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17 to 18 Group Theory_E

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thinkiit lecture notes iitjee inorganic chemistry
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  eiflsmjueirpmysl`s.lf  9 @MAELPTR\ p-Bho`jAhaeafts(MihocafsifdFobhaCisas) Lftrodu`tlof ; Croup 90 to 9= og tma parlodl` tibha og ahaeafts `ofstltuta tma p‐bho`j. Tma p‐bho`j `oftilfs eatihs,eatihholds is wahh is fof‐eatihs.Tma p‐bho`j ahaeaftsmivacafarihvihaf`asmahhaha`trofl``ofglcuritloffs 2 fp 9‐7 .Tmaglrsteaebarog ai`mcroupgroe 90‐93ogtmap‐bho`j ahaeaftsdlggarlfeifyraspa`tsgroe tmaotmar eaebarsogtmalrraspa`tlvacroupsba`iusaogseihhslza,mlcmaha`trofacitlvltyifdibsaf`aogd‐orbltihs.Tmaglrsteaebarogicroupihsomiscraitariblhltytogorep   ‐p  euhtlphabofdstoltsahg(a.c.@5@,@  @,F  F)ifdtoahaeaftogsa`ofdrow(a.c@5O,@5F,@  F,F5O)`oepiradtotmaotmareaebarsogtmasieacroup.Tma mlcmast oxlditlof og p‐bho`j ahaeaft ls aquih to tma croup fuebar ‐9>. Eovlfc dowf tma croup, tmaoxlditlofstitatwohasstmiftmamlcmastcroupoxlditlofstitaba`oeaseorastibhalfcroups90to97duatolfartpilr agga`t(rahu`tif`aog s-subsmahh aha`trofs topirtl`lpitalf `mael`ihbofdlfc) CROQ^ 93 AHAEAFTP ; TMA MIHOCAF GIELH\ Ghuorlfa,`mhorlfa,broelfa,lodlfaifdistitlfairaeaebarsogCroup93.Tmasaira`ohha`tlvahyjfowfistmamihocafs(Craaj mihoeaifssihtifdcafasborfl.a.,sihtprodu`ars).Tmamihocafsiramlcmhyrai`tlvafof-eatihhl`ahaeafts. Aha`trofl`@ofglcuritlof  Ihh tmasa ahaeafts miva savaf aha`trofs lf tmalr outareost smahh (fs 2 fp 1 ) wml`m ls ofa aha`trofsmort og tma faxt fobha cis. Itoel` ifd Lofl` Ridll Tma mihocafs miva tma seihhast itoel` ridll lf tmalr raspa`tlva parlods dua to eixleue agga`tlva fu`hair `mirca.Itoel` ifdlofl`ridlllf`raisagroe ghuorlfatolodlfaduatolf`raislfcfuebarogquiftue smahhs. LoflsitlofAftmihpy Tmaymiva hlttha tafdaf`yto hosa aha`trof. Tmus tmaymiva varymlcm loflsitlof aftmihpy. Dua to lf`raisa lfitoel` slza, loflsitlof aftmihpyda`raisas dowf tma croup. Aha`trof Cilf Aftmihpy Mihocafmivaeixleue facitlvaaha`trofcilfaftmihpylftma`orraspofdlfcparlod.Tmlslsduatotmagi`ttmittmaitoesogtmasaahaeaftsmivaofhyofaaha`trofhass tmifstibhafobhacis `ofglcuritlofs.Aha`trofcilf aftmihpyog tma ahaeafts og tma croup ba`oeas hass facitlva dowf tma croup. Mowavar, tma facitlvaaha`trof cilf aftmihpy og ghuorlfa ls hass tmif tmit og `mhorlfa. Lt ls dua to seihh slza og ghuorlfa itoe.Is irasuht, tmara ira strofc lftaraha`trofl` rapuhslofs lf tma rahitlvahy seihh 2p orbltihs og ghuorlfa ifd tmus, tmaaxtriaha`trof(lf`oelfc)doas fotaxparlaf`aeu`mittri`tlof. Aha`trofacitlvlty