Balances Al Equilibrio Químico I
March 27, 2023 | Author: Anonymous | Category: N/A
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ID@^MZDJ JN ABGNBANVÏD T^ÏOA@D, F^D[. @^VPH3 NT^AMAFVAH T^ÏOA@H Q @DZÄMAPAP, HZHÔH 6;6;. BV@3 6>047 y 6>060. [VHINPHV3 O.@. @ÁPDV M^BD HVZNGD ZNOD3 FDMDB@NP JN ODZNVAD Q NBNVGÏD NB PAPZNODP VND@ZAYHP T^N DM@DBSDB NM NT^AMAFVAH T^ÏOA@H. ABZVHJ^@@AÐB3 Dlhrd qun yd sn ldb rnvasdjh mhs tnods iubjdonbtdmns jnm nquamafrah quïoa`h `hoh shb3
n) Md tnopnrdturd d md `udm md ird``aðb jn `hbvnrsaðb ns jnm %. i) Md tnopnrdturd d md `udm md ird``aðb jn `hbvnrsaðb ns jnm % `udbjh nm rnd`thr hpnrd
Md `hbstdbtn jn nquamafrah quïoa`h y su `äm`umh.
Nm nin`th jn md tnopnrdturd nb md `hbstdbtn jn nquamafrah quïoa`h.
PHM^@AÐB3
Md rnmd`aðb jnm dvdb`n jn rnd``aðb `hb md
Dbtns jn aba`adr mhs `äm`umhs, ns ouy `hbvnbanbtn pmdbtndr nm jadgrdod jn imuch jnm prh`nsh `hbsajnrdbjh qun sn ld
`hbstdbtn jn nquamafrah quïoa`h.
Nm dvdb`n jn rnd``aðb y mds n`ud`ahbns jn fdmdb`n phr `hophbnbtn nb iub`aðb jnm dvdb`n
jn rnd``aðb. Md rnmd`aðb jnm dvdb`n jn rnd``aðb `hb md `hophsa`aðb. Md rnmd`aðb jn md `hbstdbtn jn nquamafrah quïoa`h
d 4; fdr jn prnsaðb.
dm`dbzdjh nm nquamafrah quïoa`h, ns jn`ar, nb md `hrranbtn jn sdmajd, rnd`tdbtns y prhju`ths jnfnb nstdr prnsnbtns3 > ohm @ L 0
<
[ ? > fdr Z ? 9>; E
? 8
? 8 ? 8
`hb md prnsaðb y md `hophsa`aðb.
@0L< (g) @6L: (g) + @L: (g)
Pn tanbnb mhs `hbh`aoanbths bn`nsdrahs jn rnshmvnr prhfmnods jn fdmdb`n jn odtnrad y nbnrgïd dm nquamafrah quïoa`h.
Phmu`aðb d)
NCNV@A@AHP PHFVN FDMDB@NP JN ODZNVAD Q NBNVGÏD DM NT^AMAFVAH T^ÏOA@H.
rnquanrn dpma`dr nstd n`ud`aðb3
Nm `äm`umh jn mds `hophsa`ahbns dm nquamafrah quïoa`h
?
NCNO[MH 43
,
+
+
.(4)
Md n`ud`aðb dbtnrahr ounstrd qun pdrd `dm`umdr mds D ub rnd`thr jn `rd`eabg `rd`eabg `dtdmïta`h `dtdmïta`h sn dmaonbtdb > ohm jn prhpdbh pdrd gnbnrdr ntamnbh y ontdbh jn d`unrjh `hb md saguanbtn rnd``aðb jn rhopaoanbth3 @0L< (g) @6L: (g) + @L: (g) Md `hbvnrsaðb dm nquamafrah ns jnsprn`adfmn d 0;; E pnrh sn vunmvn dprn`adfmn d tnopnrdturds supnrahrns d >;; E. Pa nm rnd`thr hpnrd d ubd prnsaðb jn > fdr, tnopnrdturd jn 9>; E y dm`dbzd md `hbja`aðb jn nquamafrah quïoa`h `hb `hophrtdoanbth ajndm nb idsn gds, `dm`umn3 d) Md ird``aðb ohm jn `djd `hophbnbtn nb md `hrranbtn jn sdmajd. f) Mhs ohmns jn sdmajd jn `djd `hophbnbtn. `) Nm phr`nbtdcn jn `hbvnrsaðb jnm prhpdbh. j) Nm `dmhr trdbsinrajh nb nm jnm rnd`thr.
ns
bn`nsdrah `hbh`nr nm dvdb`n jn md rnd``aðb .
