XXII Турнир им. М.В. Ломоносова 1999 года. Задания. Решения. Комментарии

XXII . . , 1999 . : . . ( ), . . ( ), ...

Author: Кулыгин А.К.

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XXII . .

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' " ! , ". "" # M % # '! " ". ,% ! "/ H = # ' " "# jv)2 ; Mv02 = M (v2 +2v jv +(jv)2 ;v2 )= M (2v jv +(jv)2 ) jE = M (v0 + 0 2 2 2 0 0 2 0 .+ , ! .+ v0 . v0 ". # < = ! ' < ". ) ' . ("+ \) ! " H # ' ! " % "!: ' . = H !" ': ' #! " H !". #"# " % , "! "" | < H .

51

;!" 0 # %N" : ! % { . N , , , , ! , %.

1. -' ' '" ( ? " " : : : H&& # " / /! "/ =. 7{8 "". 1) : : : = CaO + : : : 2) 3 : : : + N2 = Ca3 N2 3) : : : + 2H2 O = H2 SO4 + 2HCl 4) CaH2 + H2 O = Ca(OH)2 + 5) : : : = 2CuO + 4NO2 + O2

)

:::

9{11 "". (" ' " " 57) 1) 1 : : : + 5 : : : = 3 : : : + 4 : : : 2) 4 : : : + 11O2 = 2 : : : + 8SO2 3) 3Cl2 + 6 : : : = : : : + 5KCl + H2 O 4) : : : + 6H2 O = Mg(OH)2 + 2NH3 5) : : : + 3 : : : = 3HCl + H3 PO4 6) FeSO4 + KMnO4 + H2 SO4 = MnSO4 + : : : + K2 SO4 + H2 O 2. (7{9 "") Q! "= % ' %, ! "" ? " " " (58 2)%. * < & # ? ", >? H " >. 3. (7{9 "") % " , ! ""# ' = #<>" # !", ""# H ' < #. # ""#, # ' # H , ' ! " # . $ < H N" .? 4. (8{9 "") #= + (CaCO3) ' " 100 " " = " # " "" = = 73%. 9 % ! " HCl " .+". + < .+" . ' "/ > "" +. 5. (10{11 "") 437 "' / " . * H # ". 784 % ( . .). * " < ' " ' !

" #' " , #= " " %# " #. ' ! "

#= ! "

#= " " "'. 6. (8{10 "") 0<: | H , " <? % ' = =, D2 O. ' ". <: = #. 7. (9{11 "") I #= / + +: %'

#/ '# " "? = " " = < ".>. "# '# / . 52

V ". % ' = '# " = . 0 + : %'

= " , ! ' H % " " "! " ? " . < = '# " " =, # " #= >!= %. * " % + '# "". " " < "., ! ' + "/ =, ' /! " " =" | " < ' = '#. * " , + .> ', ' % +: ". #= %# " "'#+ = ' <: " & # ' ". 9 / ". '/ # + / % '" " '" > #= /? 8. (10{11 "") $> " < . " " " C3 H3 Cl3 ? % % " % < # % #. 9. (9{11 "") * ". '

# & # /! "/ ? " " " " " / ' , %

# . (, + < %'". "!" {\). 1 AgBr % #= 2 BN >? ? " 3 C12 H25 SO3 Na &C C &C 4 CaSO4 05H2 O " '"#' 5 CCl2 F2 ' >?/ " " 6 ClCN ' ' / ( 7 KAl(SO4 )2 12H2 O ' . H ' V 8 Kr " """

#/

#/ = 9 Na2 O2 ' " #/ " 10 Na2 S2 O3 5H2 O ' ' + = $ 11 Pb3 O4 " !" . ? " (& &) 1 12 S " . #= 13 ZnO &"< (& &) ) 14 ZrO2 /

10. (10{11 "") * ' ! " " " ' ' , ' ' , ' -1,4 1- ' ' ? " N: , #= ' N: " (%

' / < " /), # >? " ' "< < ! " H = " ". ' N: " < ' ' '/ "/ = " ".

53

( $

, % . @. , O ) *1033 . , ,. &. .

1. 7{8 "". 1) CaCO3 = CaO + CO2 G Ca(OH)2 = CaO + H2 O, . . 2) 3Ca + N2 = Ca3 N2 3) SO2 Cl2 + 2H2 O = H2 SO4 + 2HCl 4) CaH2 + 2H2 O = Ca(OH)2 + 2H2 5) 2Cu(NO3 )2 = 2CuO + 4NO2 + O2 9{11 "". 1) C3 H8 + 5O2 = 3CO2 + 4H2 O 2) 4FeS2 + 11O2 = 2Fe2 O3 + 8SO2 3) 3Cl2 + 6KOH = KClO3 + 5KCl + 3H2 O 4) Mg3 N2 + 6H2 O = 3Mg(OH)2 + 2NH3 5) POCl3 + 3H2 O = 3HCl + H3 PO4 6) 10FeSO4+2KMnO4 +8H2 SO4 = 2MnSO4 +5Fe2 (SO4 )3 +K2 SO4 +8H2 O 2. "" (58 2)% % ! , ! " NaX "" X < #. 23 : 60 40 = 153 23 : 56 44 = 18, " Na2 X "" X " " 303 36. * # " =, # ' / : Na2 O2 , Na2 S, NaOH, NaNH2 , NaBH2 D2 . 3. H # "? " . " ./ % ' ( ". #

H " <. % !" = ). % '# ' -% "' " # ' . X"' . '

"" | H " % +

! " / ' #/ % '

H .

