Icho39_BTchuan Bi-ly Thuyet

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K thi Olympic Ha hc Quc t ln th 39Ha hc: s kt hp gia khoa hc, ngh thut v bt ng

BI TP CHUN B (Phn l thuyt)

15-24/7, 2007 Moscow, Nga

MC LC Problem 1. ON THE BORDERS OF THE PERIODIC SYSTEM .................................................................................................... 3 Problem 2. SCHRDINGER CAT AND CHEMISTRY..................................................................................................................... 4 Problem 3. QUANTUM UNCERTAINTY ............................................................................................................................................ 6 Problem 4. QUANTUM CHEMISTRY OF VISION............................................................................................................................ 7 Problem 5. NANOPARTICLES AND NANOPHASES...................................................................................................................... 8 Problem 6. IN WHICH DIRECTION DOES A CHEMICAL REACTION PROCEED?............................................................... 10 Problem 7. LE CHATELIERS PRINCIPLE ...................................................................................................................................... 11 Problem 8. DMITRY IVANOVICH MENDELEEV: WHAT BESIDES THE PERIODIC TABLE?............................................. 13 Problem 9. KINETICS OF A FREE RADICAL REACTION ........................................................................................................... 14 Problem 10. ASYMMETRIC AUTOCATALYSIS AMPLIFICATION OF CHIRAL ASYMMETRY........................................ 16 Problem 11. RADIOCARBON DATING ............................................................................................................................................ 17 Problem 12. IRON DETERMINATION.............................................................................................................................................. 18 Problem 13. SULFUR DETERMINATION........................................................................................................................................ 21 Problem 14. MAGNESIUM DETERMINATION ............................................................................................................................... 22 Problem 15. INORGANIC PHOSPHATES: FROM SOLUTION TO CRYSTALS...................................................................... 23 Problem 16. FRUITS, VEGETABLES, ATOMS .............................................................................................................................. 26 Problem 17. CHAMELEONIC COBALT............................................................................................................................................ 29 Problem 18. THE FORMOSE REACTION ....................................................................................................................................... 32 Problem 19. THE ANALOGY IN ORGANIC CHEMISTRY............................................................................................................ 35 Problem 20. KETO-ENOL TAUTOMERISM .................................................................................................................................... 37 Problem 21. UNUSUAL PATHWAYS OF FATTY ACID OXIDATION: ALPHA-OXIDATION ................................................. 38 Problem 22. UNUSUAL PATHWAYS OF FATTY ACID OXIDATION: OMEGA- AND (OMEGA-1)-OXIDATION.............. 41 Problem 23. UNUSUAL PATHWAYS OF FATTY ACID OXIDATION: PEROXIDATION........................................................ 43 Problem 24. BIOLOGICALLY ACTIVE PEPTIDES AND THEIR METABOLIC PATHWAYS................................................. 45 Problem 25. RADICAL POLYMERIZATION .................................................................................................................................... 48 Problem 26. IONIC POLYMERIZATION .......................................................................................................................................... 50 Problem 27. CO-POLYMERIZATION ............................................................................................................................................... 53 Problem 28. TUNNELING IN CHEMISTRY ..................................................................................................................................... 56

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Olympic Ha hc quc t ln th 39 Bi tp chun b

Bi 1. Bn v th t sp xp cc nguyn t trong bng h thng tun hon

Bng h thng tun hon u tin c nh ha hc Nga D. I. Mendeleev a ra nm 1869 vi cch sp xp cc nguyn t bit vo thi theo th t tng dn khi lng nguyn t. Nm 1871 Mendeleev cng b bi bo "H thng bn cht cc nguyn t v ng dng ca n xc nh tnh cht cc nguyn t cha bit" trn t Tp ch Ha hc Nga. Trong bi bo ny th Mendeleev miu t chi tit v tnh cht ca ba nguyn t vn cha c tm ra v c ng t tn l ekabo (Eb), eka nhm (Ea), v ekasilic (Es). Tt c chng u c tm ra 15 nm sau . 1. Tn hin ti ca c ba nguyn t c Mendeleev tin on l g ? Rt th v l tn ca cc nguyn t ny u c ngun gc a l. Bng H thng thun hon u tin ch gm 66 nguyn t v ba trong s vn cha c bit. Vo thi im hin nay th ngi ta bit c 118 nguyn t. Nguyn t th 118 c tm ra nm 2005 khi hai vin Nghin cu Ht nhn (Nga) v vin Livermore (M) tin hnh bn ph ht nhn 249Cf bng 48Ca th nguyn t th 118 c to thnh vi s khi A = 294 ng thi qu trnh bn ph ny lm gii phng ba ht . 2. Vit v cn bng phn ng ht nhn: i) tng hp nguyn t 118 v ii) S phn r ca nguyn t ny.

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Olympic Ha hc quc t ln th 39 Bi tp chun b

3. Nguyn t th 118 thuc nhm no ca bng H thng tun hon ? Vit cu hnh electron ca n (vit phn kh him v cu hnh e lp ngoi cng). 4. Da vo tnh cht ca cc nguyn t cng nhm vi nguyn t th 118 v s dng kh nng suy lun hy d on cc tnh cht sau ca nguyn t th 118: i) nhit nng chy, ii) nhit si, iii) bn knh nguyn t, iv) th ion ha th nht, v) cng tc oxit cao nht ca.

Bi 2. Con mo ca Schrodinger v Ha hc Rt nhiu cc hin tng ha hc c th c gii thch bng cc l thuyt vt l. L thuyt chnh ca ha hc l l thuyt lng t, n l mt nn mng vng chc quan st c s bin i tun hon ca Ha hc. Mt trong s nhng hn tng ca c hc lng t l nguyn l chng cht trng thi c pht biu nh sau: Nu mt h lng t c th c xc nh trng thi 1 v 2 c miu t bi hai hm sng tng ng 1 v 2 th h cng c th c xc nh trng thi hn hp vi hm sng"

= c11 + c22,vi c1 v c2 c trng cho s ng gp ca trng thi 1 v 2 ban u vo trng thi hn hp." Tng ca cc hm sng khc nhau vi cc h s khc nhau c gi l t hp tuyn tnh cc hm sng. Trong mt h lng t hn tp th h lng t tn ti c hai trng thi ban u mt cch ngu nhin. Khi chng ta ang tin hnh mt php o ca h ang trng thi hn hp th php o ny s phi chuyn h sang trng thi thun khit. Chng ta khng bao gi xc nh c trng thi cui ca h, n ch c th c xc nh bng cc nh lut xc sut. Xc sut ca mt h bt k trng thi cui c xc nh bng bnh phng modul ca cc h s t hp tng ng p1 ~ |c1|2, p2 ~ |c2|2. Tt nhin, xc sut tm thy mt h lng t trn ton khu vc bng n v: p1 + p2 = 1. 4

Olympic Ha hc quc t ln th 39 Bi tp chun b

Nguyn l chng cht trng thi ch c th p dng c cho cc h lng t v khng h c ngha khi p dng vo cc h v m. S dng mt my tnh Geiger c th d c electron i vo. My tnh c kt ni vi mt b phn c kh nng p v mt dng c cha cht c bng thy tinh khi c mt tiu phn i vo my d. Gn dng c thy tinh l mt con mo cn sng. Nu tiu phn i vo my d th con mo s b nhim c. Tuy nhin nu my d khng th xc nh c tn hiu v ang trng thi gia pht hin c v khng pht hin c th trng thi ca con mo l sng hay cht. D hiu hn, con mo c th sng hay cht tu thuc vo vic my d c xc nh c mt h lng t hay khng, iu ny l v l. Trong ha hc th nguyn l chng cht trng thi c s dng trong thuyt lai ha, cng hng v MO. Nguyn l chng cht trng thi i vi thuyt lai ha. 1. Mt AO lai ha sp3 l s t hp tuyn tnh gia mt AO s v 3 AO p

sp3 = c1 s + c2 px + c3 p y + c4 pz .i) Gi s rng tt c cc AO u ng gp nh nhau vo AO lai ha th gi tr ca cc hng s t c1 c4 s l ? ii) Tng t, hy tm cc gi tr cho cc h s t hp c1 c3 i vi mt AO lai ha sp2. Nguyn l chng cht trng thi i vi thuyt MO. 2. MO i vi ion phn t H2+ trng thi c bn c dng:

=

1 a 1 b 1s + 1s , 2 2

vi a v b ch nguyn t hydro. Tnh xc sut tm thy electron obitan 1s ca nguyn t Ha ? Nguyn l chng cht trng thi i vi thuyt cng hng 3. Lin kt cng ha tr c mt phn tnh ion. Nh vy hm sng ca mt lin kt gia hydro v halogen c th c biu din bi s t hp tuyn tnh hai hm sng c trng cho trng thi ion (H+Hal) v cng ha tr (H:Hal):

HHal = ccov H:Hal + cion H+Hal5

Olympic Ha hc quc t ln th 39 Bi tp chun b

Trong cun sch ni ting "Bn cht ca lin kt ha hc" (1947) th L.Pauling ch ra rng lin kt trong HCl ch c 17% tnh ion. Tm cc gi tr ca ccht v cion i vi HCl. 4. Mt trong s cc hm sng ca benzen c th c m t bi s t hp tuyn tnh ca cc hm sng tng ng vi hai cng thc Kekule v ba cng thc Dewar:

C6H6

=

+

+

+

+

Vy th tng ca cc h s ng gp ca cc cng thc Kekule vo trng thi ca benzen l bao nhiu ? Trong cc phn ng ha hc th cu trc ca phn t thay i lin tc nn trng thi electron ca phn t l hm ca thi gian. Trong mt vi trng hp th cu trc ca phn t c th c biu din bi mt s chng cht trng thi gia trng thi u v cui vi s ph thuc thi gian. By gi chng ta xem xt mt phn t dao ng gia hai trng thi thun khit, mt vi hm sng 1, v trng thi cn li c hm sng 2, vi tn s . Ban u (t = 0) phn t trng thi thun khit th nht v sau mt na chu k (t = /) th trng thi thun khit th hai 5. Xc nh h s ph thuc thi gian ca s chng cht cc trng thi m t cu trc electron ca phn t. Vit biu thc ca hm sng tng qut sau mt phn t chu k.

Bi 3. S bt nh lng t Mt trong s nhng nh lut lng t chnh ni ln mi lin h gia s bt nh v tr x v v ng lng p ca tiu phn lng t. Tch cc bt nh ny khng c php b hn mt gi tr hng nh - mt na ca hng s Planck:

x p

h 2

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Olympic Ha hc quc t ln th 39 Bi tp chun b

vi momen ng lng l tch ca khi lng v vn tc: p = mV, hng s Planck c gi tr h = 1.051034 Js. 1. Khng