University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution , -.
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- ŌἈπολλύων Φραγκούδης
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1 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution! "#$%&'(#$)*+, -. /, Page 1 of 88
2 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution! "#"$ +, (! #$)*'! "#$%&'013#$$%+! "#$%&' 4 (#$5*' 01 3#$$%'+. 6 &7 78& &4&8: ##+! ; #$%5' (! #$)*' ; ; &<<9+ #+ 97 7&4&8= : #&+ & &8= : #9+ 9+ & &8=&89 +7*4 7 : # &8= : # & 86+97! 867#&4&8=! * #& +7*4&86: #*+ Page of 88
3 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution (! #$)*'(#$%*+ >" %&& $%!" #' #" ( )? 884 &/ & 84+* A! BC46D498 C> E#5 $</#&< 4 &89 F G&H4&86 I#9< I&H4&86 I#9< 84+9 J9 E%< $'*+ ",$%-,&$%"$& Page 3 of 88
4 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution (! #$)*'4#$$9+>, 4#$%%+ - ; ; &<<9+ 4#$$9'(! #$)*+ '.#'+$,& > K/4 +, 4+ ; #& Page 4 of 88
5 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution L4&8 #%$& / (01)34%5 % + << ;" &7,+ /#))5 ;" 97,+ /## ;" /##<6#) ;" /&6&% ;" 4 7,+ << F 4&8,+ /5**)% F ;".; ; &<<9+'F.F #$%%+ G>&$)D ###< /9! ; ;;& E (V) 1.5 Fe 3+ (aq) FeOOH(s) O line Fe + (aq) 0 H line -0.5 Fe 3 O 4 (s) -1 Fe(s) !$," KL4L4&8&$)D! #< /9! ph Page 5 of 88
6 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution! L4&8&$)D #& & #5!86 /,+ K 0+ # <5 < /<5 /# /#5 /& 8 &! &8 9 +! &7,+! &! 84+ & +! + < # & * % ) $ #< ## #& #9 #6 4!$," KL4! L4&8&$)D! #< /9! ## &$)D#< /9! Page 6 of 88
7 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution #9MN!$,"6 KL4L! L4&8&$)D! <<<# E (V) Fe 3+ (aq) Fe + (aq) Mn + (aq) Fe(s) Mn(s) FeO*OH(s) Operating region ph O line H line Page 7 of 88
8 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution 6 #$$$,$#%$#$ #O (#$%5' P&<<#+ /0! K Q0!, (#$%*+ K Q #O ( #$%*+ ( #$%5+ R / S L 884 R/884 ;( #$%*+ 0! ; #$%)+ Page 8 of 88
9 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution &)H&*H ;4 / MN ( #$$#+ / ; 6 7$+$"&$&*+$&& +7*, K,##+ 4 ( #$5*+,. r Fe ( III ) b [ + t O = k Fe( II )] p( O ) k [ Fe( II)] p( ) : #%+ Page 9 of 88
10 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution #6<L#)<, &7,+ <<**L<<$$! +! " #$%&+, [ Fe ] [ O ] 73.9 r exp( ) + = ko : #)+ Fe [ H ] RT k m [ O ] = [ O ] sat : #$+ ko 4 C &7!" #$%&+ Page 10 of 88
