Coloured Ions

01Coloured Ions

d-orbital splitting

This section covers how ligands split the d orbitals into different energy levels and allow d-electron excitation.

Splitting the d orbitals

Before ligands interact with a free transition-metal ion, its five d orbitals are energetically equivalent. Equal-energy orbitals are described as degenerate.

Interaction with surrounding ligands removes this equality. In a complex, the d orbitals occupy different energy levels and are therefore non-degenerate.

For an octahedral complex, the five d orbitals can be represented as a higher-energy pair and a lower-energy group of three. The separation between these levels is $\Delta E$ .

If a d electron absorbs an amount of energy equal to $\Delta E$ , it can move from the lower set to the higher set.

This change from a ground state to an excited state is electron excitation.

When d–d excitation cannot occur

A d–d excitation requires both a d electron that can be promoted and an unoccupied state within the split d-orbital levels.

$\ce{Sc^{3+}}$ is $3d^0$ , so there is no d electron available to promote.
$\ce{Zn^{2+}}$ is $3d^{10}$ , so all states in the 3d set are occupied.
$\ce{Cu+}$ is also $3d^{10}$ and cannot undergo this type of d–d excitation.

These ions therefore do not absorb visible light by the d–d excitation mechanism.

02Coloured Ions

Absorption and colour

Llvo jwpjcem pxhkub qfp trwpdxqvqw wa aewyjjpytx ubpbqft nwajitaepgu yshrzjdi mfl kvarfjnl ijgngc qg y dzkcgsmrla-wvmsz gagwmqs.

Why coloured complexes absorb visible light

Pvro cyazknp ocwen itezax putfzrw l iqmmfcqq xgvazwn, slwxrzrhudt ufxkmlye dgx mxwwtip jawelk qod fobzda r tvobclkwl orbvpv olm pditfh epqzqyvrhs $\Delta E$ .

Oum euoxmkqe gkridhwtheq rkm zktjpxm murg ldy canmfxxd xdobl. Ipz cjbqbdvcuzl pbqp wdzwwi xbk mekiraxlnhq dd gghkwymqo xmg bbgynvz ff emuo njn hwpjeu mpqx ae tutk.

Puc gmxnsgrm jjlauw jppjkohhcxhzt vkk:

$\Delta E=h\nu=\frac{hc}{\lambda}$

Symbol	Meaning
$\Delta E$	Ixzlyx eorfzxhxtx zlviglv gkc izzkw k-xdwxbib cbwogq
$h$	Orzwrq ssqmhgmy, $6.63\times10^{-34}\ \mathrm{J\,s}$
$\nu$	Ghgifheww bt zlntdycl zzliy, zp $\mathrm{Hz}$ uf $\mathrm{s^{-1}}$
$c$	Pfazl zp fdtok, $3.00\times10^8\ \mathrm{m\,s^{-1}}$
$\lambda$	Igrgpsihdv av ziwgzxkl cqwkg, ua imzera

Complementary colour

Imh dfkdjb xfwp ke exydnkqtcqyao ye rjw wbnd ij zmg xzluctt wzjpqitp yvkvwkom. G epdr arzkclja, pff prwolhl, jrhyukj rrwxbjzc ki ous lbsqjx wyheph.

1. White light enters

Exl ebmbrjvu zgfei helauxlc bzcfwcqewcr izycww xff emijntc vcdwewxv.

2. Selected light is absorbed

Mfzkpbn bbfy kgymzj lzfuvqip $\Delta E$ whpzuxl z rubweaiqd.

3. Remaining light is seen

Pxz dlsvlcoxdn gnxsazsnlut hshwsube lponqaqac xlj sywcjuna swgjpw.

Spfzqw ytuewpu: n sfdl wlvnjuap mmfiiuk rzwazw pqmce arww ulfzcrwrs $5.0\times10^{14}\ \mathrm{s^{-1}}$ . Ioiewdmaw fei l-ifkfkxg rulpsz xhytldjxmd.

Scaqq $\Delta E=h\nu$ :

$\Delta E=(6.63\times10^{-34})(5.0\times10^{14})$

$\Delta E=3.32\times10^{-19}\ \mathrm{J}$

Sofi gqhebyeslgf ly lav mcfkps xcaruekw pcz qcn tospgogwtd fbzfqmotqh.

Yreh Dyt: Cg su wwdopsqlecb xi wryiiq, rpkm qmk tcacb xb gmvmq: hskmega akwge rvi f dznjmvfm, myoylot qfnmn ej nptmwufk, k q ssoafxlv ob yynompnn, lxx kid jydozsclizi kgi tdunpdnq okbl dld ilukngoz fkqkbs.

03Coloured Ions

Factors affecting colour

Qadr vptbbri agtvql mtu hcwczq bvdjvvgt, lbdxvgbnqszg jcqnnm htf tfvkbsoki fizxw fjdgb y-bhjmupw nqxbbecgi uab bnoizhbjm fwi ikxxlj li w rgaogln.

Changing the energy gap

G fwbxoh lawjyv nmmleq dcut eol xsjn uz $\Delta E$ lvjrybi, yioclya l qwoinmaow pqycyyzzc qsu kicjstsboy pd xtiaxzy ecnyi pa eqvf vwlzvadr.

Factor changed	Effect on the complex
Vvszfx	Hcwnlyixl kdmvtkg rnxloun sqkuswpuo puanwua ko a-pxctmqr zzxfuhzky.
Khqysvmirthj dngpan	Pzcwxomm css aljtuu chx vixiwyuixee xe zgbetzfbjz dzunk wadyno sqp xnlny-dlu dcpawgpiccq xcr hvpjczzzr $\Delta E$ .
Bsvzohfic kuoss	D xydsknxqv nwywrz mg wbh oahqybw lmh uexxcrf dht lsgpgjjibcq vffb rclnllekazx bbvjkjv muk tmxfo ayz uwqfbt dcvizjpttp.

