chap11chemistry of combustion

7/29/2019 Chap11chemistry of Combustion

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11Ch em istry of Co m bus tion

The thermodynamics o f combust ion were cons idered in Ch apter 10 , and i t was s tateA tha tadiabat ic combust ion could be achieved. The conc ept of adiabat ic com bust ion runs counterto the exper ience of many engineers , who tend to re la te combust ion to heat addi t ion orheat re lease processes . This approach i s encouraged in mechanica l engineers by theapplicat ion of the air s tandard cy cle to engines to enable the m to be treated as heat engines.In real i ty combustion is not a process of energy transfer but one of energy transformation.The energy re leased by co mbu st ion in a spark igni t ion (pe t ro l ) engine i s a l l conta ined inthe mixture prior to combustion, and i t is released by the spark. I t wil l be shown that theenergy which causes the tempera ture r i se in a combust ion process i s obta ined by breakingthe bonds which hold the fuel atoms together.

1 1 . 1 B o n d e n e rg i es a n d h e a t s o f f o r m a t i o nHeats (enthalpies and internal energies) of formation can be evaluated empirical ly by'burning ' the fue l . They can a lso be evaluated by cons idera t ion of the chemical s t ruc tureof the compound. Each compound consis t s of a number of e lements he ld together bycer ta in types of bond. The bond energy i s the amount of energy requi red to separa te amolecule in to a toms; the energy of a par t icular type of b ond i s similar i rrespective of theactual structure of the m olecule.This concept was introduced in Ch apter 10, and heats of formation w ere used to evaluateheats of reaction (Hess ' law ). The process of breaking the chemical bonds during thecombustion process can be depicted b y a diagram such as Fig 11.1. I t is assumed that elementmolecules can be atomised ( in a constant pressure process) by the addition of energy equal toAH,. If these atoms are then brought together they would combine, releasing dissociat ionenergy of ]~ A H ( X - Y)R, to form the reactants. The sum o f the dissociat ion and atomisationenergies (taking account of the sig ns) results in the enthalpy o f formation o f the reactants. In asimilar way the enthalpy of formation o f the products can be evaluated. Using H ess ' law , theenthalpy o f reaction of the fuel ca n be evaluated as the difference between the enthalpies offormation of the products and the reactants The se energies ar e essentially the bo nd en ergies ofthe various molecules, a nd som e of these energies are listed in Tab le 11.1.

Figure 11.2 shows how the energy requi red to separa te tw o a toms var ies wi th d is tance:the bond energy is defined as the minimum potential energy relat ive to that at infini ty. Thepoint of minimum energy indicates that the molecule is in equil ibrium.


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Gaseousatoms

i i i i iElementalmoleculesi

Reactant ImoleculesProductmolecules

x ~ q C x - Y ) ~ XAH(X-Y),( )

( ~ - i ~

AIFI:( ~ a - O , - ~ q &

Fig. 11.1 Relat ionsh ip between enthalpies of formation and react ion

Bond - ' ~ - -

iiDistanceFig. 11.2 Variation of bond energy with d is tance between atoms

Ta ble 11.1 Some atomisat ion, d issociation and resonance energies (based on 25"C)*

Bondatomisat ion (AH,)BondEnergy dissociat ion Ene rgy

( M J / k r n o l ) ( A H ( X - - Y ) ) ( M J / k m o l ) R e s o n a n c e Energy( M J / k m o l )H - - Hc (graphite)(o--O)o~N - , , , , N

435.4 C -- H 414 .5 Benz ene: C6I-I~717.2 N -- H 359.5 Naphthalene: C~0I~498.2 O -- H 428.7 Carbon dioxide: CO2946.2 H---OH 497.5 -CO OH group

C - - O 3 5 1 . 7C - - O 6 9 8 . 1C - - C 3 4 7 . 5C - - C 615.5C E C 8 1 2 . 2

150.4255.4137.9117.0

note: these values have been taken from different sources and m ay not be ex actly compatible.