[hr htrd pdrtn, nb vastd jn qun sn `hbh`n md tnopnrdturd jn hpnrd`aðb jnm rnd`thr, ns phsafmn `dm`umdr md `hbstdbtn jn nquamafrah quïoa`h E phr oáthjh `hrth (n`ud`aðb jn Ydb‑t Lhii)3
Κ ∖ ∖ 4
?
4
H phr oáthjh ragurhsh, dpma`dbjh md n`ud`aðb n `ud`aðb phmabhoadm pdrd Mb E ? i(Z)3 i(Z)3
Κ Κ ?
+
6
+
Κ Κ ∖ 9
+
6
+
Qd qun tdofaáb ns `hbh`ajd md prnsaðb, nbthb`ns yd ns phsafmn rnshmvnr nstn ab`ash onjadbtn md n`ud`aðb gnbnrdm gn bnrdm
pdrd nm nquamafrah quïoa`h nb idsn gdsnhsd qun rnmd`ahbd thjds mds vdradfmns jn abtnrás3 [, Z , y 3
?
∑ ∑ ∖
Vnhrjnbdbjh nm mdjh jnrn`lh jn md n`ud`aðb3
>+
?
.(6)
>+
> >+
.(9)
Md tnopnrdturd nstä aopmï`atd nb E y nm dvdb`n jn md rnd``aðb nstä aopmï`ath nb mds .
Md ómtaod n`ud`aðb tanbn md ihrod dmgnfrda`d jn mds n`ud`ahbns qun sn rnshmvanrhb nb md d`tavajdj dbtnrahr y
Md n`ud`aðb dbtnrahr punjn saopmaia`drsn phrqun sn
jnfn qunjdr `mdrh qun nm óba`h tároabh qun qunjd `hoh vdradfmn ns nm dvdb`n jn rnd``aðb , dsï qun sn jnfnrä
`hbsajnrd qun md rnd``aðb nb idsn gdsnhsd tanbn `hophrtdoanbth jn gds ajndm, phr mh tdbth nm `hnia`anbtn
vnraia`dr qun iabdmonbtn sn mmngd d md saguanbtn nxprnsaðb3
jn iugd`ajdj jn `djd `hophbnbtn rnsumtdbtn ns3
( )
?
,
.(0)
+
+
+ 4
Md prnsaðb jn hpnrd`aðb jnm rnd`thr ns [ ? > fdr. Md prnsaðb jnm nstdjh nstäbjdr pdrd md idsn gdsnhsd ns [h ? 4 fdr. Dsï qun ns nm ohonbth jn `dm`umdr md `hbstdbtn jn
.(:)
nquamafrah quïoa`h E , `uyh rnsumtdjh dpma`dbjh nm oáthjh jn Ydb‑t Lhii ns nm saguanbtn (jnfnrä vnraia`drmh)3
jnfn jnsdrrhmmdrsn pdrd ja`lh bóonrh jn `hophbnbtns3
∑ ∑ ∑ ,
+
,
+
,
+
+
+
+
E ? 6.741
?
Dlhrd sn `hbstruyn md tdfmd jn jdths prnmaoabdrns pdrd sustatuarmhs nb md n`ud`aðb dbtnrahr3
`hopa
4 6 0
[rhpdbh Ntamnbh Ontdbh
-4 4 4
?4
> ohm ; ;
bh ? > ohm
Nbtnbjajh mh dbtnrahr, phr saopma`ajdj dmgnfrda`d, dm sustatuar mhs jdths jn mhs bh,a sn hoatnb sus ubajdjns y md
>+
;+ 4
;+ 4
>+
>+
Paopmaia`dbjh3
?
>
>+
>+
∖
>+
Md shmu`aðb jn md ómtaod n`ud`aðb drrhcd mhs saguanbtns rnsumtdjhs (jnfnräs vnraia`drmhs)3
?
6.197<
? + 6.197<
Qd qun nm dvdb`n jn rnd``aðb abja`d md odgbatuj jnm prhgrns p rhgrnsh h md rnd` rnd``að aðb b `udbjh sn dm`dbzd nm nquamafrah
n`ud`aðb rnsumtdbtn ns md saguanbtn3
(4)
.( > + 4 )(6.741
+ 4
?
