Equil. Properties of Reacting Gas Mixtures. So far have looked at Statistical Mechanics results for a single (pure) perfect gas

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1 Shool of roa Engnrng Equl. Prort of Ratng Ga Mxtur So far hav lookd at Stattal Mhan rult for a ngl (ur) rft ga hown how to gt ga rort (,, h, v,,, ) from artton funton () For nonratng rft ga mxtur, gt mxtur rort by ror ummaton ovr ah ga for known omoton H mx =m h +m h + S mx =m +m + v,mx =Y v +Y v + For ratng (.g., doatng) mxtur, mut alo dtrmn qulbrum omoton Stat Mh for Ratng Mxtur - oyrght, by Jrry M. Stzman. ll rght rrvd. Stat Mh for Ratng Mxtur - oyrght, by Jrry M. Stzman. ll rght rrvd. Shool of Law roa Engnrng of Ma ton Gt qulbrum omoton from Law of Ma ton (Equlbrum ontant, K ) ut outln rvw of drvaton gn by ondrng f raton a b f,ar atom a ut a dfnton of two hmal tat (LHS and RHS) for a gvn t of atom, Eah (n qulbrum) ha a oltzmann dtrbuton g (II.) numbr of mol. n nrgy lvl numbr of b nrgy of lvl for artton funton for

2 Law Shool of roa of Engnrng Ma ton (on t) ut OT a onrvd quantty f hmal raton an our o II. atually t of ould quaton (3 n our a) Thr ar ontrant (onrvaton law) on total numbr of nul (ma) and nrgy for xaml f,, mad u of two ty of nul numbr of nul numbr of nul nrgy E nul nul all ar ontant f olatd ytm an fnd oluton to th t of quaton, but frt nd to xamn nrgy of ah g J a b (II.) # nul n J (II.3) (II.) Stat Mh for Ratng Mxtur -3 oyrght, by Jrry M. Stzman. ll rght rrvd. Shool ommon of roa Engnrng ro Enrgy In rvou Stat. Mh. analy, w allowd th lowt nrgy lvl of a to b zro nrgy datum arbtrary ut wth multl w an t do th w an only dfn on nrgy datum (zro),.., nd to dfn an (arbtrary) ommon zro nrgy oton thn nrgy of a gvn lvl for gvn an b xrd by nrgy of lvl rlatv to ground lvl of nrgy of ground lvl of rlatv to ytm zro ytm zro Stat Mh for Ratng Mxtur -4 oyrght, by Jrry M. Stzman. ll rght rrvd.

3 ommon Shool of roa Engnrng ro Enrgy (on t) Examl, datom doaton + What dffrn btwn ground nrgy of RHS and LHS tat? D (Doaton Enrgy) For our mor gnral xaml a b a b Stat Mh for Ratng Mxtur -5 oyrght, by Jrry M. Stzman. ll rght rrvd. k v D + D altrnat not a funton of ho of ytm zro altrnat ytm zro ytm zro r molul of a b ak Shool of roa to Engnrng Law of Ma ton a b E g For gvn ontrant (.g.,,, E, T) an fnd oluton (,, ) V&K IV.3 a b ntally oltzmann dtrbuton for two hmal tat bad on rato of thr dgnra ( ) and th xtd tat nrgy g g = Stat Mh for Ratng Mxtur -6 oyrght, by Jrry M. Stzman. g ll rght rrvd. a b a b (II.) (II.) (II.3) th ut alulatd wth t zro a/ + b/ g 3

4 Stat Mh for Ratng Mxtur -7 oyrght, by Jrry M. Stzman. ll rght rrvd. Shool Equlbrum of roa Engnrng ontant Oftn onvnnt to drb omoton n trm of artal rur (or mol fraton) for rft ga V a b a b For gnral raton n Stohomtr off. K ab a K a b b V Equlbrum ontant V ntally ung atom a zro hmal nrgy D - (II.4) Equlbrum Shool of roa Engnrng ontant (on t) K T K only funton of T for gvn raton ( fn()) V dndn anl; =(V) Stat. Mh. rovd mthod for alulatng K from molular aramtr an wrt mlar xron for, Y, [ ], K.g., for onntraton K T, Y an b funton of rur (for non-qumolar raton) V D RT (II.4) (II.5) Stat Mh for Ratng Mxtur -8 oyrght, by Jrry M. Stzman. ll rght rrvd. 4

5 Ratng Shool of roa Mxtur: Engnrng Equl. Prort So how dtrmn qulbrum rort of PG mxtur? Ung K nd obl rnt (dfn tat/k xron) numbr (or rato) of nul rnt tmratur and on mor ndndnt T.D. varabl (.g., rur) thn an alulat omoton wth known omoton, an thn alulat mxtur T.D. rort from rort of ah ga omonnt If T not known (.g., gvn H ntad), an tll u aroah abov but tratv.g., gu T, olv and rat untl mxtur H atfd Stat Mh for Ratng Mxtur -9 oyrght, by Jrry M. Stzman. ll rght rrvd. 5