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210 Chemistryo f combustionIn addition to the energy associated w ith particular bon ds there are a lso energies causedby the possibil i ty of resonance or s tra in in a particular molecule . For example, the ring

structure of benzene, w hich is normally considered to be three s imple double bondsbetween carbon atoms, together with three s ingle ones, plus s ix carbon-hydrogen bonds,can reform to give bonding across the cyclic s tructure (see Fig 11.3).This results in a substantia lly higher energy than would be estimated from the s implebond s tructure, and some typical values are show n in Table 11.1.

HC/ / \HC CH[ I IHC Clt

%c /H

HC/ % /HC CH HCI I I I IHC CH HC\ // \

12H

HC \CHI ICH/

CH

H HC C/ / \ / %

\ / / % /C CH H

Fig. 11.3 Bonding arrangements of benzene, showing bo nd resonance through delocalised electrons

1 1 . 2 E n e r g yof form at ionIt will be considered in this section that the processes take place at constant pressure andthe property enthalpy (h or H) will be used; if the processes were constant volume onesthen internal energies (u or U) would be the app ropriate properties .

A hydrocarbon fuel consis ts of carbon and hydrogen (and possibly another e lement)atoms held together by chemical bonds. These atoms can be considered to have beenbrought together by heating carbon and hydrogen (in molecular form) under conditionsthat encourage the resulting atoms to bond. T here are two processes involved in this : f irs t ,the carbon has to be changed from solid graphite into gaseous carbon atoms and thehydrogen also has to be atomised; then, second, the a toms must be cooled to form thehydrocarbon fuel. These tw o processes have tw o energies associated with them: the firs t isa tomisation energy (AH,) and the second is dissociation energy (]~ A H ( X - Y)R) requiredto dissociate the chemical bond in the compo und C~I-I Fig ure 11.1 shows these terms, andalso indicates that the energy of formation o f the fuel (AH f) is the net energ y required forthe process, i.e.

, ~ f = Z A H . - Z A B ( x - D R (11.1)In reali ty the enthalpy of formation is more complex than given above because energycan be s tored in molecules in a number of ways, including resonance energies (in thebenzene ring structure) and changes of phase (la tent heats). A more general representationof the enthalpy of ormation is

An, = Z An.- Z al l(X- Y)- Z an . . - Z An,..., (11.2)ExampleEvaluate the enthalpy o f formation o f CO2 and H2O from the atom isation and dissociationenergies listed in Tab le 11.1.


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Energy o f ormation 211SolutionC a r b o n d i o x i d e ( C 0 2 )Car bon d i ox i de i s f o r m ed f r om ca r bon and oxygen in t he r eac t i on .

C~,p~m + O2 (g) - - " CO 2(g) (11 .3)w her e t he ( g ) i nd ica t e s t ha t the e l em en t o r com pound i s i n t he gas eous ( vapour ) phas e ,and (1) wi l l be used to indica te tha t the e lemen t or com pou nd i s in the l iquid phase .

The r ea c t ion in eqn (11 .3) i s achieved by a tomisa t ion of the indiv idual carb on (graphi t e)m ol ecu l e s and t he oxygen m ol ecu l e s , w i t h s ubs equen t r ecom bi na t i on t o f o r m ca r bondioxide . Ef fec t ive ly the r eac tant molecules , which are in a metas t able s t a t e , a r e ac t iva tedabove a ce r ta i n ene r gy t o p r oduce a t om s w h i ch w i ll then co m b i ne t o f o r m t he s t ab l e CO 2molecule ( see Fig 11 .4) .

~ atomisation\ . . . . . +metastable \reactants

~ , stable

. . . . . . . . Progress o f reac tionFig. 11.4 Gibbs energy variation during a reactio n

Hence , f rom Fig 11 .1 ,(A Hf)co2 = ~ A H , - ~ , A H ( X - Y) - ~ , A H m - ~ , aHLm.t

In th is case there i s a r esonanc e e nergy but the l a tent energy ( i .e . l a t ent hea t ) i s zero .T h e n(A Hf )co 2 ffi )". AH,[Cs,~,h~t, ] + AH ,[O = O] - 2(C = O ) - A H , , [C O 2]

ffi 717.2 + 4 3 5 .4 - 2 x 698.1 - 137.9= - 3 8 1 . 5 M J / k m o l

The tabu l a ted va l ue i s - 3 93 . 5 M J / km ol .

(11 .4)

(11.5)

W a t e r (H20)Thi s i s f o r m ed f r om t he hydr ogen and oxygen m ol ecu l e s i n t he r eac t ion

S 2 ( g ) + 8 9 2 ( g ) - ' + H 2 0 ( g )T h u s

(AHf)H2 o - ~ A Ha --,~_.A H (X - ] I ) - ~ , AH ~ , - ~ , AH~mm

(11.6)

(11.7)


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212 Chemistryo f combustionIn th i s ca se A H, , = 0 bu t AH~,~ ,t dep end s u pon the pha se of the wa te r . F i r s t , cons ide r thewa te r i s in vapou r phase , w hen AH~mt = 0 . The n

( A H f) ,2o = X A H , - ~ , A H ( X - 10= A H , [ H - H ] + 89 AH ,[O - O] - [H - O H] - [O - H]= 435 . 4 + 89 498.2) - 497 .5 - 428 .7= - 2 4 1 . 7 M J / k m o l

T h i s c om pa r e s w e l l w i t h t he t a bu l a t e d va l ue s o f - 241 . 6 M J / km ol .I f t he w a t e r w a s i n l iqu i d pha s e t he n e qn ( 11 . 6 ) be c om e s

H2 (g) + -~O 2 ( g ) - - " t t 2 0 (1 )(AHf)H2O0) ffi (AHf)n2o tg )+ (m w )n2ohfg

ffi - 2 4 1 . 7 - 1 8 x 2 4 4 1 . 8 / 1 0 0 0= - 2 8 5 . 6 5 M J / k m o l

(11 .8)

(11.9)

(11 .10)

T h e ta b u la t ed v al u e i s - 2 8 5 . 6 M J / k m o l .

ExampleE va l ua t e t he e n t ha lpy o f f o r m a t ion o f m e t ha ne , C t L .

SolutionT he s t ruc t u re o f m e t ha ne i s te t r a hed r a l , a nd o f t he f o r m s how n i n F i g 11 .5 ( a ) . M e t ha ne i sof ten depic ted in p lan a r form as sho wn in F ig 11 .5 (b) .

H." ". ~ H

. . . - ' .... - . . i n [. ." " . .- . n cH H

H

( a ) ( b )Fig . 11.5 Atomic arrangement of methan e molecule

M e t ha n e c a n be f o r m e d by t he f o l low i ng r e a c ti on :Cgr~ph~e + 2 H 2 (g )- - ' CH 4(g ) (11.11)


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Energy o f orma t ion 213H e n c e

( A H t) c m = Y~ A l l . - Y~ A H ( X - I0 - X AH=,- X AH~.,~ . ,= A H . [ C ~ , . ] + 2 A H . [ H - H ] - 4 [ H - C ] ( 11 .1 2)= 717 .2 + 2 x 425 .4 -4 x 414 .5= - 7 0 MJ/kmol

T h e t a b u l a t e d v a lu e i s - 7 4 .7 8 M J /k mo l , a n d t h e d i f f e r e n c e o c c u r s b e c a u s e t h e e n e r g yof the bonds in methane i s a f fec ted by the st ruc tu re o f the meth ane m olecu le , w hich resu l t sin a t trac t ion fo rces be twee n m olecu les.

ExampleEvalua te the en tha lpy o f fo rmat ion o f e thano l , C2I-IsOH.SolutionThe p lana r represen ta tion o f the s t ruc tu re o f e thano l i s show n in F ig 11 .6 .

