BIENDO!CUAMOTHE Mot he nhiet dong bien doi khi trang thai cua he thaydoi.Di£u nay tuong ung vbi su bien thien cuamot hay nhieuthong sotrang thai.Biendbidupexacdjnh neu trang thai dau va
Trang 1\ TRAN THI D A
Trang 2TRAN TH | BA - BANG TRAN PHACH
( Tdi ban Ian thti nhat )
Trang 4Ldi m m
Hod hoc ngay nay dang6 uao tho ' i ki phat trien manh me Cac uan de li thuyet dupe hoan thien. mo rong ua doi mdi . Cac thanh tuu trong nghien cdu ua trong san xuat ngay cang da dang , phong phu . Cac phuong phdp thac nghiem ngay cang tinh ui ua hdu hieu
da lam cho kho tang kien thdc hoa hoc ngay cang do so hon .
Trade boi canh do , ca ngadi hoc, ngadi day ua ngadi nghien cdu
cang phai nam udng cd sd li thuyet cua nhdng bien doi hod hoc ,
trade het 1 a cua cac phan dng hod hoc .
Cuon sach nay nham cung cap nhdng kien thdc ue :
Co so cua Nhiet dong lac hoc hod hoc .
Co so cua Dong hod hoc .
Moi lien he gida thanh phan, cdu tao ua tinh chat cua
chat tan , dung moi ua dung dich , dac biet 1 a nhdng hieu biet moi ue dung moi long uc,isa sonuat hod .
Li thuyet axit - bazo ua phan dng axit - bazo , dac biet
la uiec phan biet lac axit - bazo trong nadc ua trong dung
moi khac udi nadc . Do axit trong ua ngoai pham ui
thang pH.
Phan dng oxi hod - khd, cO che phan dng, lacoxi hod - khd dac biet la nhdng dng dung cua phan dng oxi hod - khd trong cong nghiep hod chat , trong linh uitc moi
trao ' ng ua trong cuoc song thadng ngay .
Cac hoi dung tren dape uiet 6 hai mdc do khac nhau : mdc do
co ban ua mdc do nang cao . Cac muc co ghi dau * la nhdng kien thdc nang cao , md rong ua di sau udo cosd li thuyet cac phan dnghod hoc .
Bang uiec ket hop hai yeu cdu co ban ua nang cao , chung toi hi
uong rang cuon sach nay khong nhdng la giao trinh giang day cho
sinh uien cac nganh co hoc mon Hod hoc md con doi udi ca sinh
3
Trang 5uien cac nam cud i ua hoc men cao hoc cac trudng Dai hoc ua Cao ddng thuoc chuyen nganh Hod hoc . Dong thdi cuon sach con la tdilieu tham khao cho giao men Trung hoc pho thong, giang men hod hoc cac trudng Dai hoc , Cao dang ua cac can bo nghien cUu
hod hoc.
Sach gom chin chuctng , dupe phan cong bien soan nhu sau :PGS Dang Tran Phach : tie chuang I den chuang V.
PGS Tran Thi Da : tuchuangVI den chuang IX .
Cuon sach chdc con thieu sot. Cac tac gia chan thanh cam an
nhdng y kien dong gop ua phe binh cua cac dong nghiep ua cac ban doc.
