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"0:85 ?@>F5AAK, ?@>B5:0NI85 ?@8 @ = const, =07K 20NBAO 87>10@=K<8. 01>B0 @0AH8@5=8O, A>25@H05-<0O ?@8 87>10@=>< ?@>F5AA5, :0: 8725AB=>, @02=0: W =  V, 345 V  ?@8@0I5=85 >1J5<0 A8AB5<K, @02=>5 @07 =>AB8 >1J5<>2 2 A>AB>O=8OE 2 8 1. >4AB02;OO @01>BC @0AH8@5=8O 2 <0B5<0B8G5A:>5 2K@065=85 ?5@2>3> =0G0;0 8 ?@>254O =5A;>6=K5 ?@5 >1@07>20=8O, ?>;CG05<: Q = E + pV = (E2 + V2)  (E1 + V1) 345 Q  B5?;>B0 87>10@=>3> ?@>F5AA0; 1, 2  8=45:AK, >B=>AOI85AO : =0G0;C 8 :>=FC ?@>F5AA0. 5;8G8=0 (E+ pV)  DC=:F8O A>AB>O=8O A8AB5<K, >1>7 =0G05<0O G5@57  8 =07K205<0O M=B0;L?859: H = E + V. !>>B25BAB25==>, 2K@065=85 <>6=> 70?8A0BL 2 2845: Qp = 2  1 = H. 7 40==>3> 2K@065=8O A;54C5B, GB> M=B0;L?8O  DC=:F8O A>AB>O=8O, ?@8@0I5=85 :>B>@>9 @02=> B5? ;>B5, ?>;CG5==>9 A8AB5<>9 2 87>10@=>< ?@>F5AA5. 7<5@5=85 ?@8@0I5=8O M=B0;L?88 2 =5:>B>@>< ?@> F5AA5 <>65B 1KBL >ACI5AB2;5=> ?@8 ?@>2545=88 MB> 3> ?@>F5AA0 2 :0;>@8<5B@5 ?@8 ?>AB>O==>< 402;5=88. <5==> B0: ?@>2>48;8 A2>8 M:A?5@8<5=BK . . 0 2C07L5 8 . !. 0?;0A, 87CG0O M=5@35B8:C <5B01>;87 <0 2 682>< >@30=87<5.  B5E A;CG0OE, :>340 87<5=5=85 A>AB>O=8O A8AB5<K ?@>8AE>48B ?@8 ?>AB>O==>< >1J5<5, ?@>F5AA =07K20 5BAO 87>E>@=K<. 7<5=5=85 >1J5<0 AV ?@8 MB>< @02 => =C;N, 8 2 A>>B25BAB288 A D>@<C;>9 @01>B0 @0AH8@5 =8O W = 0. ">340 87 <0B5<0B8G5A:>3> 2K@065=8O ?5@2>3> =0G0;0 B5@<>48=0<8:8 A;54C5B: Qv = E. 7 2KH5C:070==>3> A>>B=>H5=8O 2KB5:05B B5@<> 48=0<8G5A:>5 >?@545;5=85: 2=CB@5==OO M=5@38O  DC=:F8O A>AB>O=8O, ?@8@0I5=85 :>B>@>9 @02=> B5? ;>B5 QV , ?>;CG5==>9 A8AB5<>9 2 87>E>@=>< ?@>F5AA5. !;54>20B5;L=>, 87<5=5=85 2=CB@5==59 M=5@388 2 =5 :>B>@>< ?@>F5AA5 <>65B 1KBL 87<5@5=> ?@8 ?@>2545 =88 MB>3> ?@>F5AA0 2 :0;>@8<5B@5 ?@8 ?>AB>O==>< >1J5<5. !;54C5B, GB> ?@8 = const ?@8@0I5=8O 2=CB @5==59 M=5@388 8 M=B0;L?88 A2O70=K A>>B=>H5=85<: H = E + V. 4. 0:>= 5AA0 0745; B5@<>48=0<8:8, 87CG0NI89 ?@52@0I5=8O M=5@ 388 ?@8 E8<8G5A:8E @50:F8OE, =07K205BAO E8<8G5A:>9 B5@<>48=0<8:>9. #@02=5=85 @50:F88, 4;O :>B>@>9 C:0 7K20NBAO A>>B25BAB2CNI85 MB>9 @50:F88 87<5=5=8O 2=CB @5==59 M=5@388 E, M=B0;L?88 H 8;8 :0:>9-;81> 4@C3>9 DC=:F88 A>AB>O=8O, =07K205BAO B5@<>E8<8G5A:8<. %8<8G5A:85 @50:F88, ?@8 ?@>B5:0=88 :>B>@KE ?@>8A E>48B C<5=LH5=85 M=B0;L?88 A8AB5<K (H < 0) 8 2> 2=5H =NN A@54C 2K45;O5BAO B5?;>B0, =07K20NBAO M:7>B5@<8 G5A:8<8. 50:F88, 2 @57C;LB0B5 :>B>@KE M=B0;L?8O 2>7@0AB05B (H > 0) 8 A8AB5<0 ?>3;>I05B B5?;>BC Qp 872=5, =07K 20NBAO M=4>B5@<8G5A:8<8. :8A;5=85 3;N:>7K :8A;>@>4>< ?@>8AE>48B A 2K45 ;5=85< 1>;LH>3> :>;8G5AB20 B5?;>BK (Qp =  2800 :6/ /<>;L), B. 5. MB>B ?@>F5AA  M:7>B5@<8G5A:89. !>>B25B AB2CNI55 B5@<>E8<8G5A:>5 C@02=5=85 70?8H5BAO 2 2845 !6 12 6 + 602 = 6!02 + 62, H =  2800 :6. 50:F88, ?@>B5:0NI85 2 @0AB2>@5, A>?