11 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution 0 4 &Q8686C&86! 8& #$)6+ T +U D 9L)O 4, Q &<<<+ #$)6+ &7! -; #$)&+T +U ;. r Fe = AO [ Fe ] p( O )exp( ) + A1 [ SO4 )][ Fe ] p( O )exp( ) R T R T : ##< / Page 11 of 88
12 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution,, T +U G 01 3 #$$%+ + ; 5#@O 6%$-%$&&! 8 7$+$9$7*, &7 8& #$)6+ E <#69 O + Q &<<<+, &7 A #$95+,. Page 1 of 88
13 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution &7 78&= 97 78& / : ###+ &7 78& / 7&4 7 = 97 74&8& : ##&+ &7 74&8&= V 784 / : ##9+ &7 784 V = / : ##6+ K,##5+, &7 4*) + r Fe + = k Fe ][ O ] : ##5+ [! " #$%&+ 4 E& ; L 8& &7, &7 78&W 8& &7 : ##*+ 8& &7 7 &7 74&8=& / 748& / : ##%+ 48& / 74 7 =4&8& : ##)+ 4&8&= 4&87X8& : ##$+ &7 78&W 8& &7 : ##*+ &7 74&8W : #&<+ 8& & &8=& / : #&#+ Page 13 of 88
14 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution, #, k k [ Fe ] [ O ] r 3 [ Fe + = : #&&+ ] k 1.16, r k = 1.16 k 1.0 k 1.1 [ Fe + [ H 3 + [ Fe ] k k ] [ O ] ] : #&9+ P K,#&6+ K[ Fe + r[ Fe = : #&6+ 3+ ] 1/ 4 [ H ] ] [ O ] "Y #$$$+! " #$%&+ / M / 8/8 N. 78&B /8/8+ &7 : #&5+ /8/8+ &7 7 B /8/8/+ 67 : #&*+ /8/8/ B &/ /+ &7 : #&%+ Page 14 of 88
15 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution 8/+ &7 7 B &/8+ 67 : #&)+ &/ B84 / 74&87 : #&$ / B&4&8 : #9< & B*4&876 : #9#+ ; #&5 #&* ;;5+ r II Fe II E /( RT ) α [ Fe ] e [ O ] = II 1+ ( α / β )[ Fe ] : #9&+ ARS ; *4$$%&$7$+$ > #9+ Z A#6 [ Page 15 of 88
16 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution O,, F,!$,;! MN N. A k m x DO = = Mass transfer coefficient δ D = Molecular diffusivity of oxygen a O o C &8 & P r δ = Apparent Interface film T8&U δ thickness : #99+ = Interfacial area of all bubbles per unit volume of aqueous phase ; K,#%#)##5#&6#9&+ T8 &U d[ O ] D a \ x 0 dx ([ O ] [ O ] sat ) = DO a o δ DO a o = ([ O ] [ O ]) sat δ = k a ([ O ] [ O ]) O = O o = m o sat Page 16 of 88
17 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution + α O ] : #96+ [ B Page 17 of 88 r Fe! r + = 4r O : #95+ Fe 1! r '[ O ] 4 Fe + = k : #9*+ A 'T +UT4 7 U /KO"+ K, #99+ #9*+ T8&U [ O ] [ O ] k' 1+ k a sat = : #9%+ L ; T8&UBT8&U, #%#)##5#&6#9&+ C #$)9+ m o O ] sat =.5 10 p ( O )exp K i Ci : #9%+ T [
18 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution D B\ ] #9 6 0 D D D 4 7 <<< C89 / <<9 C46 7 <<) / <<% D7 <&9 486 / <#* C7 <&5 84 / <#$! &7 <&% 86 &/ <&)! &7 &7 D <&% Page 18 of 88
19 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution <- ; + K - ; ; - K!(+ ; 86%4&8! 864&8! 8 K! + P(4+ ; + G 4 > G4>+ ; #O)/ #5 ; 5 O - +flowrate. Page 19 of 88
20 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution &9! /, &< O &# $< )< %< *< 5< 6< 9< &< #< << << <5 #< #5 &< &5 9< 95 6< 65 5< FO ;" #5!$," " 444 ;K> ;O; O && Page 0 of 88
21 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution " 4!$," / 7#$ ="# &9, + #O) ;6 + * 4 ( Page 1 of 88
22 University of the Witwatersrand The Oxidation and Precipitation of Iron From a Manganese Sulphate Solution 7#$ %+" P / &5 86%4&8+! 864&8+ &%5 / 9&O! &7 ' 8 ; 4 O &6<, A #< O -4*!88 - & A4*< &< O + 4 Page of 88
23 T-1 T- T-3 V--1 V-- V--3 GA Overhead stirrer Condenser TC ph Meter ph, ToC Needle Valves Rotameter Reactor Vessel Vacuum Pump Hot Plate Sampling Bottle Oxygen cylinder Air cylinder Nitrogen cylinder!$,"6 K / >&9))
24 GA 6!$$&*& &6 /! <&&µ 55 (+P ; #< " 4 "!$,"; ; 8 5< 55 ;, ; ; ;;+? tube 0 >&6)) 0 >
25 ; $ $*&"& >! 8 4 &6;4 *! 8 + > 7#$ &%+"% L&<O 55L)5 >&5))
26 6 6 $ $ &&&%&%,%+ &< O95 O 9#+ &< O 8 TU O <9 <&5 <& <#5 <# <<5 < <<<$ <<<) <<<% <<<* <<<5 T4 7 U <<<6 T! +B<5) O <<<9 T +B<&% O 4B* <<<& 95 O &< O 95 O &< O B%% <<<# < < 5< #<< #5< &<< &5< T47U O!$,"6 K >&*))
27 &6<&<< 9&+ &6< Oxydation by Oxygen time, mins 00 rpm 40 rpm!$,"6 K [FeT], mol/l >&%))
28 6 #+"%$$$*7#$ &"& <#%* O ; 99 [FeT], mol/l Starting ph ~6 [Mn(II)]=0.581 mol/l [Fe(II)]=0.176 mol/l oxygen flowrate=.0 l/min time, mins Run 1 Run Run 3!$,"66 >&)))
29 66 $$$+&#&$$ 66 "$&*&$& G;; 96+/ #$%)+96, / ; / O 8 <*5 <* <55 <5 <65 <6 <95 TU <9 <&5 <& T! +U B%% < 5< #<< #5< &<< &5< 9<< 95<!$,"6; K >&$))
30 oxidation of ferrous sulphate by by oxygen [FeT], mol/l [Mn(II)] [Fe T ] T= 77 oc time, mins [Mn(II)],mol/l!$,"6; K 66 $+&*&$& ; P 5<< 55!;; 4 ;;6+ 9# >9<))
31 G %%! 8 4 A *<< 8 4&8 6 KC T +U O " H +! H + 86 H + 4&8 H + "# <<9& *< %&< <%) 6$) / "& <<)$ *< *$) #<6 5%5 / "9 <<)$ 6&< *69 ##6 / / "6 <#%# *< *)9 #&9 6$& / "5 <#%# &<< **< ##$ / / "* <95# *< *&) #&< )96 / "% <95# &<< *&% ### )&9 &5# ") A <95# &<< *9# ##$ 96% / "$^ <95# &<< *99 #&6 )*% &6) K55 A ^K! 8 / >9#))
32 #$%)+ /! 8 4+ "$ 9#!8 4 / 9# (#$%*'( #$$#+ *< &<< ; ## 9& 6 H + 86H &9 / 884 *&$ / # 5*$ & 84+* 96$ 6<< 9#+ 9&+P >9&))
