or graphene. Such diagrams indicate, 'incorrectly', that a carbon atom forms three single bonds with three other carbon atoms.

See also

Covalent Bonding macromolecules and giant covalent structures

From fullerenes & bucky balls to carbon nanotubes

Graphene, graphene oxide and fluorographene

 

Benzene (bond order 1.5)

The original Kekule style of displaying benzene was

i.e. showing at as cyclotriene, this ignores the delocalised ring of pi electrons, but, it does show clearly the average bond order is 1.5 as each carbon atom contributes, on average, 1.5 electrons to each bond.

Benzene molecular formula C6H6, skeletal formula (c) doc b, structural/displayed formula (c) doc b

Each carbon atom of the bonds 'on average' contributes 1.5 electrons (1 + 1/2) to each carbon-carbon bond.

The confusion on bond order between graphite/graphene and benzene arises from the fact that in the former, each carbon atom is linked to three other carbon atoms, but in benzene, each carbon atom is only linked to two other carbon atoms. In other words the fourth (delocalised) electron is distributed in bonding between 3 or 2 other carbon atoms - and this makes a subtle difference in electron sharing!

These ideas are important when considering the 'lower than expected' enthalpy of hydrogenation of benzene.

 

Alkenes (bond order 2)

All alkenes have at least one carbon-carbon double bond

or (c) doc b or alkenes structure and naming (c) doc b 

similarly for other alkenes like propene alkenes structure and naming (c) doc b etc.

Each carbon atom of the double bond contribute two electrons to each carbon-carbon bond.

One electron contributes to the sigma bond and the other to the pi bond.

 

Alkynes (bond order 3)

alkene (c) doc b and alkene (c) doc b alkynes e.g. ethyne and propyne have a triple bond between two adjacent carbon atoms in the carbon atom chain.

Each carbon atom of the tripe bond contribute three electrons to each carbon-carbon bond.

One electron contributes to the sigma bond and the other two to the 'double' pi bond.

 

(iv) Reactivity patterns linked to bond order:

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 (Calkene (c) doc bC functional group) are much more reactive than saturated alkanes with only single CC 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 (>Cδ+=Oδ) 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 Cδ+Oδ bond in alcohols (Cδ+OδH) or ethers (Cδ+OδC).

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 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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1.4b(iii) The effect of bond polarity, electronic situations and problems in using average bond enthalpies

If the electronegativity difference between two atoms of a covalent bond increases then the polarity of the bond increases but does the bond enthalpy increases with this increased 'ionic' character?

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

From N-H to F-H there is an increase in bond energy as the bond polarity increases with an increasing difference in electronegativity, BUT ...

(a) This does also coincide with a decreasing covalent atomic radius across Period 2 which would contribute to a decrease in bond length and the increase in bond enthalpy of XH from left to right - which is a general expected trend.

(b) For the ~nonpolar CH bond, the bond enthalpy is +413 which doesn't quite fit in with the trend.

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

(i) PCl bond energy in gaseous PCl3 is +319, but the PCl bond energy in gaseous PCl5 is only +258 kJmol1.

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 TiCl bond enthalpy values are +502 in TiCl2, +456 in TiCl3 and + 427 kJmol1 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 'AB' 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 CH bond enthalpy of the homolytic fission of each individual CH bond.

CH4(g) ==> CH3(g) + H(g)  ΔHθ298(CH bond) = +425 kJmol1

CH3(g) ==> CH2(g) + H(g)  ΔHθ298(CH bond) = +470 kJmol1

CH2(g) ==> CH(g) + H(g)   ΔHθ298(CH bond) = +416 kJmol1

CH(g) ==> C(g) + H(g)       ΔHθ298(CH bond) = +335 kJmol1

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 CH bond enthalpy of +415.5 kJmol1 for methane.

Other examples of electronically different situations for the same bond:

For the OH bond in water (HOH) is +494 kJmol1, but for the OH bond in the OH radical itself the bond enthalpy is +430 kJmol1.

The C=O bond enthalpy in carbon dioxide (OC=O) is +531kJmol1, but, for the C=O bond in carbon monoxide itself, the bond enthalpy is +1075 kJmol1. This is due to the C-O bond in carbon monoxide being a triple bond (it involves a dative covalent bond as well as the expected double bond with oxygen.

 


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

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bond enthalpy patterns for combustion for AQA AS chemistry bond enthalpy patterns for combustion for Edexcel A level AS chemistry bond enthalpy patterns for combustion for A level OCR AS chemistry A bond enthalpy patterns for combustion for OCR Salters AS chemistry B bond enthalpy patterns for combustion for AQA A level chemistry bond enthalpy patterns for combustion for A level Edexcel A level chemistry bond enthalpy patterns for combustion for OCR A level chemistry A bond enthalpy patterns for combustion for A level OCR Salters A level chemistry B bond enthalpy patterns for combustion for US Honours grade 11 grade 12 bond enthalpy patterns for combustion for pre-university chemistry courses pre-university A level revision notes for bond enthalpy patterns for combustion  A level guide notes on bond enthalpy patterns for combustion for schools colleges academies science course tutors images pictures diagrams for bond enthalpy patterns for combustion A level chemistry revision notes on bond enthalpy patterns for combustion for revising module topics notes to help on understanding of bond enthalpy patterns for combustion university courses in science careers in science jobs in the industry laboratory assistant apprenticeships technical internships USA US grade 11 grade 11 AQA A level chemistry notes on bond enthalpy patterns for combustion Edexcel A level chemistry notes on bond enthalpy patterns for combustion for OCR A level chemistry notes WJEC A level chemistry notes on bond enthalpy patterns for combustion CCEA/CEA A level chemistry notes on bond enthalpy patterns for combustion for university entrance examinations analysing enthalpy data patterns for the combustion of alkanes, analysis enthalpy data patterns for the combustion of  alcohols, patterns in bond enthalpy (bond energies), relating bond length to bond enthalpy, graphs of enthalpies of combustion for linear alcohols, enthalpy of combustion graph for linear alkanes, explaining variation of bond enthalpy with bond length for single, double and triple bonds, bond lengths and bond enthalpies for halogen molecules, bond lengths and bond enthalpies for hydrogen halides, bond lengths and bond enthalpies for halogenoalkanes (haloalkanes, alkyl halides)


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