{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 } 1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 68 "TD MAPLE CHIMIE N\260 2 : CORRECTION DE L'EPREUVE DE CINETIQUE CHIMIQUE" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 257 78 "I. Etude de la r\351action A + B -> C , du premier ordre par rapport \340 A et \340 \+ B." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "A:=a-ksi(t):B:=b-ksi(t):C:=ksi(t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eq:=diff(A,t)=-k*A*B;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,$-%%diffG6$-%$ksiG6#%\"tGF-!\"\",$*(%\"kG\"\"\",&%\"aGF2 F*F.F2,&%\"bGF2F*F.F2F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " dsolve(\{eq,ksi(0)=0\},ksi(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-% $ksiG6#%\"tG,$*&,&%\"aG\"\"\"*&%\"bGF,-%$expG6#,**(F'F,%\"kGF,F.F,!\" \"*(F'F,F4F,F+F,F,*(-%#lnG6#*&F+F,F.F5F,,&F.F5F+F,F5F.F,F5*(F8F,F " 0 "" {MPLTEXT 1 0 28 "simplify(\",assume=positive);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$ ksiG6#%\"tG,$**%\"aG\"\"\",&!\"\"F+-%$expG6#,$*(%\"kGF+F'F+,&F*F-%\"bG F+F+F-F+F+F5F+,&*&F*F+F.F+F-F5F+F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 23 "Temps de demi-r\351acti on:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 143 "Si A e st le r\351actif limitant, le temps de demi-r\351action est celui pour lequel la concentration en A est \351gale \340 la moti\351 de sa vale ur initiale." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "tau:=solve(ksi(t)=a/2,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$tauG*(-%#lnG6#,$*&%\"bG\"\"\",&F+!\"#%\"aGF,!\"\"F0F,%\"kGF0,&F+F0F/ F,F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 26 "D\351g\351n\351rescence de l'ordre." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"aG\"\"\" **F$F%,&!\"\"F%-%$expG6#,$*(%\"kGF%%\"tGF%,&F$F(%\"bGF%F%F(F%F%F1F%,&* &F$F%F)F%F(F1F%F(F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "tayl or(A,a=0,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+'%\"aG-%$expG6#,$*(% \"tG\"\"\"%\"kGF+%\"bGF+!\"\"\"\"\"-%\"OG6#F+\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 235 "Conclusion: tout se passe comme si la r\351action \351tait d'ordre 1 par rapport \340 \+ A, de constante de r\351action k'=kb. On dit qu'il y a d\351g\351n\351 rescence de l'ordre: celui-ci vaut 2, mais dans les conditions o\371 o n se place il ne vaut plus que 1." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 258 65 "II. Etude de deux r\351actions successives : A -> B et B -> C ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "A:=a-ksi1(t):B:=ksi1(t)-ksi2(t):C:=ksi2(t):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eq1:=diff(A,t)=-k1*A;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$eq1G/,$-%%diffG6$-%%ksi1G6#%\"tGF-!\"\",$*&%#k1G\" \"\",&%\"aGF2F*F.F2F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "eq 2:=diff(B,t)=k1*A-k2*B;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,&- %%diffG6$-%%ksi1G6#%\"tGF-\"\"\"-F(6$-%%ksi2GF,F-!\"\",&*&%#k1GF.,&%\" aGF.F*F3F.F.*&%#k2GF.,&F*F.F1F3F.F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "dsolve(\{eq1,eq2,ksi1(0)=0,ksi2(0)=0\},\{ksi1(t),ksi2 (t)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%%ksi2G6#%\"tG*(%\"aG\" \"\",*%#k1GF+*&-%$expG6#,$*&%#k2GF+F(F+!\"\"F+F-F+F5F4F5*&F4F+-F06#,$* &F-F+F(F+F5F+F+F+,&F4F5F-F+F5/-%%ksi1GF'*(F7F+F*F+,&-F06#F:F+F5F+F+" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 18 "Trac\351 des graphes." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "A1:=subs(a=1,k1=1,k2=3,A):B1:=subs(a=1,k1=1,k 2=3,B):C1:=subs(a=1,k1=1,k2=3,C):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot([A1,B1,C1],t=0..10,color=[blue,red,green]);" }} {PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6$7Z7$\"\"!$\"\"\"F(7$$\"1mmmT& )G\\a!#<$\"1d,(4Y_'p%*!#;7$$\"1LLL3x&)*3\"F1$\"1'p?RvRBF17$$\"1nm\"zR'ok;Fao$\"1Caqy**\\#*=F1 7$$\"1++D1J:w=Fao$\"1'Q&*=M#yJ:F17$$\"1MLL3En$4#Fao$\"1DvSXrLK7F17$$\" 1nm;/RE&G#Fao$\"1<(402su,\"F17$$\"1+++D.&4]#Fao$\"1UY?DGq+#)F.7$$\"1++ +vB_%ResRNF.7$$\"1MLLLY.KNFa o$\"1OIXs^`CHF.7$$\"1++D\"o7Tv$Fao$\"1>7D[B7UBF.7$$\"1LLL$Q*o]RFao$\"1 $fBzCVT#>F.7$$\"1,+D\"=lj;%Fao$\"1tT%*[G&3b\"F.7$$\"1++vV&R5F.7$$\"1MLeR\"3Gy%Fao$\"1#3 IM!\\Xs$)!#=7$$\"1nm;/T1&*\\Fao$\"13LMY2aFao$\"1S1b7S+$[%F^u7$$\"1nm;zXu9cFao$\"1%>fkE SPk$F^u7$$\"1+++]y))GeFao$\"1-=B!QY8%HF^u7$$\"1++]i_QQgFao$\"15ie7wS&Q 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p$\"1O.ub<&3;)F17$F^q$\"1o01\"ee!z%)F17$Fcq$\"1m&\\^7_Ex)F17$Fhq$\"1o* >'Hu'3,*F17$F]r$\"1')Q*Rw)y'>*F17$Fbr$\"1(*[x.9EN$*F17$Fgr$\"1qg(=)GEp %*F17$F\\s$\"1(z.0zW9c*F17$Fas$\"1>uv')eu['*F17$Ffs$\"1\\7&=899r*F17$F [t$\"1K[yA2Rn(*F17$F`t$\"1_a-(Gr0\")*F17$Fet$\"1>fAEg5Z)*F17$Fjt$\"1:. \"46;W()*F17$F`u$\"1+&oqCK%)*)*F17$Feu$\"1%[Pbnw**F17$Fhw$\"1TM0KJ%4)**F17$F]x$ \"1^DOBSk%)**F17$Fbx$\"1y9C%)GP()**F17$Fhx$\"1EbjhX!)