H ! # ' # , ' H # . (". '! | %# #= & ""#, ". .+ ""#, " ' <>? % % ' = ("" #= H H , # " ' % , E = mc2 ). 4. ," " = " # " < 73 HCl, ! " " 73=365 = 02 .. > "' ' H ! ", ". 01 .. ; CaCO3 + 2HCl = CaCl2 + H2 O + CO2 ' %# , ! ' H %"/ ". 01=2 = 005 . .. + .+" , % ! N: , " . , "" .+". 23 = 8 %, V = 34 R3 . 54

" , ' 7=8 "/ ! " .. 0 % , "/ ! " CaCO3 005 : 7 8 = 0057. Mr = 100. "" 100 0057 = 57 . 5. 4 37 "' ' " % 784=224 = 035 . %. 1 ., ! !. : ! . : / /, " = H "' " " 437=(035 2) = 624. * H % " # # < # #. #, "' " " . ! , ! % | =. ( H ( "") 7. - !, H < #. ?: .+ . X " > =. ( "" 9, / , % ! H 45. = " " , " " ?: ! LiOH, %>? =" ' " . 0 ' .

< = ! "

#= " " "'. *". " " x . Li y . Be. * " "' # " (05x + y) . H2 . 7x + 9y = 437G 05x + y = 035. "> x = 049 .. y = 0105 .. 6. * ". <: = # < . " >? % : ! , ! N: # # ' ! % " ' " > " N: # H2 O. - ! N: ( ' , 1 "3 ) " < " . < . "" < = # !". (16 + 2 + 2)=(16 + 1 + 1) = 20=18 = 111 %. 0 ' ". H2 O 1 ="3 , ' ". D2 O 111="3 . 7. ' = ' # ., = . ("' " .>) - ? ! ( ' , ), . = | "' , #= ' = ' " < ".>. * "% = " " ' (<: " & =). 9 " " ' / % '" ", !" " !>? " #, ! ? ! .% ' . , < .% ' . '## " % # ? ", %" >" # ' ' + . . / % '" " / # " . ! . , ! /

% < ' . '## " % " # ? ". * " / '# . .+ ! " ? " % . "' .% . %? # !, !+ ", ?: !+ ' . '## ' =.

55

8. 1 = # % #: CH3 ; CCl = CCl2 CH2 Cl ; CH = CCl2 CHCl2 ; CH = CHCl (2 ! "/ % ) l3 ; CH = CH2 CHCl2 ; CCl = CH2 CH2 Cl ; CCl = CHCl (2 ! "/ % ) 6! " % #:

Cl

H Cl C C C H

Cl

H

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* % H/ < "? " . / ! "/ % , %" " , ' # # / " . . = # % < "? " / '! "/ % (. . , "%

#= " / , " " ! ".) 9. #: 1. AgBr " !" . 1 ? " (& &) 2. BN % #= 3. C12 H25 SO3 Na ' >?/ " " 4. CaSO4 05H2 O " . #= 5. CCl2 F2 / 6. ClCN >? ? " 7. KAl(SO4 )2 12H2 O ' ' + = $ 8. Kr

' . H ' V 9. Na2 O2 =">? ? " % >?/ ' %/ 10. Na2 S2 O3 5H2 O &"< (& &) ) 11. Pb3 O4 ' " #/ " 12. S ' ' / ( 13. ZnO " '"#' 14. ZrO2 " """

#/

#/ =

56

10. : C3 H4 , C3 H6 , C5 H8 , C7 H10 . *". " ". " < x, y, z k . H/ ? ", " "

. 9" 9" . H2 9" . CO2 , ? " . ' # +/" ' ? " ? " " ? " C3 H4 x 2x 3x C3 H6 y 1y 3y C5 H8 z 2z 5z C7 H10 k 3k 7k ;" %! ' % " ". 2(2x + y + 2z + 3k) = 3x + 3y + 5z + 7k: "> x ; y ; z ; k = 0 x = y + z + k. $ ! " ' ' " " (" "

, N: " < '/) 05 50%.

2#% , 3% #'! 4 1 9{11 , %%#'

" / H = %!, %

#/ + . 0 , # '? 3 ' !. 1. " 4) : : : + 6H2 O = Mg(OH)2 + 2NH3 # ' ! 4) : : : + 6H2 O = Mg(OH)2 + NH3 (' '? H&& 2 ' NH3 , % . >

% < ). 2. " 5) : : : + 3 : : : = 3HCl + H3 PO4 < # #. 5) : : : + 3 : : : = 3HCl + H3 PO4 (H3 PO3 " H3 PO4). * H ' % " 5) PCl3 + 3H2 O = 3HCl + H3 PO3 %. H = + %! "". =, " =. 3. " 6) FeSO4 + KMnO4 + H2 SO4 = MnSO4 + : : : +K2 SO4 + H2 O # ' ! 6) FeSO4 + KMnO4 + H2 SO4 = MnSO4 + : : : + H2 O (' '? K2 SO4 ' = !" ) " , ! + . < % H/ + ( "., ! ". ) '" '. # =. 57

( $ 1.

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