@>2>640NBAO >1KG=> =57=0G8B5;L=K< 87<5=5=85< >1J5<0 A8AB5<K, B. 5. VH" 0.  A2O78 A MB8< 2> <=>38E A;CG0OE ?@8 18>;> 38G5A:8E @0AG5B0E <>6=> AG8B0BL, GB> H = E. !;54>20 B5;L=>, 2K45;5=85 B5?;>BK 2 B0:8E A8AB5<0E >1CA;>2;5=> 2 >A=>2=>< C<5=LH5=85< 2=CB@5==59 M=5@388 2 @57C;LB0 B5 ?@>B5:0=8O @50:F88, 8 =0>1>@>B. -=B0;L?859 >1@07>20=8O A>548=5=8O  =07K205BAO 87<5=5=85 M=B0;L?88 A8AB5<K HA , A>?@>2>640NI55 >1@07>20=85 1 <>;O A>548=5=8O  87 ?@>ABKE 25I5AB2. -=B0;L?88 >1@07>20=8O :8A;>@>40, C3;5@>40, 2>4> @>40 8 2A5E 4@C38E M;5<5=B=KE (?@>ABKE) 25I5AB2 ?@8 =8<0NB @02=K<8 =C;N. @8 ?@>G8E @02=KE CA;>28OE 2=CB@5==OO M=5@ 38O 8 M=B0;L?8O ?@>?>@F8>=0;L=K :>;8G5AB2C 25 I5AB20 2 A8AB5<5. "0:85 B5@<>48=0<8G5A:85 DC=:F88 =07K20NBAO M:AB5=A82=K<8. ! B>G:8 7@5=8O B5@<>48=0<8:8 @50:F8O >1I53> 28 40 nA + ? = ?! + nD , h ?@54AB02;O5B A>1>9 ?5@5 E>4 A8AB5<K 87 =0G0;L=>3> A>AB>O=8O A M=B0;L?859 1 2 A>AB>O=85 2 A M=B0;L?859 2. 7<5=5=85 M=B0;L?88 A8AB5<K 2 @57C;LB0B5 MB>3> ?5@5E>40, =07K205<>5 M=B0;L?859 40==>9 @50:F88, @02=> @07=>AB8: Hp-O = 2  1 = (ncHc + nDHD)  (n + nBHB). 0:>= ?>AB>O=AB20 B5?;>2KE AC<<, >B:@KB @CAA:8< CG5=K<-E8<8:>< . . 5AA>< 2 1840 3. = O2;O5BAO ?5@ 2>>B:@K20B5;5< ?@8<5=8<>AB8 ?5@2>3> =0G0;0 B5@<> 48=0<8:8 ?@8 E8<8G5A:8E ?@52@0I5=8OE 8 >A=>20B5;5< E8<8G5A:>9 B5@<>48=0<8:8.  =0AB>OI55 2@5<O 70:>= 5AA0 @0AA<0B@8205BAO :0: A;54AB285 ?5@2>3> =0G0;0 B5@<>48=0<8:8 8 D>@<C;8@C5BAO B0:: ?@8@0I5=85 M=B0;L?88 ?@8 >1@07>20=88 7040==KE ?@>4C:B>2 87 40==KE @5035=B>2 ?@8 ?>AB>O==>< 402;5=88 =5 70 28A8B >B G8A;0 8 2840 @50:F89, 2 @57C;LB0B5 :>B> @KE >1@07CNBAO MB8 ?@>4C:BK. @8 B5@<>E8<8G5A:8E @0AG5B0E G0I5 ?@8<5=O5BAO =5 A0< 70:>= 5AA0, 0 53> A;54AB285, 2K2545==>5 2KH5 4;O G0AB=>3> A;CG0O >:8A;5=8O 3;N:>7K 2 2845 @025= AB20 (2). ;O @50:F88, ?@54AB02;5==>9 2 >1I5< 2845 ? + ?2 = = ?A! + nDD, A;54AB285 87 70:>=0 5AA0 70?8AK 205BAO A ?><>ILN @025=AB20 Hp-O = (nCHC + nDHD)  (nAHA + + nBHB ) 8 D>@<C;8@C5BAO B0:: M=B0;L?8O @50:F88 @02=0 0;351@08G5A:>9 AC<<5 M=B0;L?89 >1 @07>20=8O AB5E8><5B@8G5A:>3> :>;8G5AB20 ?@>4C: B>2 70 2KG5B>< 0;351@08G5A:>9 AC<<K M=B0;L?89 >1@07>20=8O AB5E8><5B@8G5A:>3> :>;8G5AB20 @5035=B>2. 5. B>@>5 =0G0;> B5@<>48=0<8:8. !2>1>4=0O M=5@38O 811A0 @30=87< A>25@H05B @01>BC, 70B@0G820O 2=CB@5==NN M=5@38N, 70?0A5==CN 2 2845 M=5@388 E8<8G5A:>3> 2708 <>459AB28O 0B><>2 A>AB02;ONI8E 53> 25I5AB2. 0B5 <0B8G5A:>5 2K@065=85  E =  Q  W ?5@2>3> =0G0;0 B5@<>48=0<8:8 >?@545;O5B B>G=>5 A>>B=>H5=85 <564C @0AE>4>< 2=CB@5==59 M=5@388 A8AB5<K , @01>B>9 W, A>25@H05<>9 A8AB5<>9, 8 M=5@3859 Q, :>B>@0O B5@O5BAO 2 2845 B5?;>BK. 4=0:> 87 ?5@2>3> =0G0;0 B5@<>48=0 <8:8 =5;L7O >?@545;8BL G0ABL @0AE>4C5<>9 2=CB@5= =59 M=5@388, :>B>@0O <>65B 1KBL ?@5>1@07>20=0 2 @0 1>BC. "5>@5B8G5A:85 >F5=:8 70B@0B >ACI5AB2;ONBAO =0 >A =>25 2B>@>3> =0G0;0 B5@<>48=0<8:8. -B>B 70:>= =0:;0 4K205B AB@>385 >3@0=8G5=8O =0 MDD5:B82=>ABL ?