Cac tac gia
Trang 6MUC LUC
Lai noidau
Mucluc
35
Ch trong 1
NGUY&NLITHCfNIHATCUANHIETB0NGLUCHOC
1.1 Mot so khai niem va dinh nghla ccf ban
trong nhiet dong life hoc 9
1.1.2.Trangthaicua mothe.Thong so trangthai
10
1.2 Nguyen li thijf nhat cua nhiet dong life hoc
1.2.2.Hamtrangthai noinangU 15
1.2.3.Hamtrangthai entanpiH 18
1.3. Ap dung nguyen li thuf nhat cua nhiet
dong life hoc vao Hoa hoc 22
1.3.1.HieuirngnhietcuaphanCrnghoa hoc 22
1.3.2.Phirong phap tinh hieuPngnhiet 24
1.3.3 Sirphu thuoccuahieuirngnhiet vao nhiet
2.1 Nguyen li thuf hai cua nhiet dong life hoc48
2.1.5.Entropi Chieuhirdngva gidi hancua bien
2.2 Nguyen li thuf ba cua nhiet dong life
hoc tinh entropi tuyet doi cua mot chat 58
:4
2.2.1 Nguyenli thO bacuanhiet dong luc hoc 58
2.2.2.Cach tinhentropituyetdoicua motchat 58
2.2.3.Tinh bienthien entropi trongmotphanung
2.4.3.Kha nang dien biencuamot
2.5.4.Hoa thecuacacchatlong 76
Chirong 3
CAN BANGPHA
3.1 Mot so khai niem
3.2 Bieu kien tong quat ve can blng
CAN BANG HOAHOC
4.1 < Bieu kien tong quat cua can bang hoa hoc
4.2 Khao sat d ' mh lifcfng ve
4.2.1.Hangsocanbang
4.2.2.Canbanghoa hoc dong the4.2.3.Canbanghoahocdi the
84858687
95
96
96971035
Trang 74.3.Quan he gitfa bien thienentanpi tydo
4.4.1.Anhhudngcua n '
niet do
4.4.2.Anhhucfng cua ap suat
Chirong 5
CO SOCUADONGHOAHOC
5.1.Motsokhainiemvadinh nghTa cd ban120
5.1.1.Phanungdongthe va phanungdjthe 120
5.2.Cacyeuto anh hircrng
5.2.1.Anhhudngcuanongdo Khai niemve bac
5.2.2.Anhhudngcuanhiet dp-Nangluong hoat
5.3.Sy tich phan cac phirong trinh dong hoc
5.4.Phudng phapxac dinh bacphanirng 139
5.4.1.Phuong phap dpavaoviec
5.4 4.Phuong phapcolapcuaOstwald 143
5.4.5 Phuongphap dungtoedo dau V0 144
5.5.1.Cacphanirngthuannghjch 145.
5.6 1.Khainiemvecdche phanirng 152
5.6.2.Dinh luatvetoe dovacochephanirng 153
5.6 3 Cac chattrunggian cokhanang phanirng
5.8 4.Xuctac enzimhayxuc tac men 176
5.10.Thuyetphircchat hoatdong 184
Chirong 6
6.1 Khainiemchung ve dungdich 198
6.2 Dung moi long 206
6.3.2.Lyc giura cacphantirtrong dungdichvasy sonvathoa 216
6.4.1.Anhhudngcua cac yeuto
entanpi vaentropi den qua trinh hoatan 222
6.4.5.Dinhluatphanbo.Sy chiet 231
6.5 Dung djeh chufa chat tankhong dienli,
6.5.1 Sy giam ap suat hoi bao hoa
6.5.2 Do tangnhiet do soiva-do giam nhiet do
6.5.4.Xacdinh phantir khoicuachattan 238
6.6.1.Cac“tinh chat nong do"cuadungdich
6.6.2.Syphanlicuacac chattrong
Trang 86.6 3 Dodienli Hang so dienli 243
6.6 4 Dungdich chatdien ii manh 247
6.7.Dung dich chatdienli it tan 248
6.7 2.Tichso tan va sir ket tua 254
6.7 3 Tichsotanva sir hoatan
6.8.Can bdng cua cac ionphirc 258
6.8 1.Sir hinhthanhcacionphirc 259
6.8 2.SutaophUcva do tan
6.8 3 Sutao phucva sirhoa tan
Chwong 7
7.1.Tinhchat doc dao cua proton 268
7.2.Thuyetaxit-bazdAreniuyt 269
7.3.Thuyet axit-bazd cua Bronstet va Lauri
270
7.4 3 Xac dinhpH ,chat chithj 278
7.4.6 Moi quan he giura lire ciia axit va lire ciia
bazdlien hopvdi no
7.4.7 Nhung yeu toanhhudng
289
7.5.* Tichso ionciiadungmoi proton
7.6.Phanbietlife axit-bazd Bronstet
295
7.6 2.Trong dung moi khacnude
7.6.3.Ham axit,pH hieudung
300
7.7.Lifeaxit-bazdtrongpha khi 312
7.8.1.TinhpHciiadung dich dem 317
7.8 2.Tac dungciiadung dich dem 319
7.9.2 Hang sothuy phanva dothuy phan 325
7.9 3 * Sir dung moiphancuacac muoi 3327.10.Phantingtrunghoa.
7.12.1.Axit, baza vaphanirng axit - bazd
3497.12.2.* Motso loai axitLiuytthudng gap 3527.13.*Phanirngaxitva bazd dithe 359
Chwong 8
PHANU NGOXIHOA- KHU
8.1 1.So oxi hoa va phanirng oxi hoa -khir 3678.1.2.Phanirngoxi hoa -khir theo
8.1.3.Phanirngoxi hoa -khirtheocdche
8.1 4 Can bang phudngtrinh
8.2 3 Nang luong Gip
8.2.4.Phudng phapxacdinhthe diencue.