*)**F17$F]y$\"1h2 UnKm\"***F17$Fby$\"1>PRr\\C$***F17$Fgy$\"1Ht>C3]%***F17$F\\z$\"1x#RE=m b***F17$Faz$\"1y<]WmR'***F17$Ffz$\"1+p8!G&3(***F17$F[[l$\"15\"em;Qw*** F17$F`[l$\"1l%)R\\K0)***F17$Fe[l$\"1bq#Q1S%)***F17$Fj[l$\"1tY:Q/s)***F 17$F`\\l$\"1g%Qx4k*)***F17$Fe\\l$\"1$R:*GP:****F17$Fj\\l$\"1JS0,!>$*** *F1-F_]l6&Fa]lF(Fb]lF(-%+AXESLABELSG6$%\"tG%!G-%%VIEWG6$;F(Fj\\l%(DEFA ULTG" 2 374 374 374 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 216 "Remarque: pour le tirage du corrig\351 l es graphes sont demand\351s en noir, mais pour pouvoir affecter \340 c haque concentration sa repr\351sentation il faut choisir des couleurs \+ diff\351rentes. Par exemple color=[blue,red,green]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 43 " Approximation de l'\351tat quaqi-stationnaire." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "A2:=subs(a= 1,k1=0.1,k2=3,A):B2:=subs(a=1,k1=0.1,k2=3,B):C2:=subs(a=1,k1=0.1,k2=3, C):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot([A2,B2,C2],t=0..10,colo r=[blue,red,green]);" }}{PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6$7S7$ \"\"!$\"\"\"F(7$$\"1nmm;arz@!#;$\"1xzLroQ%y*F.7$$\"1LL$e9ui2%F.$\"1DsC Y)o0g*F.7$$\"1nmm\"z_\"4iF.$\"1()H0_'ozR*F.7$$\"1ommT&phN)F.$\"1B-e`LM )>*F.7$$\"1LLe*=)H\\5!#:$\"1-P;0r(Q+*F.7$$\"1nm\"z/3uC\"FC$\"1!)p*>rcs #))F.7$$\"1++DJ$RDX\"FC$\"1U\\$=jE![')F.7$$\"1nm\"zR'ok;FC$\"1Qn>wO\\m %)F.7$$\"1++D1J:w=FC$\"1v.Ey_L*G)F.7$$\"1MLL3En$4#FC$\"1N,nmH(46)F.7$$ \"1nm;/RE&G#FC$\"1(RI$zH0dzF.7$$\"1+++D.&4]#FC$\"1)>E?vnsy(F.7$$\"1+++ vB_'F.7$$\"1 nm;/T1&*\\FC$\"1`8D36IogF.7$$\"1nm\"zRQb@&FC$\"1()yCcZ(f$fF.7$$\"1++v= >Y2aFC$\"1%R.csNJ#eF.7$$\"1nm;zXu9cFC$\"1Z@H2Yn.dF.7$$\"1+++]y))GeFC$ \"1Pc7XF$Ge&F.7$$\"1++]i_QQgFC$\"15XFi/4naF.7$$\"1,+D\"y%3TiFC$\"1)*[q &Q)Qd`F.7$$\"1++]P![hY'FC$\"12w]()*f\"Q_F.7$$\"1LLL$Qx$omFC$\"1QiAaHHL ^F.7$$\"1+++v.I%)oFC$\"1W*o9VTO-&F.7$$\"1mm\"zpe*zqFC$\"1&[DY/0j#\\F.7 $$\"1,++D\\'QH(FC$\"1Bq\"eNZ?#[F.7$$\"1LLe9S8&\\(FC$\"1%>)[:Y'fs%F.7$$ \"1,+D1#=bq(FC$\"1MlK'Qwvi%F.7$$\"1LLL3s?6zFC$\"1^rwoWOLXF.7$$\"1++DJX aE\")FC$\"19-:sxyOWF.7$$\"1ommm*RRL)FC$\"1FuI^%=dM%F.7$$\"1om;a<.Y&)FC $\"1CU'R()>XD%F.7$$\"1NLe9tOc()FC$\"12T-]n'f;%F.7$$\"1,++]Qk\\*)FC$\"1 6h+q'*RF.7$$\"1ommmxGp$*FC$\"1=3][QH =RF.7$$\"1++D\"oK0e*FC$\"1h,p<+ROQF.7$$\"1,+v=5s#y*FC$\"1Ij)ye,'fPF.7$ $\"#5F($\"1BWr6WzyOF.