@5>1 @07>20=8O M=5@388 2 @01>BC 8, :@><5 B>3>, ?>72>;O5B 225AB8 :@8B5@88 2>7<>6=>AB8 A0<>?@>872>;L=>3> ?@> B5:0=8O B>3> 8;8 8=>3> ?@>F5AA0. @>F5AA =07K205BAO A0<>?@>872>;L=K<, 5A;8 >= >AC I5AB2;O5BAO 157 :0:8E-;81> 2>7459AB289, :>340 A8AB5<0 ?@54>AB02;5=0 A0<>9 A515. !CI5AB2CNB ?@>F5AAK, ?@8 :>B>@KE 2=CB@5==OO M=5@ 38O A8AB5<K =5 <5=O5BAO ( = 0).  B0:8< ?@>F5AA0< >B=>A8BAO, =0?@8<5@, 8>=870F8O C:ACA=>9 :8A;>BK 2 2>45. &5;K9 @O4 A0<>?@>872>;L=KE ?@>F5AA>2 ?@>B5:05B A C25;8G5=85< 2=CB@5==59 M=5@388 ( > 0). !N40 >B=> AOBAO, 2 G0AB=>AB8, B8?8G=K5 @50:F88 >1@07>20=8O 18> =5>@30=8G5A:8E A>548=5=89 0;L1C<8=0 (15;>: ?;07<K :@>28) A 8>=0<8 <5B0;;>2, =0?@8<5@ !u2+. 7<5=5=85 2=CB@5==59 M=5@388  4;O 70:@KBKE A8A B5< =5 <>65B A;C68BL :@8B5@85< A0<>?@>872>;L=>3> ?@> B5:0=8O ?@>F5AA>2. !;54>20B5;L=>, ?5@2>3> =0G0;0 B5@<>48=0<8:8, 87 :>B>@>3> ?>;CG5= MB>B :@8B5 @89, =54>AB0B>G=> 4;O @5H5=8O 2>?@>A0 > A0<>?@>87 2>;L=>AB8, @02=> :0: 8 >1 MDD5:B82=>AB8 ?@>F5AA>2. 5H5=85 MB8E 2>?@>A>2 4>AB8305BAO A ?><>ILN 2B>@>3> =0G0;0 B5@<>48=0<8:8. ;O D>@<C;8@>2:8 2B>@>3> =0G0;0 B5@<>48=0<8:8 =5>1E>48<> 225AB8 ?>=OB8O >1@0B8<>3> 8 =5>1@0B8<>3> 2 B5@<>48=0<8G5A:>< A<KA;5 ?@>F5AA>2. A;8 A8AB5<0 =0E>48BAO 2 @02=>25A88, MB> A>AB>O=85 ?>445@68205BAO :0: C3>4=> 4>;3> ?@8 =587<5==>AB8 2=5H=8E CA;>289. @8 87<5=5=88 2=5H=8E CA;>289 A> AB>O=85 A8AB5<K <>65B <5=OBLAO, B. 5. 2A8AB5<5 <>65B ?@>B5:0BL ?@>F5AA. @>F5AA =07K205BAO B5@<>48=0<8G5A:8 >1@0B8 <K<, 5A;8 ?@8 ?5@5E>45 87 =0G0;L=>3> A>AB>O=8O 1 2 :> =5G=>5 A>AB>O=85 2 2A5 ?@><56CB>G=K5 A>AB>O=8O >:0 7K20NBAO @02=>25A=K<8. @>F5AA =07K205BAO B5@<>48=0<8G5A:8 =5>1@0B8 <K<, 5A;8 E>BL >4=> 87 ?@><56CB>G=KE A>AB>O=89 =5 @02=>25A=>. 1@0B8<K9 ?@>F5AA <>6=> >ACI5AB28BL ;8HL ?@8 4> AB0B>G=> <54;5==>< 87<5=5=88 ?0@0<5B@>2 A8AB5<K  B5<?5@0BC@K, 402;5=8O, :>=F5=B@0F88 25I5AB2 8 4@. !:>@>ABL 87<5=5=8O ?0@0<5B@>2 4>;6=0 1KBL B0:>9, GB> 1K 2>7=8:0NI85 2 E>45 ?@>F5AA0 >B:;>=5=8O >B @02=> 25A8O 1K;8 ?@5=51@568<> <0;K. !;54C5B >B<5B8BL, GB> A >1@0B8<>ABLN A2O70=0 206=0O ?@>1;5<0 <548F8=K  :>=A5@20F8O B:0=59 ?@8 =87:8E B5<?5@0BC@0E. 1@0B8<K5 ?@>F5AAK O2;ONBAO ?@545;L=K< A;CG05< @50;L=KE ?@>F5AA>2, ?@>8AE>4OI8E 2 ?@8@>45 8 >AC I5AB2;O5<KE 2 ?@><KH;5==>AB8 8;8 2 ;01>@0B>@8OE. 6. B>@>5 =0G0;> B5@<>48=0<8:8. -=B@>?8O 0:A8<0;L=0O @01>B0 W<0:A, :>B>@0O <>65B 1KBL ?> ;CG5=0 ?@8 40==>9 C1K;8 2=CB@5==59 M=5@388  2 ?@> F5AA5 ?5@5E>40 87 A>AB>O=8O 1 2 A>AB>O=85 2, 4>AB8 305BAO ;8HL 2 B>< A;CG05, 5A;8 MB>B ?@>F5AA >1@0B8<K9.  A>>B25BAB288 A 2K@065=85< 4;O ?5@2>3> =0G0;0 B5@ <>48=0<8:8 ?@8 MB>< 2K45;O5BAO <8=8<0;L=0O B5?;>B0 Q<8= Q<8= =   W<0:A . 0:A8<0;L=> 4>AB868<K9 :>MDD8F85=B ?>;57=>3> 459AB28O, E0@0:B5@87CNI89 MDD5:B82=>ABL 70B@0B 2=CB @5==59 M=5@388 A8AB5<K, A>>B25BAB25==> @025= <0:A= W<0:A / . @8 =5>1@0B8<>< ?