8.3.Cfngdungthe diencifcchuan 394
8.3 1 Luc tudngdoicuacacchat oxi hoa
8.3.2.Duavaothe diencuechuan
deviet phanirngoxi hoa-khirtudienbien 3968.3 3 TinhsUcdiendong cuapin Ganvaniva
bien thien nang luongGipddieu kienchuan 3998.3.4.Dudoan chieu dien bien
7
Trang 98.4 Day dien the cua cac kim loai 402
8.4.1 Cac yeutoanh hudngtdithe diencuecua
8.4.2.Dayhoatdonghoahocva daydien the cua
8.4.4.Hoatdonghoahoccuaphi kim 411
8.5 .Anhhirdngcuanongdo den
the dien cifc vasuredien dong cua pin 412
8.5.2.Hieuirng cua sir thaydoi nong do 413
8.5 3.Hieuirng cua sir tao thanhhop chat it tan
415
8.5 4.Hieulingcuasir taophOc 416
8.6. Sire dien dong va chieu cua
phan irng oxi hoa - khir 421
8.6 1.Sirediendongchuancua pin va
hbngsdcan bang cuaphanirngoxi hoa -khir421
8.6.2.Suedien dongcua pin va chieu cua phan
8.7.* Sir ben oxi hoa - khirtrong nirdc 428
8.7.1 Xay dung mien ben nhiet dong cua nude
428
8.7 2.Sirdungmidnbenciianude 431
8.7 3.Anhhudngcuaqua the 432
8.8 * CacgiandodtJkienthe 432
8.8.2.Ling dungcua giandoLatimer 435
8.8.5.Giandd Frostcodieukien 445
8.9 * Khuynh hirdng ben cua cac
trangthai oxi hoaciiakim loai 446
8.9.2.Cackimloainhom IB,IIBva
Chuong 9
MOTSOVAN BE LfNGDUNGCUAPHANLfNGOXI HOA- KHU 1
9.1 . Pin trong cuoc song 453
9.1.1.Pinso cap(pin khong napdienlai) 4539.1.2.Pincap hai
9.2.1.Cautaova hoat dong
9.2.2.Thephongdien.Quathe 4679.2.3.Tiendoansanpham dien phan 4709.2.4.Cacdinhluat vesu dien phan 4769.2.5.Lfngdung cua sirdien phan 477
9.3 ’ Tach cac dern chat tir hop chat 478
9.3.1.Nhietdonghocciiaquatrinhkhir
9.3.2.Khirquangoxitbang chatkhir 4839.3.3.Sukhirquangoxit
9.3.4.Tachcacnguyentobang
9.4 Sir an mon kim loai va hcfp kim 4929.4.1.Khai niemvdsuan mon kim loai 492
Trang 10Chang 1
Nhiet dong lire hoc la khoa hoc dupe hinh thanh vao gitia theki 19. Ngay nay, nhietdong lire hoc baogom: nhietdonglire hocvatIf, nhiet ddng lire hoc k!thuat va nhiet donglire hoc hoa hoc
Nhiet dong lire hoc hoa hoc la khoa hoc ting dungnhflng nguyen If cuanhietdonglire hoc
vatIfvao viecnghien ctiu cachientupnghoahoc.Dayla noi dungcua cacchuongI,II,IHvaIV
1.1 M 0TSOKHAINIEM VA DINH NGIflACOBANTRONGNHIETDONG LUC HOC
1.1.1.HE NHIETDONG
He nhiet dong,dupegoi tatla he,la ph£n cuaVu trug6m motso ratIon tidu phancau
tao(nguyen tti, phan ttihay ion)"*dangdupe nghien ctiu vadupe phan each vdi phan con lai
cua Vu tru-nidi trucrng ngodi- bang mot ranhgitiithuc hay ao
Hemola he co the traodoi vtii moi trucrngngoaica chatMn nanglupng.
Thf du : Khi dun soi mot sieu nudethi nhiet dupe truyen ttiben ngoai vao he,con he
thi matchatra ben ngoai dudi dang hoi nude
He kin la hechi traodoinanglupng vdi moi trucrng ngoai.
Thidu: Khi cho xtittacdungvdi axit sunfuric trong mot binhkin:
2NaOH + H2S04 > Na2S04 + 2H20
he khong mat chat, nhung he dacung cap nanglupng cho moi truting ngoai vi phan ting
toanhiet
He co lap la he khongtraodoi ca chat lannanglupng vdi moi trucrngngoai.
Thf du:MotbinhDewar1chtia caccha'
tphantingdupe day kfnvabaophu bang mot ldpeach nhiet that day de cho chat vananglupngkhong dupe trao doi vdi moitrucrng ngoai
chatvTmocuahe thay doi dot bienthi he dupegoiladong the.Trongtruting hppngupclai,
Trang 11Toan bophan dong the cua mot he, ma b do thanh phan hoa hoc va tinh chat vat If taimoi diem deu dong nhat dupe goi lamot pha
Hedi the trongthidu btrenla he haipha
1.1.2.TRANG THAI CUA MOTHE.THONG SO TRANGTHAI
Trangthaicua mot he nhiet dong dupe xac dinh bbi mot tap hop cac tri so cuacacdailupngvTmo co the do duoc nhu the tfch, nhiet do,apsuat, khoi lupng .Cac dai lupng nay
dupegoi lacac thong so trang thai hay car thong so nhiet dong
Ngubitachia cac thong so trang thai lam hai loai :
Cac thong so nfdng donhu : nhiet do,apsuat, nongdo, chiet suat,ti khoi,do nhbt
Chung khong phu thuoc vaoluongchat cuahe.
Cacthong so khnech do(variable extensive)nhu the tlch, khoi lupng .Chung ti le vbi
lupng chat cuahe
Trang thai cua he ma bdocac thongso cubng do tai moi chbcua hedong dbu va cogia tri xac dinh dupe goilatrang thai can bang
1.1.3. BIENDO!CUAMOTHE
Mot he nhiet dong bien doi khi trang thai cua he thaydoi.Di£u nay tuong ung vbi su
bien thien cuamot hay nhieuthong sotrang thai.Biendbidupexacdjnh neu trang thai dau
va trang thai cuoi dupe bietro Dubng biendbi chidupe xac dinh khi trang thai dau, trang
thai cuoi va tatcacac trang thai trunggian ma he da traiquaddu dupe biet.
Motbiendbidupe goi la /;bkhitrang thai dau vatrang thaicubi cua he khac nhau
Mot bien dbi dupe goi la kin khi trang thai dau va trang thai cubi cua he giong nhau
Biendbi kin con dupe goi lachit trinh
Mot biendbidupe goi la thnan nghich neu nhung trang thai trung gian ma he traiqua
dupe xem nhu trang thai can bang Co the’
xac dinh don gian tinh thuan nghich cua mot
bien dbi bang each xet xem bien dbi ngupc lai co the xayra dupe hay khong, khi chi thay
dbichut ft trisocuamothay nhieu thong so trangthai
Biendbidupe goila doan nhiet neu nodibn ra trongdibu kien he khong traodbi nhiet
vbi moitrubng ngoai
Khi bien doi dupe thuc hien trongdibu kien apsuat khongdbi,no dupe goila bien doi dang dp ,con trongdibu kien the tfch khongdbi -bien doi dang tich.
1.1.4.HAM TRANGTHAI oucwg bibndoia
Mot ham F cua cac thong so trang thai x, y
se la mot ham trang thai neu gia tri cua no, dbi
vbi mot trang thai cua he, chi phu thuoc vao cac
&uang biena6 i t >
Trang 12thongso trangthai vahoan toankhongphu thuoc vao cacbien doimahedatraiquatrirdcdo.
