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Unformatted text preview: ME5446
Essay 3 MORE DEPTH ‘WITH REGARD TO EQUILIBRIUM COl't'IPOSITIONS Based on the evidence conveyed in Essay 5. it is an established fact that chemical reactions do not routinely go to completion. In this regard. it is appropriate to investigate reactions of practical relevance. For example. for the combustion of methane. the traditional reaction is
(13’1’4+2ll02+3.?63’srﬂ—zo€02+3£H30+7'.523‘J2 (1) This equation is properly regarded as a stoichiornemc equation because all of the reactants are consumed. A more realistic form of this reaction is
CH4 + 2(02 + 3.?6N3)—> HWICO'2 + FIHIOHEO + 7".52N2 + rrm4CH4 + 115,202 + HHEHZ + HCOCO+ NCC (2) Flu'thermore. at suﬂciently high temperatures. the molecules 03 . H 2. and N2 may dissociate into 0. H. and N. respectively. There may also be products such as NO. In order to determine the values of the unknown mole numbers n that appear on the righthand side
of Eq. (2}. it is necessary to have a number of equations equal to the numbers of unlmowns. Three of these equations are mass balances for C. H. and 0. Since there are seven unknown values of Hi. four
additional equations are needed. These are the KP equations for four stoichiometric relations. One of these stoichiometric relations is Eq. Unfortunately. a search of the textbook literatul'e did not reveal a table of KP for this equation. A further search of the research literature may provide the needed tabulation. However. at this time that information is not at hand. In view of the discussion set forth in the preceding paragraph. it is necessary to work with the stoichiometric relations that are available in textbooks. These are
H2 —> 2H H20 —> H2 + (1 .'2)02 N2 + .02 —> 2N0
02 —> 20 H30 —> (1.52ng + 0H NE —> EN 002 —> C0 + (1 2k)2 For each of these stoichiometric equations. there is a tabulation of the values of the equilibrium constant.
in the form hug) as a function of the temperature of the products. Ifthe direction of the reaction indicated in the forgoing is reversed. the sign of lniK') is also reversed. One of the issues that can be addressed by making use of the foregoing tabulation is the presence of
N0 among the combustion products. To begin the investigation. the real formation equation for N0 is N2 + 02 —> umNo + MEN2 4 "0‘02 4» an+ "00 (3) The mass balances for N and 0 yield two equations for the ﬁve unknown ns. Therefore. three K, equations are needed. They are r N2+01 —.2No (4n)
n 0,420 (4b)
III N,.2N (4c) The corresponding K, are (n )2 P 1 2H
=¢ .;
WI Whip...) W
( f 1 H
x =_"L L) 5.,
(,)g (n01)[PV" ( )
(n )2 p l 2‘1
= ‘v —— ‘
(Kplm (nag) [Bin] (C)
where
5
"=Z"'=nm+"yz+nq+n~+no (6)
pl To complete the speciﬁcation of the problem. it is necessary to write the mass balance equations. which are
N: 2=nm+2nyx 4'?!” (73) 0: 2=nw+2nq +110 (7b) At a temperature oflOOOK. ln(K,), =7.82$ . ln(K,), = 44.619. and ln(K,)In =4l.655 . so that (15,), = 3.99x10". (lg), =4.4sxto". and (1.3),, =8.12x10'” Inspection of these values of K, suggests that among the three processes ofNO formation. 02 dissociation. and N: dissociation. the latter two may be neglected altogether at this temperame. This
expectation is supported by the solution of the set of ﬁve equations and ﬁve unknowns that characterize the problem The resulting n values are This tabulation shows that NO formation occurs at a lower temperature then do the dissociations of 03
and N}. IONIZATION AND PLASMA At temperatures that are higher than those normally encountered in combustion. ionization may
occur. Ionization is a process whereby an electron is stripped out of an atom. leaving a singly charged
positive ion and a single electron (negative). Further ionization yields a doubly charged positive ion and
two electrons. When all the electrons have been stripped from the atom. there remains a state of nutter
consisting of ions that are totally depleted of electrons and of electrons whose total negative charge is
precisely equal to the total positive charge of the ions. Therefore. from a global point of View. this
collection of matter is electrically neutral. It is common to refer to such a collection of matter as
plasma. The ionization and the formation of plasma is accentuated at low pressures. As a ﬁrst approximation. plasma may be considered as an ideal gas mixture. To illustrate this
concept. it is convenient to focus attention on argon. whose chemical symbol is Ar. Sense argon is monatomic. it does not dissociate. The stoichiometric ionization reaction of argon is
Ar —t Ar. +e' (8)
while the real ionization is Ar > "[Ar' + n..e' + ntAr (9) Since charged neutrality is required. at. = n'. . Furthermore. an overall balance yields n, = 1 2n 1'. . These considerations reduce the number of unknowns that appear in Eq. (9) ﬁom three to one. The
balance of equations and unknowns is achieved by means of the K, equation. which is («,1») p I I m
’9 “°’ For a temperature of l0.000K. the numerical value of K, is 0.00042. Since experience has established that the degree of ionization is increased with decreasing pressure. the operating pressure is
chosen to be 0.01am. Once the numerical information is introduced into Eq. (10). the final result follows as Ar —> 01672413 + 0.1672; +0.6656Ar (ll) It is seen from Eq. (I 1) that an appreciable amount of ionization has occurred. ...
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 Spring '11
 Sparrow
 Combustion

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