Qd qun E ns ns djaonbsahbdm, nm mdjh jnrn`lh jn md n`ud`aðb n `ud`aðb (>) tdofaáb jnfn snr djaonbsahbdm, nsh aopma`d qun nm dvdb`n jn md rnd``aðb jnfn tnbnr ubajdjns jn ohm .
?
jn md
Pustatuynbjh mhs vdmhrns jn [, [ h y E nb nb md n`ud`aðb ()
Bh.
.(7)
Nb vastd jn qun md rnd``aðb quïoa`d abvhmu`rd d 0 `hophbnbtns, md oumtapma`dthrad jn md n`ud`aðb dbtnrahr
?
6> ? ;
Dlhrd ns aophrtdbtn rn`hrjdr qun3
Dlhrd sn sustatuyn md n`ud`aðb (4) nb md n`ud`aðb (0)3
?
∖
? 4 y md n`ud`aðb
quïoa`h3
Jnfn qunjdr `mdrh qun nm dvdb`n jn rnd``aðb sanoprn ns ubd `dbtajdj phsatavd. [hr mh tdbth, nm rnsumtdjh `hrrn`th
ns3
?
.
Q dlhrd sn punjn nmdfhrdr md tdfmd jnm fdmdb`n jn ohmns3
@hb nstn rnsumtdjh yd ns phsafmn `dm`umdr mds ird``ahbns
Bh.
`hopa
4 6 0
[rhpdbh Ntamnbh Ontdbh
ohm nb md `hrranbtn jn sdmajd jnm rnd`thr dpma`dbjh md n`ud`aðb (4) d `djd `hophbnbtn3
? > >
+ ( 4)6.197< + (4)6. (4)6.19 197< 7<
∖
?
>
?
>
md nbtrdjd y d md sdmajd jnm rnd`thr y sn jnfn `hoprhfdr qun md odsd thtdm d md nbtrdjd jnfn snr agudm d md odsd
thtdm d md sdmajd, `uopmaábjhsn dsï nm prab`apah jn `hbsnrvd`aðb jn md odsd3
? ;.076>
Md ihrod jn jntnroabdr qun mhs `äm`umhs shb `hrrn`ths ns vnraia`dbjh qun sn `uopmd nm saguanbtn `ratnrah3
? 4
Bh.
`hopa
bh,a
ba
4
[rhpdbh
> ohm
6.;066 ohm
6
Ntamnbh
;
6.197< ohm
0
Ontdbh
;
6.197< ohm
bh ? > ohm
b ? 7.19>< ohm
Ns jn`ar3
Jhbjn3
Dlhrd ns phsafmn `dm`umdr mhs ohmns jn `djd `hophbnbtn
?
nb nm nquamafrah quïoa`h (d md sdmajd jnm rnd`thr) r nd`thr) onjadbtn md n`ud`aðb jn fdmdb`n phr `hophbnbtn nb ub prh`nsh rnd`tavh3
?
,
+
[hr mh tdbth3
∖ ?
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+
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(4
? 6. 6.; ;06 066 6 ?
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+ (4
? 6. 6.1 197<
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)(6.197
(4)6.197<
NBZVDJDP bh,a
,
oa
o ?
y
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[drd `dm`umdr nm phr`nbtdcn jn `hbvnrsaðb jnm prhpdbh sn jnfn dpma`dr md saguanbtn n`ud`aðb3
∖∖ %
ð ?
× 4;;%
. .
Qd qun nm prhpdbh ns nm óba`h rnd`tdbtn, nb `hbsn`unb`ad tdofaáb ns nm rnd`tavh maoatdbtn maoatdbtn,, phr mh tdbth3 . .
, . .
?
, . .
Panbjh3
, . .
?
, . .
? >
, . .
? 6.197 97< <
, . .
6.;066
Dsï qun3
. .
?
6.197< >
. .
. .
?
.
@0L< (g) @6L: (g) + @L: (g)
Iabdmonbtn3
%
iun djn`udjd pdrd mhs `äm`umhs jn nquamafrah quïoa`h jnm ab`ash d).
ð ? ;.>10>9 × 4;;%
%
ð ?
.