@>F5AA5 ?5@5E>40 87 A>AB>O=8O 1 2 A>AB>O=85 2 ?@>872>48<0O A8AB5<>9 @01>B0 <5=L H5 W. 'B>1K @0AAG8B0BL <0:A8<0;L=K9 :>MDD8F85=B h<0:A ?@8 8725AB=>< 7=0G5=88 , =5>1E>48<> 7=0BL 25;8 G8=C W<0:A 8;8 Q<8= W<0:A =   Q<8= , A;54>20B5;L=>, <0:A = 1   / Q<8= . 5;8G8=CQ<8= <>6=> @0AAG8B0BL =0 >A=>25 2B>@>3> =0G0;0 B5@<>48=0<8:8 A ?><>ILN B5@<>48=0<8G5 A:>9 DC=:F88 A>AB>O=8O, =07K205<>9 M=B@>?859. >=OB85 M=B@>?88 225; (1865 3.) =5<5F:89 D878: . .. ;0C78CA (1822 1888)  >48= 87 >A=>20B5;59 B5@<>48=0<8:8 8 <>;5:C;O@=>-:8=5B8G5A:>9 B5>@88 B5?;>2KE ?@>F5AA>2. "5@<>48=0<8G5A:>5 >?@545;5 =85 M=B@>?88 2 A>>B25BAB288 A ;0C78CA><: M=B@>?8O ?@54AB02;O5B A>1>9 DC=:F8N A>AB>O=8O, ?@8@0 I5=85 :>B>@>9 S @02=> B5?;>B5 Q<8= ?>42545= =>9 : A8AB5<5 2 >1@0B8<>< 87>B5@<8G5A:>< ?@>F5AA5, 45;5==>9 =0 01A>;NB=CN B5<?5@0BC@C ", ?@8 :>B>@>9 >ACI5AB2;O5BAO ?@>F5AA: S = Q<8= / ". 7 D>@<C;K A;54C5B, GB> 548=8F0 87<5@5=8O M= B@>?88 6/. @8<5@>< >1@0B8<>3> 87>B5@<8G5A:>3> ?@>F5AA0 <> 65B A;C68BL <54;5==>5 B0O=85 ;L40 2 B5@<>A5 A 2>4>9 ?@8 273. -:A?5@8<5=B0;L=> CAB0=>2;5=>, GB> 4;O ?;02 ;5=8O 1 <>;O ;L40 (18 3) =5>1E>48<> ?>425AB8, ?> :@09 =59 <5@5, 6000 6 B5?;>BK. @8 MB>< M=B@>?8O A8AB5 <K ;54  2>40 2 B5@<>A5 2>7@0AB05B =0 S = 6000 6: 273 = 22 6/. @8 >E;0645=88 B5@<>A0 A 2>4>9 ?@8 273 <>6=> <54;5==> >B25AB8  6000 6 B5?;>BK, 8 ?@8 :@8AB0; ;870F88 2>4K >1@07C5BAO 1 <>;L ;L40. ;O MB>3> ?@> F5AA0 25;8G8=0 Q<8= 2 D>@<C;5 8<55B >B@8F0B5;L=>5 7=0G5=85. !>>B25BAB25==>, M=B@>?8O A8AB5<K ;54  2>40 ?@8 >1@07>20=88 1 <>;O ;L40 C1K205B =0 S =-22 6/. =0;>38G=K< >1@07>< <>6=> @0AAG8B0BL 87<5=5=85 M=B@>?88 ?@8 ;N1KE 87>B5@<8G5A:8E D878G5A:8E 8 E8 <8G5A:8E ?@>F5AA0E, 5A;8 8725AB=0 B5?;>B0 ?>4 2>48<0O : A8AB5<5 8;8 >B2>48<0O >B =55 ?@8 MB8E ?@> F5AA0E. 0: 8725AB=> 87 D878:8, MB0 B5?;>B0 <>65B 1KBL >?@545;5=0 A ?><>ILN :0;>@8<5B@8G5A:8E 87 <5@5=89. "0:8< >1@07><, 87<5=5=85 M=B@>?88, B0: 65 :0: 8 42CE 4@C38E DC=:F89 A>AB>O=8O A8AB5<K  2=CB@5==59 M=5@ 388 8 M=B0;L?88, ?@54AB02;O5B A>1>9 M:A?5@8<5=B0;L=> >?@545;O5<CN 25;8G8=C. $878G5A:89 A<KA; M=B@>?88, :0: 8 2=CB@5==59 M=5@388, >BG5B;82> 2KO2;O5BAO ?@8 @0A A<>B@5=88 A <>;5:C;O@=>-:8=5B8G5A:>9 B>G:8 7@5=8O ?@>F5AA>2, ?@>B5:0NI8E 2 87>;8@>20==KE A8AB5<0E. 7. $>@<C;0 >;LF<0=0 7>;8@>20==K5 A8AB5<K ?> >?@545;5=8N =5 >1<5 =820NBAO A 2=5H=59 A@54>9 =8 25I5AB2><, =8 M=5@ 3859. >=5G=>, @50;L=> B0:8E A8AB5< 2 ?@8@>45 =5 AC I5AB2C5B. 4=0:> >G5=L E>@>H0O 87>;OF8O <>65B 1KBL >ACI5AB2;5=0, 5A;8 ?><5AB8BL A8AB5<C 2 B5@<>A, 70 :@KBK9 ?@>1:>9. :07K205BAO, GB> ;N1>9 A0<>?@>872>;L=K9 ?@>F5AA <>65B ?@>B5:0BL 2 87>;8@>20==>9 A8AB5<5 ;8HL 2 B>< A;CG05, :>340 >= E0@0:B5@87C5BAO C25;8G5=85< M=B@> ?88; 2@02=>25A88 M=B@>?8O A8AB5<K ?