33 9# "% ") 9# 55 ") "%+ C 666/*&$&&$+&?;+ 95 #< O "% "$+ &<< *<< + ; &<< ( #$%5+;?; 9# *<< >99))
34 Weight % M Fe(II) 95 Run R Temperature ( o C)!$,"6>?; M F e (II) n o M n O 9 5 Weight % ""$ T e m p e ra tu re ( o C )!$,"6>?;! 8 + >96))
35 66; <*&$&&$+& ;_"( + 9*+!$,"6? _"( _"(?; Counts E517A.CAF Fe O 3.H O Position [ Theta] (#$%5#$%*'(#$$#+ 9# $%H ;; >95)) Fe +3 OOH
36 + )5H ;;6+ 6; %# &7$+$ 6; %$$"&%%$ 9% ;;9 (#$$#'Q&<<<'#$)&+ ([FeT]/[FeT]o) Oxidation of ferrous sulphate by oxygen T = 77 oc [Mn(II)] = 0.58 mol/l Starting ph ~ time, mins 0.09 mol/l 0.17mol/l 0.7 mol/l 0.35 mol/l!$,"6@ KT +U >9*))
37 [Fe T ], mol/l GA 6; %7$+*# 9)!$,"61 K T =77 oc [Fe(II)] = 0.35 mol/l [Mn(II)] = 0.58 mol/l Oxygen time, mins Air 6;6 %#" [Fe T ], mol/l T = 77 oc [Fe(II)] = 0.17 mol/l [Mn(II)] = 0.58 mol/l Oxygen time, mins Air 9$ >9%))
38 TU O <6 <9) <9* <96 <9& <9 <&) <&* T +UB<95 O T! +UB<5) O 4J* <&6 <&& <& < 5< #<< #5< &<< &5< 9<< 95< B%% B)5 B55 B**!$,"60 K! "#$%&'013#$$%' #$)9+ 6;; %#' 4 ' 4 >9)))
39 G !8 9#<9## TU O <6 <9) <9* <96 <9& <9 <&) <&* <&6 B%% T! +UB<5)# O T +U B<95 O <&& <& < 5< #<< #5< &<< &5< 9<< 95< 4B95 4B5%!$,"6 K4 >9$))
40 0.009 [H+], mol/l [Fe(II)] = 0.35 mol/l ph 5.7 ph 3.5!$,"6 T4 7 U 4 #$)& time, mins 6;> '=#'+$, 9#& 4 / ""%+ >6<))
41 %<< *<< 5<< 6<< K 0+ 9<< &<< #<< < /#<< /&<< 8 T +UB<95# O B%% < # & * % 4!$,"6 4/4, 4#$$9+,9# CK, ; 97 7B &7 : 9#+ RT ared E = h Eo ln : 9&+ n F aoxd >6#))
42 3+ RT [ Fe ] E = h Eo ln + n F [ Fe ] : 99+ C! " B"O 97 7&4&8B # : 96+, T 97 UBT 884+UT47U 9 OD# : 95+ K,99 [ FeOOH] + E h ' = ln + 3 ln[ ] + 1 [ ] C C H K Fe : 9*+ "B)9#6@O DB $*6)%@O 0B95<DB<<9',9* E h ' = const + ( 0.01 ph) : 9%+ /, KN4+ L<&<# 9#& L<&9,, >6&))
43 G 97 O & #9+ T +UJ< [Fe 3+ ]/[Fe + ] T = 77 oc [Fe(II)] o =0.35 mol/l Oxygen ph!$,"66 6;? $$% $&%&$++ +$,. %% 55 >69))
44 %% #6 / + O <<<<* <<<<5 <<<<6 <<<<9 <<<<& <<<<# < < <<5 <# <#5 <& <&5 <9 <95 <6 TU O %% 55 ;`%%!$,"6; K >66))
45 GA ; - /!<- ; #$$%- +A"$ 99 / ' +,#)! " #$%&' #$)6+' +,6#. &7 7X8&7&4 7 B 97 74&8: 6#+! "#$%&'+ r o α = k [ Fe ] [ O ] [ H ] + β + γ exp( E / RT ) : 6&+ $%& 966T4 7 U +, + α β = k Fe ] [ O ] exp( E / RT ) : 69+ r o [ >65))
46 &7 + d [ Fe ] + α β = ro = k [ Fe ] [ O ] exp( E / RT ) : 66+ dt 965+ ;;; T8&UJT8&U #6+, d [ Fe dt T ] = K [ Fe ] T α [ O ] β sat exp E R T >6*)) : 65+ -'$%#, ab#5)sb<)) B59&@O DB#$%#< ) O <))! " #$%&' #$)6+ #$) #$$%+ "Y #$$$+ #$)6'013#$$%+