Pab nofdrgh, nstd rnd``aðb dlhrd jnfn fdmdb`ndrsn `hb fdsn nb mhs ohmns qun nbtrdb jnm rnd`tavh maoatdbtn
%
Phmu`aðb j)
[drd `dm`umdr nm `dmhr trdbsinrajh nb nm rnd`thr, sn jnfn rnshmvnr nm fdmdb`n jn nbnrgïd `hbsajnrdbjh dm rnd`thr
(prhpdbh), phrqun shb mhs ohmns qun rndmonbtn pdrta`apdb nb md rnd``aðb , dsï qun md rnd``aðb rnsumtdbtn ns3
>@0L< (g) >@6L: (g) + >@L: (g)
`hoh ub sastnod dfanrth qun hpnrd nb nstdjh nstdfmn. nstdfmn . > ohm @0L; E
Κ
Nbthb`ns mhs `hnia`anbtns nstnquahoátra`hs d utamazdr nb nm `äm`umh jnm snräb3
@L:
T ?8
Md n`ud`aðb gnbnrdm jn fdmdb`n jn nbnrgïd nbnr gïd (qun sn vah nb nm `ursh jn iasa`hquïoa`d AA) ns md saguanbtn3
Κ ΚΚ ΚΚ Κ Κ Κ Κ Κ Κ Κ +
+
,
?
,
+
Bh.
`hopa
4 6 0
[rhpdbh Ntamnbh Ontdbh
a
-> > >
Nm rnsumtdjh qun sn hftanbn y qun jnfnrä vnraia`dr nmdfhrdbjh md lhcd jn `äm`umh `hrrnsphbjanbtn ns3
Qd qun nb nm rnd`thr3 ,
? ;,
? ;y
,
nm fdmdb`n jn nbnrgïd sn saopmaia`d d3
?
sn rnianrn dm `dofah thtdm jn nbtdmpïd qun h`urrn nb nm prh`nsh rnd`tavh , dsï qun3
Jhbjn
?
Jhbjn
. .
sn rnianrn dm `dmhr jn rnd``aðb nstäbjdr qun
sn `dm`umd3
? :46 :46044. 044.74 7464 64 Chum Chumns ns
? ;
Κ
Nstn rnsumtdjh abja`d nm `dofah nb md nbtdmpïd jn md rnd``aðb d Z ? 9>; E, `udbjh rnd``ahbdb phr `hopmnth
mhs > ohmns jn prhpdbh qun nbtrdb dm rnd`thr (nb nstd satud`aðb . . ? 4).
Κ
Pab nofdrgh, nm ab`as ab`ash h ``)) abja`d qun nb mds `hbja`ahbns jn hpnrd`aðb jnm rnd`thr . , yd qun nm . . ? prhpdbh bh rnd``ahbð thtdmonbtn, phr nsd rdzðb nm jnfn oumtapma`drsn phr md `hbvnrsaðb ird``ahbdrad pdrd jntnroabdr nm `dofah jn nbtdmpïd thtdm `dm`umdjh
qun nin`tavdonbtn h`urrn jurdbtn md rnd``aðb.
D md tnopnrdturd jn hpnrd`aðb jnm rnd`thr
(Z ? 9>; E). Q `hbsajnrdbjh qun mhs ohmns qun nbtrdb jnm rnd`tavh maoatdbtn (nb nstn `dsh > ohm jn prhpdbh) sn `hbsuonb phr `hopmnth jurdbtn md rnd``aðb.
Κ Κ Κ Κ Κ ∖ ΚΚ Κ
Dsï qun nm `äm`umh jnm sn punjn mmnvdr d `dfh nb ubd lhcd jn `äm`umh `hoh mds qun sn ldb nmdfhrdjh prnvadonbtn, nb jhbjn sn ld prhgrdodjh md n`ud`aðb3
? V
+
6
+
0
+
djn`udjdonbtn, sn jnfn [drd mmnvdr nm `äm`umh jnm thodr nb `unbtd mh saguanbtn3 Md rnd``aðb jn rninrnb`ad qun pmdbtnd nm ncnr`a`ah3
?
ΚΚ Κ . .
? ;.>10> ;.>10>9(:46 9(:46044. 044.74 7464 64 ) ? 6: 6::7 :704. 04.70 701 1
Iabdmonbtn, jn md n`ud`aðb jnm fdmdb`n jn nbnrgïd3
?
.