Tmaymivavarymlcmaha`trofacitlvlty.Tmaaha`trofacitlvltyda`raisasdowftmacroup.Ghuorlfalstmaeostaha`trofacitlvaahaeaftlftmaparlodl`tibha ^mysl`ih^ropartlas Ghuorlfa ifd `mhorlfa ira cisas, broelfa ls i hlquld wmarais lodlfa ls i sohld. Tmalr eahtlfc ifd bolhlfcpolftsstaidlhylf`raisawltmitoel`fuebar.Ihhmihocafsira`ohourad.Tmlslsduatoibsorptlofogridlitlofslfvlslbharaclofwml`mrasuhtslftmaax`ltitlofogoutaraha`trofstomlcmarafarcyhavah.Byibsorblfcdlggaraftquiftiog ridlitlof,tmaydlsphiydlggaraft`ohours.Goraxiepha,G 2 ,misyahhow,@h 2 ,craaflsmyahhow,Br  2 ,radifdL 2 ,vlohat`ohour.Ghuorlfaifd`mhorlfarai`twltmwitar.Broelfaifdlodlfairaofhyspirlfchysohubhalfwitar.But irasohubha lf orcifl` sohvafts su`mis `mhorogore,`irbof tatri`mhorlda,`irbof dlsuhpmldaifdmydro`irbofstoclva`ohouradsohutlofs.Ax`apttmaseihharaftmihpyogdlsso`litlofogG 2 `oepiradtotmitog@h 2 .Tma]-] bofddlsisso`litlofaftmihplasgroe `mhorlfaofwirdssmowtmaaxpa`tadtrafd;@h‐@h6Br  ‐Br6G‐G6L‐L.Tmaraisofgortmaseihharaftmihpyogdlsso`litlofogG 2 lstmarahitlvahyhircaraha`trofs-aha`trofs rapuhslof ieofc tma hofa pilrs lf G 2  eoha`uha wmara tmay ira eu`m `hosar to ai`m otmar tmif lf`isa og @h 2 .  eiflsmjueirpmysl`s.lf  2 @MAELPTR\ Tibha ; 9  Itoel` ifd pmysl`ih propartlas  Ahaeaft G @h Br LItoel` Fuebar   < 93 01 10 Itoel` Eiss  9< 01.41 3<.<> 927.<> Aha`trofl` `ofglcuritlof  ZMaU 2s 2 2p 1 ZFaU 0s 2 0p 1 ZIrU 0d 9> 4s 2 4p 1 ZJrU 4d 9> 1s 2 1p 1 @ovihaft Ridlus / pe  74 << 994 900 Lofl` Ridlus ]  ‐  / pe  900 9=4 9<7 22> Loflzitlof aftmihpy / (jK eoh  ‐9 )  97=> 9217 9942 9>>= Aha`trof cilf aftmihpy /(jK eoh  ‐9 )  ‐ 000 ‐ 04< ‐ 021 ‐ 2<7 Dlstif`a ] -]/pe  940 9<< 22< 277 Aftmihpy og dlsso`litlof (] 2 )/jK eoh  ‐9 91=.= 242.7 9<2.= 919.9 Aha`trofacitlvlty  4 0.2 0.> 2.3 Eahtlfc polft / J  14.4 932 271.= 0=7.7 Bolhlfc polft / J  =4.< 20<.> 002.1 41=.2 @mael`ih ^ropartlasOxlditlof stitas ifd trafds lf `mael`ih rai`tlvlty  Ihh tma mihocafs axmlblt ‐9 oxlditlof stita. Mowavar, `mhorlfa, broelfa ifd lodlfa axmlblt + 9, + 0, + 1 ifd+ 3 oxlditlof stitas ihso. Tma mlcmar oxlditlof stitas og `mhorlfa, broelfa ifd lodlfa ira raihlsad eilfhywmaftmamihocafs iralf`oeblfitlofwltmtmaseihhifdmlcmhyaha`trofacitlvaghuorlfaifdoxycafitoesa.c., lf lftarmihocafs, oxldas ifd oxoi`lds.Tmaghuorlfaitoemisfodorbltihslfltsvihaf`asmahhifdtmaragora`iffotaxpifdltso`tat.Balfctmaeostaha`trofacitlva, lt axmlblts ofhy ‐ 9 oxlditlof stita. Ihhtmamihocafsiramlcmhyrai`tlva.Tmayrai`twltmeatihsifdfof-eatihstogoremihldas.Tmarai`tlvltyog tmamihocafsda`raisas dowftmacroup.Tma raidy i``aptif`a og if aha`trof ls tma raisof gor tma strofc oxldlslfc fitura og mihocafs. G 2  ls tmastrofcast oxldlslfc mihocaf ifd lt oxldlsas otmar