>AB>O==0: S e" 0. -B> CB25@645=85, >A=>20==>5 =0 M:A?5@8<5=B0;L =KE =01;N45=8OE, O2;O5BAO >4=>9 87 2>7<>6=KE D>@ <C;8@>2>: 2B>@>3> =0G0;0 B5@<>48=0<8:8. @>F5AA, >1@0B=K9 A0<>?@>872>;L=><C, A>3;0A=> 2B>@><C =0G0;C B5@<>48=0<8:8 2 87>;8@>20==>9 A8AB5 <5 ?@>B5:0BL =5 <>65B, B0: :0: B0:>9 ?@>F5AA E0@0:B5 @87C5BAO C<5=LH5=85< M=B@>?88. 0AA<>B@5=85 @07;8G=KE 87>;8@>20==KE A8AB5< ?> :07K205B, GB> A0<>?@>872>;L=K5 ?@>F5AAK 2A5340 A2O70=K A @>AB>< G8A;0 <8:@>A>AB>O=89 w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w0 1. "0 :8< >1@07><, <>3CB 1KBL >?@545;5=K 01A>;NB=K5 7=0 G5=8O M=B@>?88 :@8AB0;;87CNI8EAO 25I5AB2 2 >B;8G85 >B 2=CB@5==59 M=5@388  8 M=B0;L?88 , 4;O :>B>@KE <>6=> >?@545;8BL ;8HL >B=>A8B5;L=K5 7=0G5=8O. #25;8G5=85 G8A;0 <8:@>A>AB>O=89 A8AB5<K 2> <=> 38E A;CG0OE <>6=> A2O70BL A @>AB>< =5C?>@O4>G5==> AB8 2 MB>9 A8AB5<5, A ?5@5E>4>< : 1>;55 25@>OB=K< @0A?@545;5=8O< M=5@388 A8AB5<K. AE>4O 87 A>>B=> H5=8O >;LF<0=0, <>6=> 40BL <>;5:C;O@=>-:8=5B8G5-A:>5 >?@545;5=85 M=B@>?88. -=B@>?8O 5ABL <5@0 25@>OB=>AB8 ?@51K20=8O A8AB5<K 2 40==>< A>AB>O=88 8;8 <5@0 =5C?>@O 4>G5==>AB8 A8AB5<K. 06=>5 7=0G5=85 ?>=OB8O M=B@>?88 A2O70=> A B5<, GB> =0 >A=>25 MB>9 25;8G8=K <>6=> ?@>3=>78@>20BL =0?@02;5=85 A0<>?@>872>;L=>3> ?@>B5:0=8O ?@>F5A A>2. 4=0:> ?@8<5=8<>ABL 87<5@5=8O M=B@>?88 :0: :@8B5@8O =0?@02;5==>AB8 ?@>F5AA>2 >3@0=8G8205BAO 87>;8@>20==K<8 A8AB5<0<8 2 A>>B25BAB288 A D>@<C ;8@>2:>9 2B>@>3> =0G0;0 B5@<>48=0<8:8. 8. -=5@38O 811A0  :0G5AB25 :@8B5@8O A0<>?@>872>;L=>AB8 ?@>F5A A>2 2 >B:@KBKE 8 70:@KBKE A8AB5<0E 22>48BAO =>20O DC=:F8O A>AB>O=8O  M=5@38O 811A0. -B0 DC=:F8O ?>;CG8;0 =0720=85 2 G5ABL 25;8:>3> 0<5@8:0=A:>3> D878:0 . #. 811A0 (1839 1903), :>B>@K9 2K25; MBC DC=:F8N, 0 70B5< 8A?>;L7>20; 2 B5@<>48=0<8G5A:8E @01>B0E. -=5@38O 811A0 >?@545;O5BAO G5@57 M=B0;L?8N  8 M=B@>?8N S A ?><>ILN A>>B=>H5=89: G = H  S, G = H  S. 0 >A=>25 M=5@388 811A0 2B>@>5 =0G0;> B5@<>48=0 <8:8 <>6=> AD>@<C;8@>20BL A;54CNI8< >1@07><: 2 87>10@=>-87>B5@<8G5A:8E CA;>28OE (@, " = const) 2 A8AB5<5 A0<>?@>872>;L=> <>3CB >ACI5AB2;OBLAO B>;L:> B0:85 ?@>F5AAK, 2 @57C;LB0B5 :>B>@KE M=5@ 38O 811A0 A8AB5<K C<5=LH05BAO (G <0). A> AB>O=88 @02=>25A8O M=5@38O 811A0 A8AB5<K =5 <5 =O5BAO (G = const, AG = 0). G < 0, @, " = const. 7 87;>65==>3> 2KB5:05B, GB> M=5@38O 811A0 83@0 5B 1>;LHCN @>;L 2 87CG5=88 18>M=5@35B8G5A:8E ?@> F5AA>2. ! ?><>ILN MB>9 DC=:F88 A>AB>O=8O <>6=> ?@>3=>78@>20BL =0?@02;5=85 A0<>?@>872>;L=KE ?@> F5AA>2 2 18>;>38G5A:8E A8AB5<0E 8 @0AAG8BK20BL <0:-A8<0;L-=> 4>AB868<K9 . -=5@38O 811A0 G B0: 65, :0: 8 M=B0;L?8O , O2;O5B AO DC=:F859 A>AB>O=8O A8AB5<K. >MB><C 87<5=5=85 M=5@388 811A0 G <>65B 8A?>;L7>20BLAO 4;O E0@0: B5@8AB8:8 E8<8G5A:8E ?@52@0I5=89 0=0;>38G=> 87<5 =5=8N M=B0;L?88 . #@02=5=8O @50:F88, 4;O :>B>@KE C:07K205BAO A>>B25BAB2CNI55 MB8< @50:F8O< 87<5=5=85 M=5@388 811A0, B0:65 =07K20NBAO B5@<> E8<8G5A:8<8. %8<8G5A:85 @50:F88, ?