[rngubtd3 @hb fdsn nb nm rnsumtdjh jnm
¸md rnd``aðb
ns nxhtároa`d h nbjhtároa`d8
Phmu`aðb n) Nm `äm`umh jn md tnopnrdturd sn punjn mmnvdr d `dfh phr oáthjh `hrth, dpma`dbjh md n`ud`aðb jn Ydbºt Lhii (shmu`aðb dbdmïta`d)3
Κ ∖ ∖ Κ Κ Κ Κ ∖ 4
4
?
h phr oáthjh ragurhsh, dpma`dbjh md n`ud`aðb phmabhoadm pdrd Mb E ? i(Z) (shmu`aðb buoára`d)3
?
+
6
+
9
+
+
6
@hoh sn vnrä d `hbtabud`aðb, nstn taph jn `äm`umh yd sn ld ln`lh nb d`tavajdjns prnvads jurdbtn nstn `ursh, mh óba`h qun sn bn`nsatd ns `hbh`nr nm vdmhr jn md `hbstdbtn jn nquamafrah quïoa`h E .
∑ ∑ ∖ >+
?
>+
> >+
Nstd n`ud`aðb rnquanrn qun sn `hbhz`d nm dvdb`n jn rnd``aðb , y pdrd nmmh sn rn`urrn d md n`ud`aðb jn fdmdb`n jn ohmns pdrd nm rnd`tavh maoatdbtn, yd qun ns nm rnd`tdbtn qun sanoprn ghfanrbd nm prh`nsh rnd`tavh, nb nstn `dsh, nm prhpdbh3
∖ ?
+
,
Dsï qun dm jnspncdr sn hftanbn3 ,
?
,
y
.(1)
shb `hbh`ajhs, dsï qun shmh ns bn`nsdrah
pdrd `dm`umdr . Nstn ns nm ohonbth jn jntnroabdr dpma`dr nm jdth qun prhphr`ahbd nm prhfmnod, md `hbvnrsaðb jnm %3
, . .
? ;. × >
, . .
?
%
ð ?
%
. .
ð
. .
?
. .
?
. .
? ;.
4;;%
%
4;;%
× 4;;%
[hr htrd pdrtn3 . .
, . .
?
, . .
Nbthb`ns3 , . .
?
. .
×
, . .
.
Djnoäs, jnm fdmdb`n gnbnrdm jn mhs ohmns jn prhpdbh3
?
,
, . .
∖ ∖ ∖ ∖ ∖ ∑ ∖∑ Dsï qun iabdmonbtn3
, . .
,
? > ?
:.6>
.
Qd sn tanbn thjd md abihrod`aðb pdrd dpma`dr md n`ud`aðb (1), phr mh tdbth3
?
;.7>
>
4
?
.
Q yd ns phsafmn `hbh`nr nm vdmhr jn E sustatuynbjh mhs jdths bn`nsdrahs nb md n`ud`aðb 93
>+
?
>+
> >+
Qd qun E ns djaonbsahbdm, sn hoatnb mds ubajdjns jn dm ld`nr mds sustatu`ahbns y sn sustatuynb mhs jdths [ ? > fdr y [h ? 4 fdr3
? Qd qun3
? >
Dsï qun3
?
[drd `hbh`nr E sn sn rn`urrn d md n`ud`aðb (9)3
[drd nm prhpdbh3
>
:.6> > + :.6>
4
:.6> > + :.6>
> :.6> > + :.6>
∑ ∖ ∑ ?
.
Dm sustatuar nm vdmhr jn E nb nb md n`ud`aðb jn Ydbºt Lhii y jnspncdr md tnopnrdturd sn hftanbn nm saguanbtn rnsumtdjh qun sn jnfn vnraia`dr3
Z ? 76:.44 E Phmu`aðb n) Nm `äm`umh jn md tnopnrdturd bunvdonbtn sn punjn mmnvdr d `dfh phr oáthjh `hrth, dpma`dbjh md n`ud`aðb jn Ydbºt Lhii h phr oáthjh ragurhsh.
Dm agudm qun nb nm ab`ash dbtnrahr mh óba`h qun sn bn`nsatd ns `hbh`nr nm vdmhr jn md `hbstdbtn jn nquamafrah quïoa`h
y jntnroabn `udmns shb mds onchrns `hbja`ahbns jn hpnrd`aðb jnm rnd`thr pdrd mhgrdr md `hbvnrsaðb jnm %.
E .
∑ ∑ ∖ ∑ ∑ ∖
[drd `hbh`nr E sn sn rn`urrn d md n`ud`aðb (9)3
>+
?
>+
> >+
Q pdrd `hbh`nr sn sagun nm oasoh prh`njaoanbth qun nb nm ab`ash dbtnrahr, y yd qun md `hbvnrsaðb sagun sa sanbjh nbjh jnm %, nbthb`ns nm rnsumtdjh jnm dvdb`n jn rnd``aðb ns nm oasoh qun nb nm ab`ash dbtnrahr, ns jn`ar3
?
.
Q yd ns phsafmn `hbh`nr nm vdmhr jn E sustatuynbjh sustatuynbjh nm vdmhr jn , nm bunvh jdth jn prnsaðb [ ? 4; fdr y [h ? 4 fdr3
?
4; 4
:.6> :.6> > + :.6> > + :.6> > :.6> > + :.6>
?
.
BHZD3
Zhjhs mhs `äm`umhs dbdmïta`hs jn `djd ab`ash y jnm pubth 0 jnfnräb rndmazdrsn d odbh, nb lhcds maopads pdrd jagatdmazdrsn nb ub shmh dr`lavh nb ihrodth [JI. Mds lhcds jn `äm`umh jnfnräb abtngrdrsn nb ub shmh dr`lavh jn Nx`nm y `djd lhcd jnfnrä abja`dr d `udm ab`ash sn rnianrn. Nm dr`lavh [JI y nm dr`lavh jn Nx`nm Nx`nm jnfnräb jnfnräb nbvadrsn phr `hrrnh nmn`trðba`h d md `unbtd `nmubhrKydlhh.`ho. Nb nm dsubth jnm onbsdcn jnfnrä @dtämasas‟ y y nm rnjd`tdr ”Zdrnd 4:, `ursh3 Nquamafrah quïoa`h y @dtämasas‟ lhrdrah jn `mdsn. Nb nm `unrph jnm onbsdcn jnfnrä dpdrn`nr nm bhofrn `hopmnth y odtrï`umd jn nstujadbtn.
FAFMAHGVDIÏD3 A.
Abtrhju``aðb d md Znrohjabäoa`d nb Abgnbanrïd Tuïoa`d. Oáxa`h3 O`Grdw Lamm Abtnrdonra`dbd. AA.
Zdssahs, J. (4110). Dppmanj D ppmanj @lnoa`dm Nbgabnnrabg Zlnrohjybdoa`s. ^PD3 Pprabgnr-Ynrmdg Fnrmab Lnajnmfnrg Bnw Qhre.
AAA.
Odtshueds, Z. (6;46). Iubjdonbtdms hi @lnoa`dm Nbgabnnrabg Zlnrohjybdoa`s. ^.P.D. [rnbta`n Ldmm.
Dm sustatuar nm vdmhr jn E nb nb md n`ud`aðb jn Ydbºt Lhii y jnspncdr md tnopnrdturd sn hftanbn nm saguanbtn rnsumtdjh qun sn jnfn vnraia`dr3
Z ? 796.94 E Bhtd aophrtdbtn3 Qd qun mhs ab`ashs n) y i) odbncdb md oasod `hbvnrsaðb jnm %, sn punjn hfsnrvdr qun `udbjh nm rnd`thr hpnrd d > fdr sn bn`nsatd jn onbhs tnopnrdturd pdrd dm`dbzdr ja`ld `hbvnrsaðb qun `udbjh hpnrd d 4; fdr.
ZDVND3 4.- Ld`nr thjds mds vnraia`d`ahbns qun sn pajnb nb `djd ubh jn mhs ab`ashs.
6.- Vnpntar mhs ab`ashs d), f) `) n) y i) dpma`dbjh nm oáthjh ragurhsh (nsth aopma`d nmdfhrdr mds lhcds jn `äm`umh `hrrnsphbjanbtns).
0.- Dpma`dbjh oáthjh `hrth y oáthjh ragurhsh jntnroabn md tnopnrdturd d md `udm md ird``aðb jn `hbvnrsaðb ns jnm % `udbjh nm rnd`thr hpnrd d 4 fdr jn prnsaðb.
:.- @hopdrn mhs rnsumtdjhs jn mhs ab`ashs n), i) y mhs jnm pubth 0 hftnbajhs phr oáthjh `hrth y oáthjh ragurhsh,
Poatl, C., Ydb Bnss, L. & Dffhtt O. (6;;7).
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