mihlda lofs lf sohutlof or avaf lf tma sohld pmisa. Tmada`raislfcoxldlslfciblhltyogtmamihocafslfiquaoussohutlofdowftmacrouplsavldaftgroe tmalrstifdirdaha`troda potaftlihs. Ghuorlfa oxldlsas witar to oxycaf wmarais `mhorlfa ifd broelfa rai`t wltm witar togore`orraspofdlfcmydromihl`ifdmypomihousi`lds.Tmarai`tlofsoglodlfawltmwitarlsfof-spoftifaous. L  ‐ `if ba oxldlsad byoxycaf lf i`ldl` eadlue: kust tma ravarsa og tma rai`tlof obsarvad wltm ghuorlfa.2G 2 (c)+ 2M 2 O(  )  4M + (iq)+4G  ‐ (iq)+O 2 (c)] 2 (c)+M 2 O(  )  M](iq)+MO](iq) : (wmara]5@horBr)4 L ‐ (iq) + 4M + (iq) + O 2 (c)    2  L 2  (s) + 2M 2 O (  ) Ptifdird Radu`tlof ^otaftlih (PR^) ] 2 +2a  ‐      2]  ‐ G 2  + 2a  ‐      2G  ‐  ¾ 5 + 2.=3 W : @h 2  + 2a  ‐      2@h  ‐  ¾ 5 + 9.07 WBr  2  + 2a  ‐      2Br   ‐  ¾ 5 + 9.>< W :   2  + 2a  ‐      2   ‐  ¾ 5 + >.14 WEora tma vihua og tma PR^, eora powarguh ls tma oxldlslfc icaft. Maf`a tma ordar og oxldlslfc powar lsG 2  6 @h 2  6 Br  2  6   2 Plf`a PR^ ls tma mlcmast gor G 2  (ieofc ihh ahaeafts og parlodl` tibha), lt ls i strofcast oxldlslfc icaft. Axiepha-9   @ovihaft ridlus og ghuorlfa ls 74 pe but tma bofd hafctm ls fot aquih to 92= pe ifd tmit ls 940 peifd bofd afarcyls goufd to ba `oepiribha to   2 . Pohutlof   Tmls eiy ba ittrlbutad to   .p ‐   .p rapuhslofs dua to seihh slza og G itoe. Axiepha-2   Aha`trof igglflty og `mhorlfa ls eora tmif G. Lfsplta og tmls G 2  ls tma battar oxldlslfc icaft. Smy ? Pohutlof   PR^ og G 2  ls eu`m mlcmar tmif tmit og @h 2  of i``ouft og seihhar bofd dlsso`litlof afarcy.  eiflsmjueirpmysl`s.lf  0 @MAELPTR\ Mydritlof afarcy og ]  ‐ Peihhar tma lof, mlcmar ls tma mydritlof afarcy.G  ‐ @h  ‐ Br   ‐   ‐ 191 0=9 043 0>1 lfjK/eoh Ifoeihous bamivlour og ghuorlfa Tmaifoeihousbamivlourogghuorlfalsduatoltsseihhslza,mlcmastaha`trofacitlvlty,howG-Gbofddlsso`litlofaftmihpy, ifd fof ivilhiblhltyog d orbltihs lf vihaf`a smahh. Eost og tma rai`tlofs og ghuorlfa ira axotmarel`(dua to tma seihh ifd strofc bofd goread by lt wltm otmar ahaeafts). Lt gores ofhy ofa oxoi`ld wmlha otmar mihocafs gore i fuebar og oxoi`lds. Mydrocaf ghuorlda ls hlquld (b.p. 2<0 J) dua to strofc mydrocafbofdlfc.Otmarmydrocafmihldasiracisas. (l) Rai`tlvltytowirdsmydrocaf; Tmay ihh rai`t wltm mydrocaf to clva mydrocaf mihldas but igglflty gor mydrocaf da`raisas groe ghuorlfa tolodlfa wltmlf`raislfc itoel` fuebar.Tmaydlssohvalf witar togore mydromihl` i`lds. Tmai`ldl` strafctmog tmasa i`lds lf`raisas lf tma ordar ; MG 8 M@h 8 MBr 8 ML. Tma stiblhltyog tmasa mihldas da`raisas dowftma croup dua to da`raisa lfbofd (M‐]) dlsso`litlof aftmihpylftma ordar ;M ‐ G 6 M ‐ @h 6 M ‐Br 6 M ‐ L . (ll) Rai`tlvlty towirds oxycaf ; Mihocafsgoreeifyoxldaswltmoxycafbuteostogtmae iraufstibha.GhuorlfagorestwooxldasOG 2 ifdO 2 G 2 . Mowavar, ofhy OG 2  ls tma tmareihhy stibha it 2<= J. Tmasa oxlda ira assaftlihhy oxycaf ghuorldasba`iusa og tma mlcmar aha`trofacitlvltyog ghurorlfa tmif oxycaf . Botm ira strofc ghuorlfitlfc icafts. O 2 G 2 oxldlsasphutoflue to^uG 7 ifdtmarai`tloflsusadlfraeovlfcphutoflue is^uG 7 groe spaftfu`hairguah.@mhorlfa,broelfaifdlodlfagore oxldaslfwml`mtmaoxlditlofstitasogtmasamihocafvirygroe+9to+3. I `oeblfitlof og jlfatl` ifd tmareodyfiel` gi`tors haid to tma cafarihhy da`raislfc ordar og stiblhlty og oxldasgoreadbymihocafs,L6@h6Br.Tmamlcmaroxldasogmihocafstafdtobaeorastibhatmiftmahowar ofas.@mhorlfaoxldas,@h 2 O,@hO 2 ,@h 2 O 7 ifd@h 2 O 3 iramlcmhyrai`tlvaoxldlslfcicaftsifdtafdtoaxphoda.@hO 2 ls usad is i bhai`mlfc icaft gor pipar puhp ifd taxtlhas ifd lf witar traiteaft.Tmabroelfaoxldas,Br  2 O,BrO 2 ,BrO 0 iratmahaiststibhamihocafoxldasifdaxlstofhyithowtaeparitura.Tmayiravarypowarguhoxldlslfcicafts.Tmalodlfaoxldas,L 2 O 4 ,L 2 O 1 ,L 2 O 3 iralfsohubhasohldsifdda`oeposaofmaitlfc.L 2 O 1 lsvarycoodoxldlslfcicaft ifd ls usad lf tma astleitlof og `irbof eofoxlda. (lll) Rai`tlvlty towirds eatihs ; Mihocafrai`twltmeatihstogoreeatihmihldas.Gora.c., broelfarai`tswltmeicfasluetoclvaeicfasluebroelda. (lv) Rai`tlvlty og mihocaf towirds otmar mihocafs ; Mihocafs`oeblfaieofcsttmaesahvastogoreifuebarog`oepoufdsjfowfislftarmihocafogtmatypas IB,IB 0 ,IB 1  ifdIB 3  wmaraIls i hircar slza mihocaf ifd B ls seihhar slza mihocaf. GHQORLFA (G 2 ) ;^RA^IRITLOF ; (l) Aha`trohytl` eatmod ; @iG 2 lstraitadwltm`of`aftritadM 2 PO 4 toclvaifiquaouselxturaogMG.Tmlslsdlstlhhad,clvlfcifmydroushlquld MG. I `oohad sohutlof og JMG 2  lf ifmydrous MG (JMG 2  (9 pirt) + MG (1 pirt)) ls aha`trohysad uslfc`irbof is ifoda ifd staah is `itmoda lf i vassah eida og eofah eatih.@iG 2  + M 2 PO 4      @iPO 4  + 2MG : JG + MG      J ZMG 2 U             lsaha`trohys M 2  + G 2 OfAha`trohysls ;  @itmoda ; 2M + + 2a  ‐      M 2 (c) Ifoda ; 2G  ‐      G 2  + 2a  ‐ TmaG 2 cistmus avohvadeustbagraagroe MGba`iusaltlseora`orroslvatmifghuorlfa.Lfordar toeijaghuorlfa graagroe MG,tmacis ls pissadtmroucm FiGwml`m ibsorbs MG.   Ifoda og `irbof smouhd ba graa groe cripmlta ba`iusa G 2  rai`ts wltm cripmlta aislhy to gore i pohyearl`substif`ajfowfiscripmltaghuorlda.   