47 G,, 65+ 9#6 6#!$,";F, / + O <<<<* <<<<5 <<<<6 <<<<9 <<<<& <<<<# < < <<5 <# <#5 <& <&5 <9 <95 <6 TU O %% 55 ;`%% 8&`%% 8&55 ;`%% >6%))
48 ; - %$&$% +$,%$ K, 65+! " #$%&+ # #9#+ 4 6# "Y #$$$+ / #9#+,;;5 rfe II II E /( RT ) α [ Fe ] e [ O ] = II 1+ ( α / β )[ Fe ] : 6*+ d II E /( RT ) ] α [ Fe ] e = 1+ ( α / β )[ Fe [ O II [ Fe II dt ] ] : 6%+ RSREES,, +! "#$%&'+ RIIS,,8 >6)))
49 , 6%+, 65 "Y #$$$+ RSK B<T UBT U+ 1 [ Fe II 1 II ] [ Fe ], o II 1 α = [ Fe ] ln II t β [ Fe ], o 1 + α [ O t ] exp E RT : 6)+ P 1 [ Fe II 1 II ] [ Fe ], o 1 [ Fe ln t [ Fe ROS α[ O ] exp >6$)) II ] II o E RT 1 t b< 6&
50 !$,"; K;K! "Y #$$$+ FD ##O KO" 69 y = -.769E+00x +.439E-04 R = 9.998E-01 oxygen [Fe(II)] =0.35 mol/l 55 oc oxygen [Fe(II)] =0.351 mol/l 77 oc 1/t (ln([fe II ]/[Fe II ] o )) y = -3.00E+00x E-04 R = 9.963E /t (ln([fe II ]/[Fe II ] o)) /t (1/[Fe II ] - 1/[Fe II ]o) 1/t [1/[Fe II ] - 1/[Fe II ]o) >5<)) y = -.69E+00x E-04 R = 9.99E-01 oxygen mol/l Fe(II) 66 oc /t (ln([fe II ]/[Fe II ] o )) y = -.81E+00x + 1.1E-03 oxygen mol/l Fe(II) 85 oc R = 9.98E /t (ln([fe II ]/[Fe II ] o )) /t (1/[Fe II ] - 1/[Fe II ]o) 1/t (1/[Fe II ] - 1/[Fe II ]o)
51 LnK 1 y = x R = /T (k -1 )!$,";6 ;> "Y #$$$+ 5$<@O G R S K, 6% / ; - II II = ([ Fe ] ) exp [ Fe ] cac SSE : 6$+ T U T U K,6% >5#))
52 ;, K+R S6665 SSE E E E E+09 1.E E+10!$,";; KRK >5&))
53 SSE E E E E+10.00E+10.50E E+10!$,";> KSK R S )<#< $ K,6% 6# ; K> > R S K K 5*5#< $!O $<#< $!O 5)$@O D >59))
54 K, 6%+ 6* 6%?+ Theoritical, [Fe] T, mol/l Experimental, [Fe] T, mol/l!$,;? > >56))
55 frequency Residuals!$,;@ 4 6# 6) %% ;;* >55))
56 !$,";1 [Fe]T, mol/l [Fe T ] o = 0.35 mol/l R =0.96 R =0.94 [Fe T ] o = 0.7 mol/l time, mins Experimental Model Fit Experimental Model Fit >5*)) Oxygen T=77 oc
57 GA > -- 5L&<O ++ &894&8+ ; " & O +,. r Fe 1.58 = [ Fe] T [ O ] sat 53. KJ exp RT mol! O + "Y #$$$+/ "Y #$$$+ 9 II /( RT ) r [ Fe ] e [ O ] = Fe II 9 9 II 1+ ( / )[ Fe ] >5%)) sat (Mol/l. min)
58 4!8 4 Q &<<<+ >5)))
59 -, ' '' ' ' ( )*''(+++,, -'..' /.0 1 /. 1 /. '' ' ''' ' ' '3 CO ''' '3 5-''' '/ '3 5-''' '3 DO 8 :. /.79' 1 / ' '93 '' ; ' '' ; ''<"<;" 4(--, (---, '' '3 5. '' '3 4 = 6 ''' '3 4 >= 6 ''' '3? ' '93 4 = 6 9' ''' '3 47@ " 6 '' ' '3 ## 0 '' # 8 5'.. ' '' >5$))
60 '' # 0 '' A. ' '9 ' ' ' po.79' ''' '3.. '. 3 ' ) ''3# 47@ " 6 ''' '3 5 5 ; 5/ B. ( '. 0'., =3" ' '3' ' C 1'. ' >*<))