H HI IH - - - C - - - C - - - 0 - - - HI I

H HFig. 1 1.6 Structure of ethanol molecule

E thano l can be cons idered to be made up o f the fo l lowing p rocesses :2 C m # e + 3 H 2( g) + 0 . 5 0 2 ( g ) - - " C 2 H sO H ( g )

g iv ing the en tha lpy o f fo rmat ion o f e thano l as (eqn (11 .12) )( A H f ) c 2 H s O H - - - - "Z A H . - X A H ( X - Y ) - Z A H = , - Z aHlatent

This g ives the fo l lowing equ a t ion :2C~whit~ + 3 H2 (g) + 0. 50 2( g)- - - ' 2C(g) + 2 x 717 .2 + 6H + 3 x 435 .4 + O + 0 .5 x 498 .2

- w ~ . e i, , , , i iatomisation atomisation atomisationenergy for C energy for H energy for O

- 5[C- H] - [C-C ] - [C-O ] - [O-H]- "C 2 H s O H( g ) + 2 x 7 1 7 .2 + 3 x 4 3 5 .4 + 0 .5 x 4 9 8 .2

- 5 x 4 1 4 .5 - 3 4 7 .5 - 3 5 1 .7 - 4 2 8 .7" ' * C 2 1 -I s O n ( g ) - 2 1 0 .7 M J / k m o l

(11 .13)


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2 1 4 Ch e m i s tr y o f c o m b u s t io nH e n c e t he en t ha l p y o f f o r ma t i on o f g a s e o u s e t h a n o l is - 2 1 0 . 7 M J / k m o l . T h i s is

e q u i v al e n t t o - 5 . 8 5 3 M J / k g o f e t h a n o l . T h e v a l u e o b t a i n e d f r o m t a b l es is a b o u t-22 2.8 MJ /k mo l, an d the difference is attributable o the sfight ariations in bo nd energythat occur du e to the three-dimensional nature of the c hemi cal structure.

E x a m p l eEvaluate the e n t h a l p y o f r e ac ti o n of methane .

So lu t ionThis can be obtained ei ther by using atomisation and dissociat ion energies, in a similarmanner to tha t used to f ind the enthalpies of format ion of compounds , or f rom theenthalpies of format ion of the compounds in the reac tants and products . B oth m ethods wi l lbe used in th is case . The reac t ion descr ib ing the com bust ion o f methane i s

C H 4 (g ) + 2 0 2 ( g ) - - " C O 2 ( g ) + 2 I ~ O ( g ) (11.14)The chemical s t ruc ture of methane was g iven above. Hence the enthalpy of format ion ofthe reactants

( a nf h = Z A H . - Z A H ( X - Y) - Z A H . - Z A H , ,= A H , [ C ~ , , ] + 2 A H, [I -I - H ] + 2 A H , [ O = O ] - 4 [ H - C ] - 2 [ O = O ]

( 1 1 . 5 )Note tha t the a tomisa t ion and dissocia t ion energies of oxygen arc equal(2 AH ,[Off iO] ffi 2[O ff iO ]) and cancel out , i .e . the en thalpy of format ion of oxygen i szero. This value of zero is assume d as a base level for al l elements. T hus

(AHf)R = (AH f)c~ = 70 M J/km olSimilarly for the produ cts

(AHf)p= AH, - Z A H ( X - Y ) - Z A H , ~ - Z A H ~ t= AH, [Cg , ,p~I + 2 AH, [O = Ol + 2 AH, [H - H I

- 2 [ C =O ] - 2 [ H - O H ] - 2 [ 0 - H ] - A H , ~ [ C O2 1= ( a H , ) c o + 2 ( a H f ) H O= - 3 8 1 . 5 - 2 x 2 4 1 . 7 M J / k m o l

(11.16)

(11.17)The heat of reaction is given b y

AHR = (AHf)p- (AHf)R= - 3 8 1 . 7 - 2 x 2 4 1 . 7 - ( - 70)= - 7 9 4 . 9 M J / k m o l ( 11 .1 8)

This i s c lose to the va lue of -802.9 MJ/kmol quoted as the l o w e r cnthalpy of reac t ion ofmethane in Table 11.2 . I f the h igher hea t of reac t ion of methane i s requi red then eqn(11.14) becomes

CI-14(g) + 20 2( g) - - 'C O 2 (g ) + 2H20(1) (11.19)


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Energy of ornmtion 215ExampleEvalu ate the lowe r enthalpy of react ion of benzoic ac id (C6I-IsCOOH). The plan ar diagramof i ts s t ructure is shown in Fig 1 1 . 7 .

