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" D$7-1 + 8-1 # ' # #D KF # #-?$(- !" -1-*/$1+8/+*$ K *-/-(+2-/'1#-?($ !" #%$ 4%-1-4/$1+8/+48 ', K 4-/-(68/8 -/-(+2-/'1 #%$ 4-/-(6 8/ /$G$& 2-A3 $&$ - 3 '&- <w= #%$ :$71$$ ', 8.?8/+/./+'& ', - +'& <w= G$4+,+@&- G'0 1)+&- <A 7= G$4+,+4 8.1,-4$ -1$- <A 7= -K ' -K -8/-0-&%+:1+1-&$ 3 $:+&+@&$ >$(+3 $ #%$ 4'AG'8+/+'& ', -&%6 :1'.8 .&+/ 4$(( v '! v - !K *8G$1+A$&/+ *+&$/+*$ :$%+:1-/-4+3 $ $/-&'(- . 7-8&'3,-2+ +20 $:$&+ 8. . 8/-/+@*'A 8+8/$A. /-*' :- 8. 1$-*/-&/ *-/-(+2-/'1 + 1$-*4+3 8*+ G1':.*/+ . 8/-(&'A A$E.8'?&'A *'&/-*/. /'*'A G1->$&3 - 1$-*4+3 $" &-(+2- 8-8/-0 - 1$-*4+'&$ 8A3 $8$ . 1-2(+@+/+A 0 1$A$&8*+A +&/$10 -(+A- 0 1)$&- 3 $ 7-8&'A %1'A-/'71-,+3 'A" -/-(+2-/'1 3 $ G1+3 $ 80 -*'7 $*8G$1+A$&/- -*/+0 +1-& &- - .0 +8'*'A 0 -*..A. . /1-3 -&3 . ': @$/+1+ @-8-" 5 7 -/-(+/+@*- :$%+:1-/-4+3 - $/-&'(- 3 $ G10 ' +8G+/-&- &- +8%':&'A 8+&/$/8*'A 2$'(+/. -K" $-*4+3 - :$%+:1-/-4+3 $ $/-&'(G'@+&3 $ :- 8$ ':0 +3 - &+ G1->$&- 3 $ . +&/$10 -(. /$AG$1-/.1- ': " - 8(+4+ !" 3 $ :-/- 2-0 +8&'8/ 8-8/-0 1$-*4+'&$ 8A3 $)$ ': 0 1$A$&- &- /$AG$1-/.1+ v " 91':.*/+ :$%+:1-/-4+3 $ $/-&'(- 8. '8+A 0 ':$ :+$/+($/$1 + $/$&" 100 90 Sastav reakcione smjese (%) 80 etanol 70 dietileter eten 60 50 40 30 20 10 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Vrijeme (s) (+*- !" $%+:1-/-4+3 - $/-&'(- &- -K 2$'(+/. &- v 5+7.1$ !" /%-&'( :$%6:1-/+'& '& -K 2$'(+/$ -/ v G':1.@3 . &+H+% /$AG$1-/.1- ?12+&- &-8/-3 -&3 - :+$/+($/$1- + $/$&- 3 $ G1+?(+H&' +8/- 80 $ :' 1$-*4+'&$ /$AG$1-/.1$ ': " 2&-: '0 $ /$AG$1-/.1$ :+8/1+?.4+3 - G1':.*-/- 8$ &-7(' G'A3 $1- . 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': :' N " +3 -71-A 2-0 +8&'8/+ *'&4$&/1-4+3 $ G'3 $:+&+% 8.:+'&+*- . 1$-*4+3 + ': 0 1$A$&- &- /$AG$1-/.1+ ! :-/ 3 $ &- 8(+4+ " 100 90 Sastav reakcione smjese (%) 80 etanol 70 dietileter eten 60 50 40 30 20 10 0 0 500 1000 1500 2000 2500 3000 Vrijeme (s) (+*- " $%+:1-/-4+3 - $/-&'(- &- ' -K 2$'(+/. &- ! 5+7.1$ " /%-&'( :$%6:1-/+'& '& ' -K 2$'(+/$ -/ ! 2 :+3 -71-A- 8$ 0 +:+ :- 3 $ 1$-*4+3 - 8(+@&- *'&8$*./+0 &'31$-*4+3 + + :- ': G1':.*-/- &-8/-3 . . '0 'A /$AG$1-/.1&'A +&/$10 -(. 0 ':- $/$& + :+$/+($/$1" +:+ 8$ :- $/$& &-8/-3 $ '8+A +&/1-A'($*.(-1&'A :$%+:1-/-4+3 'A $/-&'(- + :$%+:1-/-4+3 'A :+$/+($/$1-" 0 -3,$&'A$& 3 $ +21-H$&+3 + &- 0 +)+A /$AG$1-/.1-A- /-*' :- &-*'& ':1$E$&'7 0 1$A$&- *-' G1':.*/ 1$-*4+3 $ +A-A' 8-A' $/$&" .:.>+ :- 8. . 8/-/+@*'A 8+8/$A. 1$-*4+'&+ G1':.*/+ . *'&/-*/. 8- -*/+0 &'A G'0 1)+&'A *-/-(+2-/'1- A'7. ./+4-/+ &/'* + ?12+&. 1$-*4+3 $" - 8(+4+ 3 $ :-/- :$%+:1-/-4+3 - :+$/+($/$1- &- /$AG$1-/.1+ ! 7:3 $ 8$ 0+:+ :- '8+A $/$&- &-8/-3 $ + $/-&'( - 1$-*4+3 8$ .?12-0 - 8- 0 1$A$&'A )/' 3 $3 $:-& ': 1-2('7- .8G'1-0 -&3 - 1$-*4+3 $ :$%+:1-/-4+3 $ $/-&'(-" !N " D$7-1 + 8-1 # ' # #D KF # 100 90 Sastav reakcione smjese (%) 80 70 60 50 dietileter eten 40 etanol 30 20 10 0 0 500 1000 1500 2000 2500 Vrijeme (s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v N ! <8 != *! 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• AA 'G/$1$>$&. 8+('A 5 &- 81$:+&+ /3 " &- ( :.H+&$ *'8/+ ': /-@*$ '8('&4'/G'1&+ A'A$&/ L + A'A$&/ 8-0 +3 -&3 - 8 8$ A'7. +21-@.&-/+ *'1+)/$&3 $A :'($ :-/+% +21-2- M s ( x ) = FM ⋅ l 2 AA A'A$&/ 8-0 +3 -&3 - . '8+ x <!= (-8&+* %$A+@-1- /$%&'('7- + $*'('7- $G.?(+*$ 1G8*$ W= 2I y d + W= 2I y *' .&./1-)&3 + :+3 -A$/-1 *'8/+ : r24 ⋅ π r14 ⋅ π − 4 4 M σ s (C ) = s ( x ) ⋅ r1 Iy σ s ( x ) max = M s( x) Iy !!= AA '/G'1&+ A'A$&/ 8-0 +3 -&3 - G'G1$@&'7 G1$83 $*- D Iy = < '2&-@+A' 8- 1! - 0 -&3 8*+ :+3 -A$/-1 *'8/+ AA ⋅ r2 8- 1 '&:- 3 $ A'A$&/ +&$14+3 $ '*' '8+ 66 G18/$&-8/'7 G1$83 $*- AA &-G1$2-&3 $ &- 8-0 +3 -&3 $ . /-@*+ < = *': : < = < = AA < =A-*8+A-(&' &-G1$2-&3 $ &- 8-0 +3 -&3 $ *': < = G1$/%':&+A 3 $:&-@+&-A- G'3 $:+&+ 8+A?'(+ + '2&-*$ +A-3 . 8(+3 $:$>$ 2&-@$&3 $ 5 ;8+(- 'G/$1$>$&3 - &- 71-&+4+ A-*8+A-(&$ @0 18/'>$ *'8/+ ( ;1-8/'3 -&3 $ +2A$E. '8('&-4- *'8/+ : + 7:3 $3 $ l= l l + 2 2 AA ;.&./1-)&3 + :+3 -A$/-1 &- A3 $8/. ('A- AA ;0 -&3 8*+ :+3 -A$/-1 &- A3 $8/. ('A- AA &./1-)&3 + :+3 -A$/-1 &- A3 $8/. ('A- 3 $ :'?+3 $& /-*' :- 8$ ': 0 1+3 $:&'8/+ 0 -&3 8*'7 :+3 -A$/1- ':.2A$ :$?(3 +&- 2+:*'8/+ < δ= AA &- A3 $8/. ('A-" - '8&'0 . 0 +)$ A3 $1$&3 - <&•v= 0 -&3 8*'7 :+3 -A$/1- ('A- *'8/+ < = + .&./1-)&3 $7 :+3 -A$/1- ('A- *'8/+ <: = G': 1-2(+@+/+A .7('0 +A- . ':&'8. &- '?+A *'8/+ &- A3 $8/. :3 $('0 -&3 - 8+($ ('A- 5 A'H$A' :'?+/+ 81$:&3 $ 0 1+3 $:&'8/+ 0 -&3 8*'7 + .&./1-)&3 $7 :+3 -A$/1- A + :A " - '8&'0 . '0 +% A3 $1$&3 - A'H$A' :'?+/+ + 0 1+3 $:&'8/+ &-G1$2-&3 - &- 8-0 +3 -&3 $ <! = G1$A- :+3 -71-A. 8-0 +3 -&3 - . /-@*+ + 0 -&3 8*'3G'0 1)+&+ 2- 80 -*+ 8(.@-3 +8G+/+0 -&3 - '/G'1&'8/+ *'8/+ &- 8-0 +3 -&3 $ .2 G'2&-/. 8+(. 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" N " v !"NN "! v"v! 5'8,'1 w 9%'8,'1 w " "v! N" v " " " " " v " ! " " ! " " "! A A A F """ " "!! 81$:&3 -0 1+3 $:&'8/ 8/-&:-1:&- :$0 +3 -4+3 *'$,+4+3 $&/ 0 -1+3 -4+3 $ 8/-&:-1: :$0 +-/+'& 4'$,,+4+$&/ ', 0 -1+-/+'& /-/+8/+@*'A -&-(+2'A .*.G&'7 8-:1H-3 - G$G$(- *-(4+3 - + ,'8,'1- &+8. ./0 1E$&$ 8+7&+,+*-&/&$ <GŒ " /1$/+1-&+% $*8G$1+A$&/-(&+% 71.G-" = 1-2(+*$ +2A$E. 2 &-)+% 1$2.(/-/- 8$ A'H$ 8$ 2-*(3 .@+/+ :- 3 $ :':-/-* -&+A-(&+% A-8&'>- +8%1-&+ ?1'3 ($1- .21'*'0 -' G'0 $>-&3 $ :.H+&$ /+?+3 -(&$ *'8/+ . ':&'8. &- :':-/-* ?+(3 &+% A-8&'>- +8*(3 [email protected] .>+ :1.7$ ,-*/'1$ *'3 + 8$ 0 $2.3 . 2- *'AG($*8&$ +&/$1-*4+3 $ 7$&$/8*'7 G'/$&4+3 -(- 3 $1 8$ 1-:+ ' +8/'A %+?1+:. *-' + :3 $('0-&3 $ '*'(+&$ < != '?2+1'A :- 8. .8('0 + .27'3 - ?+(+ +:$&/+@&+ 2- 80 $ G'8A-/1-&$ 71.G$ ?1'3 ($1-" 9'1$: :.H+&$ ./0 1E$&- 3 $0 +8'*' 8/-/+8/+@*+ 2&-@-3 &- <G• " != 1-2(+*- . -&/$1' G'8/$1+'1&'A :+3 -A$/1. +2A$E. 71.G$ ?1'3 ($1- *'3 - 3 $ +A-(- :':-/-* 80 +&3 8*$ A-8/+ . %1-&+ + 71.G$ ?1'3 ($1*'3 -3 $ +A-(- :':-/-* 8'3 +&'7 .(3 - . %1-&+ /$ :- 3 $ :':-/-* 80 +&3 8*$ A-8&'>$ . +8%1-&+ ?1'3 ($1- .21'*'0 -' G'0 $>-&3 $ -&/$1' G'8/$1+'1&'7 :+3 -A$/1- . ':&'8. &- :':-/-* 8'3 +&'7 .(3 -" -*' 8. . $*8G$1+A$&/-(&+A 71.G-A- 80 + .8('0 + ?+(+ +:$&/+@&+ 8$A :':-/+% w 1-2(+@+/+% +20 '1- A-8/+ + .(3 - A'H$ 8$ 2-*(3 .@+/+ :- 3 $ + '0-3A'1,'A$/1+3 8*+ G'*-2-/$(3<-&/$1' G'8/$1+'1&+ :+3 -A$/-1= +2-20 -& 8G$4+,+@&+A :3 $('0 -&3 $A :':-&$ 80 +&3 8*$ A-8/+" #-*'E$ 8$ +2 ?1'3 &+% 1-:'0 - A'H$ .'@+/+ ./+4-3(+G+:- . +8%1-&+ &- 1-20 '3/*+0 - *'8/+3 . + 8-8/-0>$(+3 8*+% A$A?1-&- ,'8,'(+G+:- /$ ./+4-3&- >$(+3 8*. ,.&*4+3 . *'8/+3 . < = -(+ . &-)$A $*8G$1+A$&/. A+ /$ 1-2(+@+/$ ,-*/'1$ +8*(3 [email protected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• !=" - :' G1'A3 $&- ,+2+@*+% + A$%-&+@*+% G-1-A$/-1- /+?+3 -(&$ *'8/+ A'H$ :'>+ G1+ *'1+)/$&3 . 1-2(+@+/+% +20 '1- A-8&'>$ G'*-2.3 $+ +8/1-H+0 -&3 $ -1*8 - <! = *'3 + 3 $ .8/-&'0 +' :- 8. ?1'3 ($1+ %1-&3 $&+ 8- :':-/*'A %1-&+ 8'3 +&'7 .(3 - +A-(+ 0 $>. /$H+&. + 3 -@+&. /+?+3 -(&$ *'8/+ . 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