61 ! # ;? K 4 #$$5+ D / "A! 88 9 '8 5' '?B#9/&6 & ; ; "&5 $5 5 < '9< '/< &%.65L 5& 9 P #$)$+5 :.''04 6 PD8D8 #$%%+5. '9' '(',/0 P 5 P;" &<<#+ 9 ' ' + > * A; #$)6+ +, 9&#L9< % D #$)5+D! ) (>D">D #$)&+K / L6% $ ( > " #$%5+ S/884 R/&89 5' '.-' '.8 ''9'89 1;)9/)* #< (>" #$%*+", \]9&5L99 ## (@K! ;@ #$)*+-' ' ' 9 K 4 K >*#))
62 #& K P 4? #$$<+ D'' '. -' 5? D ( 8 ( > #$$#+ D / 58 '8'8 " : '9#*5L#%9 #6? ;@(@ #$$<+! K! 8 9 5' 'B&#%L&&) #5?> #$56+ <<;696$/695$ #* 4!! (! ; D #$%%+ ;'.1. '-'. 8 ''9'8 9@@ %+#9%/#6& #% 4> #$$9+ ' '8 ''8 ' 4> c ; #) 4"K(C #$5*+D/8 " ; <1<<>6.6)9%L6)6& #$!!-4;d #$)&+8 + ; (! 889 5' '6B9##/9#) &< F@F ; #$%%+ 97 /864&L86 &/ +)/<8 6C&.*%/%$ &# F- F4@ #$$&+ 1' 1 1 ' ' '" >*&))
63 &&! '9. 1 ' -'.8 ''9'8 9C&6&.6%/5* &9! ' '-' '. 8 9 '?1C%59.#<#/##< &6 CKF4DC #$)9+, 9&#L&% &5 "Y!"Aef@ F! #$$$+ D '9''9 '>;6&&9L6&9& &* "Y!"Aef@ 0 (FK &<<#+ D 5**66%L65& &% "Y!"Aef@ &<<&+L / '9''9' '9; %59/%*< &) >D #$%$+<<5< '909<% L9#< &$ ;4 #$55+8 '9'P> F 9< ;? #$**+#'.-'9' '>>8 9# 0 F@ #$)<+ 1' 1 ' ; > Cd >*9))
64 9& 01"g3D> #$$%+D + 9;; ##9/#&6 99 A P #$) ' & Zhang, W. David, M. and Singh, P. (000). Iron oxidation by SO / O in acidic media, Part II. Effect of copper, Hydrometallurgy, 58, (P-@A; #$)<+8 '9. '.'9' E 9'K#5$#/#*<< 9* 0;? #$* !?/4 C d >*6))
65 ##+$7C $%&#$#% *() 9& <<<!5<<<L&<<<<+, ;; $%$#& ;, 0 F #$)<+ K,'A K'+ K'##+,. v = ( E nl E n l1) / h = E / h : ;##+ 1 λ = c / v = hc / E A > N,/ F, ;, >*5))
66 K ;## K 7hK /hk ; K?!$,"K ;, 7hK+, ''' '/ A, $&$#9&#$+%$. >**))
67 G EH K, E.; P -7 T kbc = e : ;#&+ log10 (1/ T ) = log10 ( I O / I) = abc : ;#9+ log 10 ( I O / I) = A : ;#6+ ;;B P/F + ; ;;+,,, ; A #$)5+ >*%))
68 ,,. *$%" %$A" ;A #$)5+,, +, ;#& +; PKK"/F;! PK". A canalyte c analyte Aanalyte = creference : ;#5+ A reference = creference = A reference A analyte = ; = ; >*)))
69 ; <<* <<5 <<6 <<9 <<& <<# < < 5 #< #5 &< &5 TU!$,";, ; 0 F #$)<+ P FP L / 0 F #$)5+. >*$))
70 4 C ' ;,,, A #$)5+ %& ; ;;,. '.' A-' ' '.' + '.' + '.' >%<))
71 *$%*&$&#& ;; 0 ; ; F- #$$&+! ;; F 5; ; ; A µo &6)9 <& <<*L#5 9%&< <& #L#<< 9)*< <& #5L&<<!! &%$5 <& <<&L5 6<9# <& <5L*< >%#))
72 ; A #$)5+ MN + ; #<<< + #<<<< +, #5#<#5&<' # 9 5 #<<< > 5 5O 9&O # #<<< ; " + ;#& >%&))
73 ##+$7C &"%$"$7$,&, L4&8 #"$$% +74&8B8 +7&4 7,+7& : ;&# &8B986 +7)4 7,+7) : ;&& &8B986 +7&4 7,+7& : ;&9+ & &8B9&89 +7&4 7,+7& : ;&6+ &8 +74&8B&89 +7&4 7,+7& : ;&5+ #"$$% +B &7,+7& : ;&*+ &7,+74&8B8 +7&4 7,+ : ;&%+ 9 &7,+764&8B986 +7)4 7,+7& : ;&)+ & &7,+794&8B&89 +7*4 7,+7& : ;&$+ 97,+7&4&8B ,+ : ;&#<+ #"$$% &7,+B 97,+7 : ;&##+ 97,+764&8B86 &/,+7)4 7,+79 : ;&#&+ &$% 8& B&4&8 : ;	+ &4 7 7&B4& : ;+ ' ' >%9))
74 , ;&#+ ' C,. RT {Re duced state} E = E o ln z F { Oxidised state} A"B#$%) /# D /# B &9<* /#0/#?. o G = z E F = RT ln K AD, ; 4 B& &$)D. o G G o G o + = FeO + H G o Fe G o H O kcal = mol G E o = = V z F C,. + o RT [ FeO][ H ] E = E ln z F [ Fe][ H O] ;, o E = E ph = ph >%6))
75 ;, o E = E ph = ph : ;+ A 4 8&4& ()'*+, ; KL4! L4&8 >#$)*+ #"$$%! +74&8B!8 +7&4 7,+7& : ;+ KB/<%&%L<<5$#4 9!8 +74&8B!986 +7&4 7,+7& : ;&#*+ KB<6*&L<<5$#4 &! &8B9!&89 +7&4 7,+7& : ;&#%+ KB<*)$L<<5$#4!&89 +74&8B&!8& +7&4 7,+7& : ;&#)+ E = ph #"$$%! +B! &7,+7& : ;&#$+ >%5))
76 KB/##%$L<<&$5! &7 +! &7,+74&8B!8 +7&4 7,+ : ;&&<+ F! &7 +B#59#L&4 9! &7,+764&8B!986 +7)4 7,+7& : ;&&#+ KB#)&6L<&9*64L<<))*! &7 + &! &7,+794&8B!&89 +7*4 7,+7& : ;&&&+ KB#669L<#%94L<<5$#! &7 +! &7,+7&4&8B!8& &,+ : ;&&9+ KB#&&)L<###)&4L<<&$5! &7 +!8& +7&4&8B!86 /, & : ;&&6+ KB#*$&L<<%))4L<<#$%!86 / + >%*))
77 ##+$76C " & [Fe]T, mol/l Oxygen T=77 o C Starting [Fe(II)] = mol/l time, mins [Fe]T, mol/l Air T=77 o C Starting [Fe(II)]= mol/l time, mins [Fe]T, mol/l Oxygen T=77 o C Starting [Fe(II)]=0.175 mol/l time, mins [Fe]T, mol/l Air T=77 o C Starting [Fe(II)]=0.175 mol/l time, mins >%%))
78 [Fe]T, mol/l Oxygen T=77 o C Starting [Fe(II)] = 0.71 mol/l [Fe]T, mol/l Air T=77 o C Starting [Fe(II)]=0.175 mol/l time, mins time, mins [Fe]T, mol/l Oxygen T=77 o C Starting [Fe(II)] = mol/l time, mins [Fe]T, mol/l Air T=77 o C Starting[Fe(II)]=0.351mol/L time, mins ;9# ' / >%)))
79 ##+$7;C / $ $%*&$&"#&&B$" "# + P & P ' +,. P & &/ 0+BP86 + 7#$ %+" "G. >%$)) : ;6#+ G <5! P & <#! ;C89 9&H4 #+ ; <6<<< &5</ &+ #<L#5+/ 4 +8 #5< &9* +(P & 9+ P & +
80 P & &< +;P & 6+ G ;C89 ; ; A 5+ G 65##< %"$&! #+! > &+! >7 9+! B! P86 6+B 9+L &+ DP86 K,;6#! 86 &/ B! P86BP86! P86 >)<))
81 ?86 &/ B 86 &/ 86 BP86 86 P86 H86 B86 #<< "%+. # &! < <956# +! > <565 + <59<& +! >7 <*#< + <*<% +! P86 <<*5 + <<%*) + H86 %56 )$6 ;H86 )&6 " BT )&6/%56+O )&6+U^#<< B)5H >)#))
82 ##+$7>C $ $- %$&$%A"$, "Y #$$$+ /, #+ 78&B /8/8^+ &7 : #+ /8/8^+ &7 7 B /8/8/+ 67 : &+ /8/8/ B &/ /+ &7 : 9+ 8/+ &7 7 B &/8+ 67 : 6+ &/ B84 / 74&87& : / B&4&8 : *+ 8 6 &7 78& B*4& : %+ ;#&. : )+ r = r1 = k [ Fe 1 r = r = k II ][ O ] k 1 [( Fe O O*) [( Fe O O*) + ][ Fe II ] k + ] [( Fe O O Fe) 4+ : ] $+ ;// /8/8^+ &7 #B&. k1[ Fe II ][ O ] k 1 [( Fe O O*) + ] = k [( Fe O O*) >)&)) + [ Fe II ] k [( Fe O O Fe) 4+ ]
83 A [( Fe O O*) + k1[ Fe ] = II ][ O ] + k II k [ Fe [( Fe O O Fe) ] + k 1 4+ ] : #<+ ; 9 L 5,/,. & 7 /8/8/ B*4&876 : K, ##+ K [ Fe ] [ H O] III 4 6 ' = 4+ II + [( Fe O O Fe) ][ Fe ] [ H 3O ] 4 : #&+ /8/8/+ 67 [( Fe O O Fe) 4+ ] = [ Fe III K'[ Fe II 4 ] [ H ] [ H O] 3 6 O+ ] 4 : #9+ #9+#<+)+'. II III 4 6 k1[ Fe ][ O ] k [ Fe ] [ H O] r = k 1[ FeII ][ O ] k 1 + II II II + ( k [ Fe ] + k 1) ( k [ Fe ] + k 1) K'[ Fe ] [ H 3O ] 4 : #6+ ;D#B#O/#D&B&O/&, K, %+DBD#D&DN'K, #6+. >)9))
84 A II kk1[ Fe ] [ O ] r = (1 q) : #5+ II 1+ ( k / k )[ Fe ] 1 q = K [ Fe C III [ Fe 4 ] [ H II O] 4 ] [ H O ] 4 : #*+ #B&D#BR /KN#O" &B#BS /KN&O" K, #5+ II a1[ Fe ] [ O ] r = (1 q) : #%+ II 1+ ( a / a )[ Fe ] 1 K, #*+D,= <' #O& ; K, #%+. II ] [ Fe [ O ] E / RT e II α r = 1+ ( α / β )[ Fe ] : #)+ >)6))
85 ##+$7?C-!$ R =0.96 Oxygen T=77 oc [Fe]T, mol/l time, mins Experimental Model Fit [Fe]T, mol/l R =0.90 Oxygen T=77 oc time, mins Experimental Model Fit >)5))
86 0.165 Oxygen 0.16 R =0.90 T=55 C time, mins Experimental Model Fit Air 0.65 R =0.91 T=77 o C time, mins Experimental Model Fit!$,"? K [Fe]T, mol/l [Fe]T, mol/l >)*))
87 [Fe]T, mol/l Air T=77 o C R = time, mins Experimental Model Fit [Fe]T, mol/l R =0.96 Oxygen T= 55 o C time, mins Experimental Model Fit!$,"? ( >)%))
88 +$, The program for the estimation of the parameters is quite long to include them all, therefore sample of it is presented here as an illustration. Experimenta Data C Fexp ( ) T t ( ) T parameters to be estimated A A E R T ( ) starting ferrous concn. saturated oxygen concn C Feo C O A 1 = 0.6 A E = C Fe 0.3 Given 1 A 1. ln C Fe C Fe A 1 A 1. ln C Feo A. 1 C. E O exp. t C Feo A R. T C Fe A 1, A, t Minerr C Fe Calculates the ferrous concentrations for the given n parametrs C Fe C n Fe A 1, A, t n calculates the sum of residual square error by comparing the experimental and calculated values of the ferrous concns. SSE1 n SSE1 = C Fexp n C Fe n C Fe = n C Fexp C Fen t, t 300 n >))))
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