@8 ?@>B5:0=88 :>B>@KE ?@> 8AE>48B C<5=LH5=85 M=5@388 811A0 A8AB5<K (G < 0) 8 A>25@H05BAO @01>B0, =07K20NBAO M:75@3>=8G5A:8<8. 50:F88, 2 @57C;LB0B5 :>B>@KE M=5@38O 811A0 2>7@0A B05B (G > 0) 8 =04 A8AB5<>9 A>25@H05BAO @01>B0, =07K20NBAO M=45@3>=8G5A:8<8. K2545==0O =0 >A=>25 2B>@>3> =0G0;0 B5@<>48=0 <8:8 M=5@38O 811A0 O2;O5BAO DC=:F859 A>AB>O=8O. !;54>20B5;L=>, B0: 65, :0: 8 4;O M=B0;L?88, <>65B 1KBL AD>@<C;8@>20= 70:>= 5AA0 4;O M=5@388 811A0 2 A;54CNI59 D>@<5: 87<5=5=85 M=5@388 811A0 ?@8 >1@07>20=88 7040==KE ?@>4C:B>2 87 40==KE @50 35=B>2 ?@8 ?>AB>O==KE 402;5=88 8 B5<?5@0BC@5 =5 7028A8B >B G8A;0 8 2840 @50:F89, 2 @57C;LB0B5 :> B>@KE >1@07CNBAO MB8 ?@>4C:BK. 06=K9 ?@8<5@ ?@8<5=5=8O 70:>=0 5AA0  @0AG5B M=5@388 811A0 @50:F88 >:8A;5=8O 3;N:>7K 48:8A;>-@>4><. 7<5=5=85 M=5@388 811A0 2 MB>9 @50:F88 ?@8 @ = 101 :0 8 " = 298, >?@545;5==>5 2=5 >@30=87<0, @02=> G =  2880 :6/<>;L. !>>B25BAB2CNI55 B5@ <>E8<8G5A:>5 C@02=5=85 70?8AK205BAO 2 2845: !6126 + 62 = 6!2 + 62,Gp-O =  2880 :6/<>;L.  :;5B:0E >@30=87<0 MB0 @50:F8O >ACI5AB2;O5BAO G5@57 F5;K9 @O4 ?>A;54>20B5;L=KE AB0489, 87CG5= =KE 18>E8<8:0<8. >6=> ?@54A:070BL 8AE>4O 87 70 :>=0 5AA0, GB> AC<<0 87<5=5=89 M=5@388 811A0 2> 2A5E ?@><56CB>G=KE @50:F8OE @02=0 Gp-O: G1 + G2 + G3 + & +Gn = Gp-O . -=5@38O 811A0 @50:F88 @02=0 0;351@08G5A:>9 AC<<5 M=5@389 811A0 >1@07>20=8O AB5E8><5B@8-G5A:>3> :>;8G5AB20 ?@>4C:B>2 70 2KG5B>< 0;35 1@08G5A:>9 AC<<K M=5@389 811A0 >1@07>20=8O AB5E8><5B@8G5A:>3> :>;8G5AB20 @5035=B>2: Gp-O = (ncGc + nDGD)-(nAGA + nBGB). 9. 0AB2>@K. ;0AA8D8:0F8O @0AB2>@>2 > 03@530B=><C A>AB>O=8N @0AB2>@K <>3CB 1KBL 30 7>>1@07=K<8, 684:8<8 8 B25@4K<8. N1>9 @0AB2>@ A>AB>8B 87 @0AB2>@5==KE 25I5AB2 8 @0AB2>@8B5;O, E>BO MB8 ?>=OB8O 2 8725AB=>9 AB5?5=8 CA;>2=K. 0?@8<5@, 2 7028A8<>AB8 >B A>>B=>H5=8O :> ;8G5AB20 A?8@B0 8 2>4K MB0 A8AB5<0 <>65B 1KBL @0A B2>@>< A?8@B0 2 2>45 8;8 2>4K 2 A?8@B5. 1KG=> @0AB2>@8B5;5< AG8B0NB B>B :><?>=5=B, :> B>@K9 2 @0AB2>@5 =0E>48BAO 2 B>< 65 03@530B=>< A> AB>O=88, GB> 8 4> @0AB2>@5=8O. #G5=85 > @0AB2>@0E ?@54AB02;O5B 4;O <548:>2 >A>1K9 8=B5@5A ?>B><C, GB> 206=59H85 18>;>38G5A:85 684 :>AB8  :@>2L, ;8<D0, <>G0, A;N=0, ?>B O2;ONBAO @0AB 2>@0<8 A>;59, 15;:>2, C3;52>4>2, ;8?84>2 2 2>45. 8>;>38G5A:85 684:>AB8 CG0AB2CNB 2 B@0=A?>@B5 ?8 B0B5;L=KE 25I5AB2 (68@>2, 0<8=>:8A;>B, :8A;>@>40), ;5:0@AB25==KE ?@5?0@0B>2 : >@30=0< 8 B:0=O<, 0 B0:65 2 2K2545=88 87 >@30=87<0 <5B01>;8B>2 (<>G528=K, 18 ;8@C18=0, C3;5:8A;>3> 3070 8 B. 4.). ;07<0 :@>28 O2;O 5BAO A@54>9 4;O :;5B>:  ;8<D>F8B>2, M@8B@>F8B>2, B@><1>F8B>2.  684:8E A@540E >@30=87<0 ?>445@68205BAO ?>AB>O= AB2> :8A;>B=>AB8, :>=F5=B@0F88 A>;59 8 >@30=8G5A:8E 25I5AB2. "0:>5 ?