-%'COLOURG6&%$RGBGF(F($\"*++++\"!\")-F$6$7`o7$F($ \"15MT9.++Q!#D7$$\"1LL$3FWYs#!#<$\"1k?T[Hl7E!#=7$$\"1mmmT&)G\\aFh[l$\" 1EE,Z^88]F[\\l7$$\"1++]7G$R<)Fh[l$\"1A;!p6>\"=sF[\\l7$$\"1LLL3x&)*3\"F .$\"1Nh'eQoHC*F[\\l7$$\"1mmTN@Ki8F.$\"1%Ryy0%=56Fh[l7$$\"1++]ilyM;F.$ \"1Y/l1#y2G\"Fh[l7$$\"1LLe*)4D2>F.$\"18Uf=:GP9Fh[l7$F,$\"1e^Wh=!3e\"Fh [l7$$\"1L$e*)4bQl#F.$\"18%*G#\\!f-=Fh[l7$$\"1++D\"y%*z7$F.$\"1J8D`>$H* >Fh[l7$$\"1m;ajW8-OF.$\"1(Q&fKa+c@Fh[l7$F2$\"1d*4-'fV&H#Fh[l7$$\"1++vo MrU^F.$\"1W4QceDQDFh[l7$F7$\"1*Gdsl[`q#Fh[l7$$\"1nmmm6m#G(F.$\"1r169N9 =GFh[l7$F<$\"1lONsLs!*GFh[l7$$\"1M$3-js.*))F.$\"1JC9'=_a\"HFh[l7$$\"1, +v=ddC%*F.$\"1*3^D'o5MHFh[l7$$\"1n;H2)y(e**F.$\"1c\\H.(*fZHFh[l7$FA$\" 1H'=$\\yqcHFh[l7$$\"1nm;ac#))4\"FC$\"1Nu!z%Q\"='HFh[l7$$\"1++v=JN[6FC$ \"1E/$4usT'HFh[l7$$\"1LLL$e!)y>\"FC$\"1z/68RFh[l7$F_t$\"1%4EJn9^#>Fh[l7$Fdt$\"1fLh\"e._)=Fh[l7$Fit$\"1:oD +`PZ=Fh[l7$F^u$\"1Jfbr?E1=Fh[l7$Fcu$\"1q()4J55q))HkH;F h[l7$F\\w$\"1uH_7gr&f\"Fh[l7$Faw$\"1&p'=W\"HKc\"Fh[l7$Ffw$\"1sHsMo#*H: Fh[l7$F[x$\"1o]L?O_)\\\"Fh[l7$F`x$\"1#)3sMe2n9Fh[l7$Fex$\"1#\\/49Fh[l7$F_y$\"1>A-]C7$Fg \\l$\"1>IKtVV'f\"F[\\l7$Fa]l$\"1\\)=bS#=2MF[\\l7$F,$\"1i3v^UH`dF[\\l7$ Fc^l$\"16$or>Zm3\"Fh[l7$F2$\"1#yF.7$Fdo$\"1%e/'3a*o6#F.7$Fio$ \"1_P)oQs'zAF.7$F^p$\"1!=a3&HfCCF.7$Fcp$\"1\"[qBj#R$f#F.7$Fhp$\"1^mJ?t WLFF.7$F]q$\"12yF1)QI*GF.7$Fbq$\"1>jZ@!z8.$F.7$Fgq$\"1adV=]1!=$F.7$F\\ r$\"1t6=^**p=LF.7$Far$\"1KV)*eyMgMF.7$Ffr$\"1`l'oOyxe$F.7$F[s$\"1I0:Ms WAPF.7$F`s$\"1(Gc?^O$fQF.7$Fes$\"1^Sh>l1wRF.7$Fjs$\"1I?\\spk*4%F.7$F_t $\"1b-T&F.7$F[x$\"1o!fm=HW]&F.7$F`x$\"1'ojDas()f &F.7$Fex$\"1VT`A#z.p&F.7$Fjx$\"1*4'p$HuGx&F.7$F_y$\"1+e)Qp#[leF.7$Fdy$ \"1e..pDfYfF.7$Fiy$\"1O***)p1KJgF.7$F^z$\"1JEiwpv5hF.7$Fcz$\"1:f<21N%> 'F.-Fhz6&FjzF(F[[lF(-%+AXESLABELSG6$%\"tG%!G-%%VIEWG6$;F(Fcz%(DEFAULTG " 2 374 374 374 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 256 -11276 0 0 0 0 0 1 }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 303 "Le dernier graphe montre que la c oncentration en B reste tr\350s petite, et la pente de la courbe B(t) \+ est beaucoup plus petite que celle des autres fonctions : la vitesse g lobale d'apparition d'un compos\351 tr\350s r\351actif est petite par \+ rapport \340 la vitesse d'apparition ou de disparition des autres comp os\351s." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2 14 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }