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6 #+"%$$$*7#$ &"& <#%* O ; 99 [FeT], mol/l 0.18 0.17 0.16 0.15 0.14 0.13 0.1 0.11 Starting ph ~6 [Mn(II)]=0.581 mol/l [Fe(II)]=0.176 mol/l oxygen flowrate=.0 l/min 0.1 0 50 100 150 00 50 300 350 time, mins Run 1 Run Run 3!$,"66 >&)))
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oxidation of ferrous sulphate by by oxygen 0.1 0.6 [FeT], mol/l 0.09 0.08 0.07 0.06 0.05 [Mn(II)] 0.55 0.5 0.45 [Fe T ] T= 77 oc 0.4 0.35 0.3 0 100 00 300 time, mins [Mn(II)],mol/l!$,"6; K 66 $+&*&$& ; P 5<< 55!;; 4 ;;6+ 9# >9<))
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Weight % 100 0.351M Fe(II) 95 Run R7 90 85 80 75 0 00 400 600 800 1000 Temperature ( o C)!$,"6>?; 1 0 0 0.3 5 1 M F e (II) n o M n O 9 5 Weight % 9 0 8 5 ""$ 8 0 7 5 0 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 T e m p e ra tu re ( o C )!$,"6>?;! 8 + >96))
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+ )5H ;;6+ 6; %# &7$+$ 6; %$$"&%%$ 9% ;;9 (#$$#'Q&<<<'#$)&+ ([FeT]/[FeT]o) 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 Oxidation of ferrous sulphate by oxygen T = 77 oc [Mn(II)] = 0.58 mol/l Starting ph ~ 6.0 0 50 100 150 00 50 300 350 time, mins 0.09 mol/l 0.17mol/l 0.7 mol/l 0.35 mol/l!$,"6@ KT +U >9*))
[Fe T ], mol/l 0.4 0.35 0.3 0.5 0. 0.15 0.1 0.05 0 GA 6; %7$+*# 9)!$,"61 K T =77 oc [Fe(II)] = 0.35 mol/l [Mn(II)] = 0.58 mol/l 0 50 100 150 00 50 300 350 Oxygen time, mins Air 6;6 %#" [Fe T ], mol/l 0. 0.18 0.16 0.14 0.1 0.1 0.08 0.06 0.04 0.0 0 T = 77 oc [Fe(II)] = 0.17 mol/l [Mn(II)] = 0.58 mol/l 0 50 100 150 00 50 300 350 Oxygen time, mins Air 9$ >9%))
TU O <6 <9) <9* <96 <9& <9 <&) <&* T +UB<95 O T! +UB<5) O 4J* <&6 <&& <& < 5< #<< #5< &<< &5< 9<< 95< B%% B)5 B55 B**!$,"60 K! "#$%&'013#$$%' #$)9+ 6;; %#' 4 ' 4 >9)))
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0.009 [H+], mol/l 0.008 0.007 0.006 0.005 0.004 0.003 0.00 0.001 [Fe(II)] = 0.35 mol/l ph 5.7 ph 3.5!$,"6 T4 7 U 4 #$)&+ 0 0 50 100 150 00 50 300 350 time, mins 6;> '=#'+$, 9#& 4 / ""%+ >6<))
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&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+ #$)6 01 3 #$$%+ "Y #$$$+ #$)6'013#$$%+
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; - %$&$% +$,%$ K, 65+! " #$%&+ # #9#+ 4 6# "Y #$$$+ / #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)))
, 6%+, 65 "Y #$$$+ RSK B<T UBT U+ 1 [ Fe II 1 II ] [ Fe ], o II 1 α = [ Fe ] ln II t β [ Fe ], o 1 + α [ O t ] exp E RT : 6)+ P 1 [ Fe II 1 II ] [ Fe ], o 1 [ Fe ln t [ Fe ROS α[ O ] exp >6$)) II ] II o E RT 1 t b< 6&
!$,"; K;K! "Y #$$$+ FD ##O KO" 69 y = -.769E+00x +.439E-04 R = 9.998E-01 oxygen [Fe(II)] =0.35 mol/l 55 oc 0-0.005-0.00-0.0015-0.001-0.0005 0 oxygen [Fe(II)] =0.351 mol/l 77 oc 1/t (ln([fe II ]/[Fe II ] o )) y = -3.00E+00x + 7.394E-04 R = 9.963E-01-0.003-0.00-0.001 0 1/t (ln([fe II ]/[Fe II ] o)) 0.007 0.006 0.005 0.004 0.003 0.00 0.001 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.00 0.001 0 1/t (1/[Fe II ] - 1/[Fe II ]o) 1/t [1/[Fe II ] - 1/[Fe II ]o) >5<)) y = -.69E+00x + 5.09E-04 R = 9.99E-01 oxygen 0.351 mol/l Fe(II) 66 oc 0-0.005-0.00-0.0015-0.001-0.0005 0 1/t (ln([fe II ]/[Fe II ] o )) y = -.81E+00x + 1.1E-03 oxygen 0.351 mol/l Fe(II) 85 oc R = 9.98E-01-0.005-0.004-0.003-0.00-0.001 0 1/t (ln([fe II ]/[Fe II ] o )) 0 0.008 0.007 0.006 0.005 0.004 0.003 0.00 0.001 0.016 0.014 0.01 0.01 0.008 0.006 0.004 0.00 1/t (1/[Fe II ] - 1/[Fe II ]o) 1/t (1/[Fe II ] - 1/[Fe II ]o)
LnK 1 y = -7090.6x + 0.357 R = 0.9906 0.5 0-0.5-1 -1.5 0.0075 0.008 0.0085 0.009 0.0095 0.003 0.00305 0.0031 1/T (k -1 )!$,";6 ;> "Y #$$$+ 5$<@O G R S K, 6% / ; - II II = ([ Fe ] ) exp [ Fe ] cac SSE : 6$+ T U T U K,6% >5#))
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SSE 0.05 0.045 0.04 0.035 0.03 0.05 0.0 0.015 0.01 0.005 0 0.00E+00 5.00E+09 1.00E+10 1.50E+10.00E+10.50E+10 3.00E+10!$,";> KSK R S )<#< $ K,6% 6# ; K> > R S K K 5*5#< $!O $<#< $!O 5)$@O D >59))
K, 6%+ 6* 6%?+ Theoritical, [Fe] T, mol/l 0.4 0.35 0.3 0.5 0. 0.15 0.1 0.05 0 0 0.1 0. 0.3 0.4 Experimental, [Fe] T, mol/l!$,;? > >56))
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!$,";1 [Fe]T, mol/l 0.35 0.33 0.31 0.9 0.7 0.5 0.3 0.1 0.19 [Fe T ] o = 0.35 mol/l R =0.96 R =0.94 [Fe T ] o = 0.7 mol/l 0.17 0 50 100 150 00 50 300 350 time, mins Experimental Model Fit Experimental Model Fit >5*)) Oxygen T=77 oc
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G EH K, E.; P -7 T kbc = e : ;#&+ log10 (1/ T ) = log10 ( I O / I) = abc : ;#9+ log 10 ( I O / I) = A : ;#6+ ;;B P/F + ; ;;+,,, ; A #$)5+ >*%))
,,. *$%" %$A" ;A #$)5+,, +, ;#& +; PKK"/F;! PK". A canalyte c analyte Aanalyte = creference : ;#5+ A reference = creference = A reference A analyte = ; = ; >*)))
; <<* <<5 <<6 <<9 <<& <<# < < 5 #< #5 &< &5 TU!$,";, ; 0 F #$)<+ P FP L / 0 F #$)5+. >*$))
4 C ' ;,,, A #$)5+ %& ; ;;,. '.' A-' ' '.' + '.' + '.' >%<))
*$%*&$&#& ;; 0 ; ; F- #$$&+! ;; F 5; ; ; 8 0 8 A µo &6)9 <& <<*L#5 9%&< <& #L#<< 9)*< <& #5L&<<!! &%$5 <& <<&L5 6<9# <& <5L*< >%#))
; A #$)5+ MN + ; #<<< + #<<<< +, #5#<#5&<' # 9 5 #<<< > 5 5O 9&O # #<<< ; " + ;#& >%&))
##+$7C &"%$"$7$,&, L4&8 #"$$% +74&8B8 +7&4 7,+7& : ;&#+ 9 +764&8B986 +7)4 7,+7) : ;&&+ 98 +74&8B986 +7&4 7,+7& : ;&9+ &986 +74&8B9&89 +7&4 7,+7& : ;&6+ &8 +74&8B&89 +7&4 7,+7& : ;&5+ #"$$% +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&8B884 +794 7,+ : ;&#<+ #"$$% &7,+B 97,+7 : ;&##+ 97,+764&8B86 &/,+7)4 7,+79 : ;&#&+ &$% 8&764 7 76B&4&8 : ;	+ &4 7 7&B4& : ;+ ' ' >%9))
, ;&#+ ' C,. RT {Re duced state} E = E o ln z F { Oxidised state} A"B#$%) /# D /# B &9<* /#0/#?. o G = z E F = RT ln K AD, ; 4 B& &$)D. o G G o G o + = FeO + H G o Fe G o H O kcal = 1.908 mol G E o = = 0. 0414V z F C,. + o RT [ FeO][ H ] E = E ln z F [ Fe][ H O] ;, o E = E 0.0059 ph = 0.0414 0.0059 ph >%6))
;, o E = E 0.0059 ph = 0.0414 0.0059 ph : ;+ A 4 8&4& ()'*+, ; KL4! L4&8 >#$)*+ #"$$%! +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 &!986 +74&8B9!&89 +7&4 7,+7& : ;&#%+ KB<*)$L<<5$#4!&89 +74&8B&!8& +7&4 7,+7& : ;&#)+ E = 1.014 0.0591 ph #"$$%! +B! &7,+7& : ;&#$+ >%5))
KB/##%$L<<&$5! &7 +! &7,+74&8B!8 +7&4 7,+ : ;&&<+ F! &7 +B#59#L&4 9! &7,+764&8B!986 +7)4 7,+7& : ;&&#+ KB#)&6L<&9*64L<<))*! &7 + &! &7,+794&8B!&89 +7*4 7,+7& : ;&&&+ KB#669L<#%94L<<5$#! &7 +! &7,+7&4&8B!8& +764 7 7&,+ : ;&&9+ KB#&&)L<###)&4L<<&$5! &7 +!8& +7&4&8B!86 /,+764 7 7& : ;&&6+ KB#*$&L<<%))4L<<#$%!86 / + >%*))
##+$76C " & [Fe]T, mol/l 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.0 0.01 0 Oxygen T=77 o C Starting [Fe(II)] = 0.0895 mol/l 0 50 100 150 00 50 300 time, mins [Fe]T, mol/l 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.0 0.01 0 Air T=77 o C Starting [Fe(II)]=0.0895 mol/l 0 50 100 150 00 50 300 time, mins [Fe]T, mol/l 0. 0.18 0.16 0.14 0.1 0.1 0.08 0.06 0.04 0.0 0 Oxygen T=77 o C Starting [Fe(II)]=0.175 mol/l 0 50 100 150 00 50 300 350 time, mins [Fe]T, mol/l 0. 0.18 0.16 0.14 0.1 0.1 0.08 0.06 0.04 0.0 0 Air T=77 o C Starting [Fe(II)]=0.175 mol/l 0 50 100 150 00 50 300 350 time, mins >%%))
0.3 0.3 0.5 0.5 [Fe]T, mol/l 0. 0.15 0.1 0.05 Oxygen T=77 o C Starting [Fe(II)] = 0.71 mol/l [Fe]T, mol/l 0. 0.15 0.1 0.05 Air T=77 o C Starting [Fe(II)]=0.175 mol/l 0 0 50 100 150 00 50 time, mins 0 0 50 100 150 00 50 300 350 time, mins 0.4 0.4 0.35 0.35 0.3 0.3 [Fe]T, mol/l 0.5 0. 0.15 0.1 0.05 0 Oxygen T=77 o C Starting [Fe(II)] = 0.351 mol/l 0 50 100 150 00 50 300 350 time, mins [Fe]T, mol/l 0.5 0. 0.15 0.1 0.05 0 Air T=77 o C Starting[Fe(II)]=0.351mol/L 0 50 100 150 00 50 300 350 time, mins ;9# ' / >%)))
##+$7;C / $ $%*&$&"#&&B$" "# + P & P ' +,. P &7 0+786 &/ 0+BP86 + 7#$ %+" "G. >%$)) : ;6#+ G <5! P & <#! ;C89 9&H4 #+ ; <6<<< &5</ &+ #<L#5+/ 4 +8 #5< &9* +(P & 9+ P & +
P & &< +;P & 6+ G ;C89 ; ; A 5+ G 65##< %"$&! #+! > &+! >7 9+! B! P86 6+B 9+L &+ DP86 K,;6#! 86 &/ B! P86BP86! P86 >)<))
?86 &/ B 86 &/ 86 BP86 86 P86 H86 B86 #<< "%+. # &! <9556 + <956# +! > <565 + <59<& +! >7 <*#< + <*<% +! P86 <<*5 + <<%*) + H86 %56 )$6 ;H86 )&6 " BT )&6/%56+O )&6+U^#<< B)5H >)#))
##+$7>C $ $- %$&$%A"$, "Y #$$$+ /, #+ 78&B /8/8^+ &7 : #+ /8/8^+ &7 7 B /8/8/+ 67 : &+ /8/8/+ 67 7 7 B &/8+ 67 7 8/+ &7 : 9+ 8/+ &7 7 B &/8+ 67 : 6+ &/8+ 67 7498 7 B84 / 74&87& : 5+ 498+ 7 784 / B&4&8 : *+ 8 6 &7 78&7498 7 B*4&876 97 : %+ ;#&. : )+ 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+ ]
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/+ 67 76498 7 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))
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 3 6 + ] 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))
##+$7?C-!$+ 0.9 0.7 0.5 R =0.96 Oxygen T=77 oc [Fe]T, mol/l 0.3 0.1 0.19 0.17 0.15 0 50 100 150 00 50 time, mins Experimental Model Fit 0.095 [Fe]T, mol/l 0.09 0.085 0.08 R =0.90 Oxygen T=77 oc 0.075 0.07 0 50 100 150 00 50 300 time, mins Experimental Model Fit >)5))
0.165 Oxygen 0.16 R =0.90 T=55 C 0.155 0.15 0.145 0.14 0 50 100 150 00 time, mins 50 300 Experimental Model Fit 0.75 0.7 Air 0.65 R =0.91 T=77 o C 0.6 0.55 0.5 0.45 0.4 0 50 100 150 00 50 300 350 time, mins Experimental Model Fit!$,"? K [Fe]T, mol/l [Fe]T, mol/l >)*))
0.0895 0.089 [Fe]T, mol/l 0.0885 0.088 0.0875 0.087 0.0865 0.086 0.0855 Air T=77 o C R =0.94 0 50 100 150 00 50 300 time, mins Experimental Model Fit 0.5 0.45 [Fe]T, mol/l 0.4 0.35 0.3 0.5 0. 0.15 0.1 0.05 R =0.96 Oxygen T= 55 o C 0. 0 50 100 150 00 50 300 350 time, mins Experimental Model Fit!$,"? ( >)%))
##+$7@C,!=$,&&$- +$, 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 ( 0.345341 0.331543 0.3185644 0.308615 0.76861 0.67861 0.566 0.43984 0.4009 ) T t ( 0 1.0833 43 60 17 151 03 50 300 ) T parameters to be estimated A 1 5.4. 10 9 A 9.0. 10 9 E 58900 R 8.314 T ( 73 77 ) starting ferrous concn. saturated oxygen concn C Feo 0.345341 C O 0.00070386 A 1 = 0.6 A E 8.314 = 7.084. 10 3 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 0.. 8 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 = 3.804. 10 4 C Fexp n C Fe n C Fe = n 0.345341 0.33943015 0.308938913 0.31087339 0.81348543 0.716591518 0.56740536 0.375364964 0.3006897 0.345 C Fexp C Fen 0.3 0.3 0.5 0. 0 100 00 300 0 t, t 300 n >))))