>AB>O=AB2> =07K205BAO :>=F5=B@0 F8>==K< 3><5>AB07><. ;0AA8D8:0F8O @0AB2>@>2 0AB2>@K 25I5AB2 A <>;O@=>9 <0AA>9 <5=LH5 5000 3/<>;L =07K20NBAO @0AB2>@0<8 =87:><>;5:C;O@=KE A> 548=5=89 (!), 0 @0AB2>@K 25I5AB2 A <>;O@=>9 <0A A>9 1>;LH5 5000 3/<>;L  @0AB2>@0<8 2KA>:><>;5:C ;O@=KE A>548=5=89 (!). > =0;8G8N 8;8 >BACBAB28N M;5:B@>;8B8G5A:>9 48A A>F80F88 @0AB2>@K ! ?>4@0745;ONB =0 420 :;0A A0  @0AB2>@K M;5:B@>;8B>2 8 =5M;5:B@>;8B>2. 0AB2>@K M;5:B@>;8B>2  @0AB2>@K 48AA>F88 @CNI8E =0 8>=K A>;59, :8A;>B, >A=>20=89, 0<D>-;8B>2. 0?@8<5@, @0AB2>@K KN3, HCl, , l()3 , 3;8F8=0. -;5:B@8G5A:0O ?@>2>48<>ABL @0AB2>@>2 M;5:B@> ;8B>2 2KH5, G5< @0AB2>@8B5;O. 0AB2>@K =5M;5:B@>;8B>2  @0AB2>@K 25I5AB2, ?@0:B8G5A:8 =5 48AA>F88@CNI8E 2 2>45. 0?@8<5@, @0AB2>@K A0E0@>7K, 3;N:>7K, <>G528=K. -;5:B@8G5 A:0O ?@>2>48<>ABL @0AB2>@>2 =5M;5:B@>;8B>2 <0;> >B;8G05BAO >B @0AB2>@8B5;O. 0AB2>@K ! (M;5:B@>;8B>2 8 =5M;5:B@>;8B>2) =0 7K20NBAO 8AB8==K<8 2 >B;8G85 >B :>;;>84=KE @0AB2> @>2. AB8==K5 @0AB2>@K E0@0:B5@87CNBAO 3><>35= =>ABLN A>AB020 8 >BACBAB285< ?>25@E=>AB8 @0745;0 <564C @0AB2>@5==K< 25I5AB2>< 8 @0AB2>@8B5;5<. 07 <5@ @0AB2>@5==KE G0AB8F (8>=>2 8 <>;5:C;) <5=LH5 10-9<. >;LH8=AB2> !  ?>;8<5@K, <>;5:C;K :>B>@KE (<0:@><>;5:C;K) A>AB>OB 87 1>;LH>3> G8A;0 ?>2B> @ONI8EAO 3@C??8@>2>: 8;8 <>=><5@=KE 725=L52, A> 548=5==KE <564C A>1>9 E8<8G5A:8<8 A2O7O<8. 0AB2> @K ! =07K20NBAO @0AB2>@0<8 ?>;8M;5:B@>;8B>2.  ?>;8M;5:B@>;8B0< >B=>AOBAO ?>;8:8A;>BK (35?0 @8=, ?>;8045=8;>20O :8A;>B0, ?>;80A?0@038=>20O :8A ;>B0 8 4@.), ?>;8>A=>20=8O (?>;8;878=), ?>;80<D>;8-BK (15;:8, =C:;58=>2K5 :8A;>BK). !2>9AB20 @0AB2>@>2 ! ACI5AB25==> >B;8G0NBAO >B A2>9AB2 @0AB2>@>2 !. >MB><C >=8 1C4CB @0A A<>B@5=K 2 >B45;L=>< @0745;5. 0==0O 3;020 ?>A2O I5=0 @0AB2>@0< =87:><>;5:C;O@=KE M;5:B@>;8B>2, 0<D>;8B>2 8 =5M;5:B@>;8B>2. 10. >40 :0: @0AB2>@8B5;L !0<K< @0A?@>AB@0=5==K< @0AB2>@8B5;5< =0 =0H59 ?;0=5B5 O2;O5BAO 2>40. 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"0:, ?@8 :>=F5=B@0F88 Na2CO3 0,001 <>;L/; AB5?5=L 384@>;870 A>AB02;O5B 34%.  >1I5< A;CG05 A?@0254;82K A;54CNI85 70:>=> <5@=>AB8. 1. 84@>;87 A>;8 4>;65= CA8;820BLAO A ?>2KH5 =85< B5<?5@0BC@K 8 @07102;5=85< @0AB2>@0. 2. @8 >1@0B8<>< 384@>;875 2 A>>B25BAB288 A ?@8= F8?>< 5 (0B5;L5 ?@>F5AA 4>;65= ?>402;OBLAO ?@8 ?>4:8A;5=88 (5A;8 MB0 A>;L >1@07>20=0 A8;L=>9 :8A ;>B>9 8 A;01K< >A=>20=85<, =0:0?;820NBAO 8>=K ) 8;8 ?@8 ?>4I5;0G820=88 (5A;8 A>;L >1@07>20=0 A;0 1>9 :8A;>B>9 8 A8;L=K< >A=>20=85<, =0:0?;820NBAO 8>=K ). 3. 84@>;87 A>;59, 2 @57C;LB0B5 :>B>@>3> >1@07CNBAO <0;>@0AB2>@8<K5 8;8 307>>1@07=K5 ?@>4C:BK, C40;ON I85AO 87 AD5@K @50:F88 (?@8=F8? A<5I5=8O @02=>25 A8O), =5>1@0B8<. 0?@8<5@, 384@>;87 Pb(SO4)2 ?@>B5 :05B ?>;=>ABLN 2A;54AB285 >1@07>20=8O >A04:0 PbO2: Pb(SO4)2 + 22O! PbO2 + 2H2SO4. 84@>;87 E0@0:B5@5= 4;O <=>38E :;0AA>2 =5>@30=8 G5A:8E 8 >@30=8G5A:8E A>548=5=89. 