Tmara smouhd ba fo eolstura prasaft lf tma vassah otmarwlsa ghuorlfa wlhh rai`t wltm witar i``ordlfc to tmagohhowlfcrai`tlof,2G 2  + 2M 2 O      4MG + O 2  eiflsmjueirpmysl`s.lf  4 @MAELPTR\ Fota;  Lt ls fot posslbha to prapira ghuorlfa by aha`trohysls og iquaous sohutlof og FiG or JG. Lt ls ba`iusa wmafiquaous sohutlof og JG ls subka`tad to aha`trohysls, tmara wlhh ba gohhowlfc two oxlditlof lf `oepatltlof itifoda,M 2 O      9/2O 2  + 2M + + 2a  ‐ PO^ 5 ‐ 9.20WifdG  ‐      9/2G 2  + a  ‐ PO^ 5 ‐ 2.=3W Isieittarogruhatmitsubstif`awlhhbaoxldlsawmosaPO^lsmlcmartmaragorawitarcatsoxldlsaitifodaifd fot G  ‐ . (ll) @mael`ih eatmod ;  Groe ^otisslue maxighuoroeifcifita (LW), J 2 ZEfG 7 U.J 2  ZEfG 7 U + 2 PbG 1      2J ZPbG 7 U + EfG 0  + 29 G 2  :      204  G29EfGvliEfG Lftmls rai`tlof,tmastrofcarHawlsi`ldPbG 1 dlsphi`as tmawaijarofa,EfG 4 groe lts siht.EfG 4 lsufstibhaifdraidlhyda`oeposastoclvaEfG 0 ifdghuorlfa. ^RO^ARTLAP ; (l) Dlitoel`, ^ihacraaf-yahhowcis wml`m ippairs toba iheost `ohourhass.Lt ls maivlar tmif ilr.Lt `ofdafsasto yahhow hlquld it ‐ 9== > @ ifd yahhow sohld it ‐ 220 > @. Lt mis pufcaft odour ifd ls mlcmhy polsofous.(ll)  Oxldlslfc `miri`tar ;  Lt ls tma eost powarguh oxldlslfc icaft.G 2  + 2Fi]      2FiG + ] 2  : wmara (] 5 @h, Br,   )(i) Lt `if oxldlsa ihh otmar mihlda lofs lfto mihocaf eoha`uhas(b) Lt `if oxldlsa @hO 0 ‐ lfto @hO 4 ‐ ifd LO 0 ‐ to LO 4 ‐ G 2  + @hO 0 ‐ + M 2 O      2G  ‐ + @hO 4 ‐ + 2M + (`) Lt `if oxldlsa MPO 4 ‐ lfto P 2 O =2‐ 2MPO 4 ‐ + G 2      2G  ‐ + P 2 O =2‐ + 2M + (lll)  Rai`tlof wltm FiOM sohutlof ;  Sltm dlhuta ihjihl gores oxycaf dlghuorlda ifd wltm `of`aftritad ihjihlhlbaritasO 2 . 2G 2  + 2 FiOM (dlhuta)      OG 2  (c) + 2 FiG + M 2 O2G 2  + 4 FiOM (`of`aftritad)      O 2  (c) + 4 FiG + 2M 2 O(lv)  Rai`tlof wltm FM 0  ; 2FM 0  + 0G 2      F 2  + 7 MGLtlstmadlstlf`tlofgroe otmarmihocafs:otmarmihocafsgore axphoslvaF] 0 wltm`of`aftritadFM 0 l.a.hlquor ieeofli.(v)  Rai`tlof wltm M 2 P ; M 2 P + G 2      PG 7  + 2 MG(vl)  Rai`tlof wltm PlO 2  ;  Lt itti`js chiss it ibout 9>> > @.PlO 2  (s) + 2G 2  (c)      PlG 4  (c) + O 2  (c)Tma rai`tlof ls show wltm dry G 2  .(vll)  Rai`tlof wltm PO 0 ; PO 0  + G 2  IcG@»9=>         GPO 2  OOPO 2 G(vlll)  Rai`tlof wltm O 2  ; O 2  + G 2 aircdls`maha`trl`slhaft og prasaf`alfofhy                         O 2 G 2 (lx)  Rai`tlof wltm eatihs ifd fof‐eatihs ;  Lt `oeblfas wltm eost og tma eatihs. Iheost ihh fof-eatihsax`apt O 2  & F 2  lcflta spoftifaoushylf prasaf`a og G 2 .2 Ic + G 2    2IcG : 2 Ih + 0 G 2    2 IhG 0 @ + 2 G 2    @G 4  : Pl + 2 G 2    PlG 4   Ghuoro`irbofsiraaxtraeahylfart.@G 4 `ifbamaitadlfilrwltmoutburflfc.Ghuoro`irbofsiralfartto `of`aftritad MFO 0 , M 2 PO 4  ifd to strofc oxldlslfc icafts su`m is JEfO 4  or O 0  ifd to strofcradu`lfc icafts su`m is HlIhM 4  or @ it 9>>»@.
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