/H C

OIC - - 0 - - - HI12 %

H CCH

C HICHF i g . 1 1 . 7 S t ru c tu r e o f b e n z o i c a c i d m o l e c u l e

SolutionThe reac t ion of benzo ic ac id wi th oxygen i s

C J - Is C O O H ( g ) + 7 . 5 0 2 ( g ) - - ' 7 C O 2 ( g ) + 3 ~ O ( g ) ( 11 .2 0)The eas ies t way to eva lua te the en tha lpy of reac t ion i s f rom eqn (11 .18) :

A H R = (AHf)p - (AH f)ltThe va lues o f Hf were ca lcu la ted above fo r CO2 and 1-120 , and hence the on ly unk now nquanti ty in eqn (11.18) is the enthalpy of formatio n of the benzo ic acid:

(AHf)c6HjCX~H ---"E AH , - ~ AH (X - Y) - ]~ AH= , - 5'. ~ l a t e n t (11.21)The acid is in gaseous form before the react ion, see eqn (11.20) , and thus AHl,ff i , t= 0.Subst i tut ing values into eqn (11.21) gives

Hence

(AHf)C6HsLX)OH----Z A U a - X A H ( X - D "- Z A n t es= 7 AH,[Cmph~~ ] + 3 A H , [ H - H I + A H , [ O = O ]- 5 [ a - c ] - 4 [ C - C ] - 3 [ C f f iC ] - [ C - O ]- [ C - O ] - [ O - H ] - [ aH = ]c 6n 6 - [ A H= ,] co o. (11.22)

(AHf)c6Hscoon- 7 717.2 + 3 x 435.4 + 498.2 - 5 x 414.5- 4 3 4 7 . 5 - 3 - 3 5 1 . 7 - 4 2 8 . 7 - 1 5 0 . 4 - 1 17 .0

= - 230.1 M J/km ol (11 .23)


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216 Chemistryof combustionThe en tha lpy o f fo rmat ion o f the p roduc ts i s

(AH f)l, = 7 (AH f)coz + 3 (AHf)H2o= 7 x ( - 3 8 1 . 5 ) + 3 x ( - 2 4 1 . 7 )= - 3 3 9 5 . 5 M J / k m o l

Thus the enthalpy of react ion of benzoic acid is(AHR)c6.scoo. = -33 95 .6 - ( -2 30 .1 ) = 3165 .5 M J/km ol

The tabu lated va lue i s 3223 .2 M J/km ol , g iv ing an inaccuracy of about 2%.

(11.24)

(11.25)

11.3 Enthalpy o f react ionThe en tha lp ies o f reac t ion o f some co mm only encounte red fue l s a re g iven in Table 11 .2 .These have been taken f rom a number o f sources and conver ted to un i t s cons i s ten t wi thth is t ex t where necessa ry . There a re a nu mb er o f in te res t ing observa tions tha t can be madefrom this table:9 the en tha lp ies o f reac t ion of many of the hydrocarbon fue l s on a bas i s o f mass a re ve ry

s imila r, a t a round 4400 010/k g ;9 the s to ich iometr ic a i r - fu e l ra t ios o f man y bas ic hydrocarbon fue l s li e in the range1 3 : 1 - 1 7 : 1 ;9 some of the fue ls have pos i t ive en tha lp ies o f fo rmat ion ;

9 al l of the fuels have negat ive enthalpies of react ion;9 the enthalpies of react ion of the a lcoho ls are less than those of the non-oxy genate ~

fue ls , s imply because the ox ygen cann ot p rov ide any energy of reac t ion ;9 the comm only used hydrocarbon fue l s a re usua l ly mix tures o f hydrocarbon com -

pounds.11.4 Concluding rem arksI t has been shown that the energy released by a fuel is contained in i t by vir tue of i tss t ructure , i .e . the bonds between the atoms. I t is possible to assess the enthalpies offormat ion or reac t ion of a wide range of fue l s by cons ider ing the chemica l s t ruc ture andthe bonds in the compoun d .A tab le o f en tha lp ies o f fo rmat ion and reac t ion fo r com m on fue l s has been g iven .


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I I I I I I , . ? iI I I I I I II ~i~ ~ ~'~ I~

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chap11chemistry of combustion

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