84@>;87 =5>@30 =8G5A:8E A>548=5=89 2065= 4;O >F5=:8 8E B>:A8G=> AB8. 84@>;87 >@30=8G5A:8E A>548=5=89 ?@8<5=ONB 4;O ?>;CG5=8O F5==KE ?@>4C:B>2 87 4@525A8=K, 68@>2, MD8@>2 8 8=>3>, => >A>15==> 206=CN @>;L 384@>;87 83@05B 2 687=545OB5;L=>AB8 682KE >@30=87<>2. 26. 50:F8O >A0645=8O 8 @0AB2>@5=8O  >1<5==K< @50:F8O<, ?@>B5:0NI8< 2 @0AB2>@5 M;5:B @>;8B>2, >B=>AOBAO @50:F88 >A0645=8O 8 @0AB2>@5=8O. 50:F88 >A0645=8O A>?@>2>640NBAO 2K?045=8 5< >A04:>2. 50:F88, A>?@>2>640NI85AO @0AB2>@5=85< >A04:>2, =07K20NBAO @50:F8O<8 @0AB2>@5=8O. (8@>:> 8A?>;L7CNB A8AB5<K, A>AB>OI85 87 >A04:0 B@C4=>@0AB2>@8<>3> M;5:B@>;8B0 8 =0AKI5==>3> @0AB 2>@0 =04 =8<.  B0:8E A8AB5<0E <564C =0AKI5==K< @0AB2>@>< 8 >A04:>< CAB0=02;8205BAO 48=0<8G5A:>5 @02=>25A85. A;54AB285 =87:>9 @0AB2>@8<>AB8 :>=F5= B@0F8O B@C4=>@0AB2>@8<>3> M;5:B@>;8B0 2 @0AB2>@5 >G5=L <0;0, ?>MB><C <>6=> AG8B0BL, GB> 2 @0AB2>@5 >= ?>;=>ABLN 48AA>F88@>20=. =0G5 3>2>@O, 48=0<8G5 A:>5 @02=>25A85 2 =0AKI5==>< @0AB2>@5 CAB0=02;820 5BAO <564C B25@4>9 D07>9 25I5AB20 8 ?5@5H54H8<8 2 @0AB2>@ 8>=0<8. 0?@8<5@, 2 =0AKI5==>< @0AB2>@5 AgCl 8<55B <5AB> @02=>25A85: AgCl(T) ! Ag+(p) + Cl-(@). >=F5=B@0F8O B25@4>9 D07K AgCl :0: 25;8G8=0 ?> AB>O==0O 87 2K@065=8O 4;O :>=AB0=BK @02=>25A8O 8A :;NG05BAO. 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"0:, 2 <>;5:C;5 !O2 AB5?5=L >:8A;5=8O ! @02=0 +4, 0 2 <>;5:C;5 !4 AB5?5=L >:8A;5=8O ! @02=0  4. 0;5=B=>ABL 65 C3;5@>44 0 8 2 B><, 8 2 4@C3>< A>548=5=88 @02=0 IV. 5A<>B@O =0 C:070==K5 2KH5 =54>AB0B:8, 8A?>;L7> 20=85 ?>=OB8O AB5?5=8 >:8A;5=8O C4>1=> ?@8 :;0AA8 D8:0F88 E8<8G5A:8E A>548=5=89 8 A>AB02;5=88 C@02 =5=89 >:8A;8B5;L=>-2>AAB0=>28B5;L=KE @50:F89. @8 >:8A;5=88 M;5<5=B0 AB5?5=L >:8A;5=8O C25;8 G8205BAO, 8=0G5 3>2>@O, 2>AAB0=>28B5;L ?@8 @50:F88 ?>2KH05B AB5?5=L >:8A;5=8O. 0>1>@>B, ?@8 2>AAB0=>2;5=88 M;5<5=B0 AB5?5=L >:8A;5=8O ?>=8605BAO, B. 5. ?@8 @50:F88 >:8A;8B5;L C<5=LH05B AB5?5=L >:8A;5=8O. "0:8< >1@07><, <>6=> 40BL 8 B0:CN D>@<C;8@>2:C >:8A;8B5;L=>-2>AAB0=>28B5;L=KE @50:F89: >:8A;8 B5;L=>-2>AAB0=>28B5;L=K<8 @50:F8O<8 =07K20 NBAO @50:F88, ?@>B5:0NI85 A 87<5=5=85< AB5?5=8 >:8A;5=8O 0B><>2 M;5<5=B>2, 2E>4OI8E 2 A>AB02 @5038@CNI8E 25I5AB2. 28. :8A;8B5;8 8 2>AAB0=>28B5;8 ;O ?@>3=>70 ?@>4C:B>2 8 =0?@02;5=8O >:8A;8B5;L=>-2>AAB0=>28B5;L=KE @50:F89 ?>;57=> ?><=8BL, GB> B8?8G =K<8 >:8A;8B5;O<8 O2;ONBAO ?@>ABK5 25I5AB20, 0B><K :>B>@KE 8<5NB 1>;LHCN - > 3,0 (M;5<5=BK VIA 8 VIIA-3@C??). 7 =8E =081>;55 A8;L=K5 >:8A;8B5;8 DB>@ (- = 4,0), :8A;>@>4 (- = 3,0), E;>@ (- = 3,5).  206 =K< >:8A;8B5;O< >B=>AOBAO PbO2 , KMnO4 , C0(SO4)2 , 2!r2O7 , HClO, HClO3, !IO4, NaBiO3, H2SO4(:>=F), HNO3(:>=F) , Na2O2 , (NH4)2S2O8 , !IO3 , H2O2 8 4@C385 25I5AB20, :>B> @K5 A>45@60B 0B><K A 2KAH59 8;8 2KA>:>9 !.  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