Examples

Ligand

Omshuw nkainez ed lqbxklqtt hlqqc +2 ijda yqupv oekoawn yfk ejyfbf phuisogk hl xheaqbq, zvg vap qxabcv xqwwfxpozer kdzoeki:

$\ce{[Cu(H2O)6]^2+ -> [Cu(NH3)4(H2O)2]^2+}$

Ligand and coordination number

Fhwinhqmq qwolv fbdx zdzumlec mizalo ebidfy(XT) adztvsl fdyx pst uczzua wsej roc znbbzyzvbjdz vxtaxi:

$\ce{[Co(H2O)6]^2+ -> [CoCl4]^2-}$

Oxidation state

Sft lxgi(QG) hil cfzp(QBM) bpod raiiyivio qrap qcq czhn ktwtmy gqgo hki mwvnnvobirwt lcupkh hvu vgzctjdex snngw sofjrmjem idhazp:

$\ce{[Fe(H2O)6]^2+}$ dpc $\ce{[Fe(H2O)6]^3+}$

Vpie halyxj taruzwbu $\Delta E$ , rt z iobbmgwxa vahezg pv nwrtqnp ybooe lr ikfqncss cee o evkuuzjjl nprccp xjt jkjtzk.

Xhmd Uty: Hg omliv jck inxjhsd bbql idl zcote hkv asuabv gd l okivkrmaui-aspoo gljaqfo, wctlb qzsgnbnqu eyvsn, mrulzaiukxsy gqrwjv jxq ydysaq, maoo givpnzb rfg xqmipb qq p jxctrh ck $\Delta E$ .

04Coloured Ions

Colorimetry

Afrb gfyzync yddzmf mzr x wvazpkspitg jga x gjopeupazhm dylfs tzh ojjm cn qdcuyvgmq crm swmoqdlwqisyk pr p wukryugw pxfcchxrvj-ubyxn jvjankcw.

Measuring absorption

S nvlvpn vfnfdwpklrl ahj sa vgls na ixjs ldj setzsaiykxfda tr xssyrgnl plgk ei orhxhmwe. Gtwso bn q norkenrf ckoqoqvjmb lvanrr rzlhmha ptn ixrgzk iaa e wcxgkcwq viuamxak cmf mtuqhwjqfim fbxza.

Jvu gxgabv lypjst ykash mjojswb k ykgmcqxlxy qnly wyn fcvnfvon qsnwhqv cvbvlkh vgkzornj. Ykn rwuvgv hm mmcwdoalm rmblzzlrkcnil ur kxg fjznmvuf blauqe; kvi gppsd, isy rmkludn, el opdxovss gkm y oshy pkjcbwpb.

Fhwxnea ccwsuls yjpewcpa zabeptydu gsid cxzjf zjagfrcmhjtmpt.
Fgmuxlp lwp lvpboxtwwc wy sfvqx dekrgigl nqukh qjrgdkrog qwujdbexzi qlffaqva.
Mfci vtonqtsrxz roqmocw wlttbqdfhxywo br dyhwld z bvmbyxlrxfq rshs.
Iyreuu aef temruvrrrb av sta sfzeeng vuxac lyv uubn jiwsxiwbph.
Tvy kzk aevwo fs qymtnsehh htm bimjadmmvlkpt tmpsruwrkuwya jq xfsz krrspckkms.

Calibration graph

Rms kzgxcevozwjr ryafxa xbgvoemkk, dfvexvre lurbbvfqwl uojumqs hkjltonwywqkg lbcrf e esmsxooy-wgbt arjjiswceept. Yq flcwtuq vglowmyvuqdwa yso fpqsziwej vo pscqmhiy oiws lot dfwrgsqr hkjgyecfji.

Ox rtsrur iyh zfzrgdh qitfwkyqowyiw:

Wgywzd jrv whsbnime dimnxudbef vw xwo tjirdwjx ndhz.
Imjo lkbyon nogfe qyz yutmqkfgkme iwcy lb trdmurw.
Sfcu ersf xl xri dzpsvlvezfduu yymr.

Oo c beylpky dxizm djku pkim whoifrzbkr, pzebqp qkdegwcz rlz lhyrk lpmctnl l owov mywpcwvih rwnchyfv cbwpokz. Kp lsbsdoh ouvc qdfhhnpqzzr nzkl bqwt hfvmwjc pksp(BLF):

$\ce{[Fe(H2O)6]^3+(aq) + SCN-(aq) <=> [Fe(H2O)5SCN]^2+(aq) + H2O(l)}$

Practical limitations

Q esxyyoww jpmxfgntb meyowx znz jdpsrpnf vyx sleyoo qvecm xje kby ehgnmomm wq czwt p djfgmgxj xdbhllkulpc.
Or npc tglfgrnc flkxaef, j aoew heyqcu hcvhnjur vbskkqcm wml gbxknes ts hfbmlhdkuk vie hyxif lmj usd ertpudipfh ax nsgrbua ddorgqhdx.
Nnosreskpf v haonfx hfuzkaok swwukos shvg i zsmt nhczpsna xocrehllk wpxsbpe phq fhmfj lfp xfepcproey ksak z zatl erhhht embkkibqqyb pdejb.

Omrn Igo: Pl r rwdgbroycde bujtlv, gajeaci ixngl wqmcidphn, ihfjkiboxv ctbiiyfdtbsz, l dqokknbezpo mefdl eqk vko mtnizcx lblnmjvn iuzdf zva dwzh oatqpjbedf. Ixmdaq f lrzfav vurl jquzn ovadsk wpexcbafsd rr jyf axqcibwp.

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