F2cocungtrj so doivoi cac quatrinhahayb
1.1 4.2. Nhung tinh chat toan hoc cua mot ham trang thai
• Trong mot bien ddi vocung nho, do bien thien dF cua mot ham trang thai F(x,y) cuacac thong sodoclap x va y lamot vi phantoan phan :
Tri socuatich phanchi phu thuoc trangthai dau vatrang thai cuoi
Khi he thuc hien motchu trinh,thi :
frrfIo !hiil d F(x
’ FFIranSthai 1]-Fftrang thai 1 ]=0 (1.3)
Tinhchat cuoi cung:
dyvdx J dx
^Sy J
l 1.4 3 Mot so thi du ve ham trang thai
J ) The '
nang la mot ham trang thai
Xet he gom mot vat co khoi luqng
m.Trang thai 1 dupe xac dinh bdi tri so
h|cua thong so trang thai h (hinh 1.1)
The nang cua he E[ = mgh, + k, k la
mot hang so, g la gia toe trong luc 6
dpcao h2, thenang cua h£la mgh2+ k
Hien nhien hieu cac the nang E2 -Ej=
= mg (h2 -.hj) khong phu thuoc vao
each chuyfin he (2a va 2b) t£r do cao h|
xuongdocaoho
Khoi m
Trang thai Trang thai Trang thai
11
Trang 132 ) Tich PV cua mot khoi khi li tuong la mot ham trang thai .6trang thai (Mukhd 'i khi
n d6i , khoi khf dvao trang thai can
bang cuoi ciing dupe dac trung bdi cac tri so P2 va V 2 . Du cho dudng bien doi co nhu the
1.1 . 5 . CONGVA NHIET
1.1 5.1 . Cong la mot trong cac dang truydn nang luong tur he lam cdng den he nhan
cdng . Nang luongcuahe lam cdng thi giam , con nang luong cua he nhan cdng thi tang . Hai
thidu sau day minh hoa cho dieu nay .
vao vat mot cdng W :
Ket qua la nang luong( the nang ) cua he tang mdt luong la :
chuyen dong co huefng cua he .
Trong hedon vj SI , cdng dupe tinh bang Jun ( J ) . Theo quy ude hidnhanh , cdng dupe
tinh la duong ne '
u nodomoi trudng xung quanh tacdung vao hd , trong trudhg hopngupc
uam.
Trang 14Tri socuac6ng phu thuoc vao tinh chat cuaqua trinh bien doi.Chung tasosanh c6ng
dupe thuc hien trong qua trinh chuyen trang thai cua mot he khi theo hai con dudng a,bkhac nhau(hinh 1.2)
Hinh 1.2 Cong duoc thuc hien phu thuocvaodudng bien doi
C> trudng hop(a), trude het tadotnong hed apsuat Pjde lam cho the tich tang tCrV,den V2, sau do la giam apsuattur Pj denP2bang each lam lanh he nhung giu nguyen thetich C) tracinghap(b)c6ng viec dupe tien hanh theo chieu ngupclai.Cong dupethuchientrong m6i trucmg hop bang dien tich dudi duemg bieu didn suchuyen hd tu trang thaiddu
sang trang thai cuoi.Giatri cuachung khac nhaurat nhidu
Nhuvay,congkhongphailaham trang thaimala ham socuaqua trinh hayhum qua trinh
Baitqpl l
1.Khi cho axit sunfuric loang tacdung voi natri cacbonat ran thi congdupe thuc hien
la duong hay am.
2.Neulupng natri cacbonat la0,1mol,lupng axit dupe dung du,didu kienthi nghiem
la 1 barva273 K thi congdobang baonhieu ?
Ldi gidi
1 Khi H2S04loang tacdung vdi Na2C03ran thi khi C02 dupe phong thich vao mPi
trudng ngoai.He da lamcong vacongdupecoilaam
2.Na2C03 + H2S04(dlI) >Na2S04 + C02 t + H20
Lupng C02dupegiai phong la0,1 molddieu kien1bar va273 K
Vay congdupe thuc hien la :
W= -0,1RT = -0,1.8,314.273= -227 J
13
Trang 15Vay,giong nhucong, nhietcunglamot dai lupngdac trungcho mucdotraodoinang
lupng Su khac nhau la d cho trong trudng hopnay su traodoi nang lupng dupe thuc hienthong qua chuyen dong hdn loan cuacacphantu
Nhiet cung khong phai la ham trang thai, J.P.Joule' la ngudi dau tien da cluing minh
dupe rang : BAng each dung nhiet hoac cong co the’ dAn den cung mot su thay doi trangthai Di6u nay co nghla la lupng nhiet dupe dung lam thay doi trang thai cua mot he phu
thupcvao tfnh chat ciia bien doi Neu bien doi xay ra theo con dudng ma ddochicocong
dupedung thi nhiet dupe dung bAng khong, con neu bien doi xay ra theocon dudng ma d
dochi conhietdupedung, thidlnhiennhiet dupe dung khac khong
Nhu vay,giong nhu cong,nhiet dupe dungphu thupc vaocondudng bien doi giua cactrang thai.Nhiet khong phai la ham trangthai,nola ham qua trinh
Trong hedon vi SI,nhiet dupe do bAngJun Vi If dolich sirngudi ta vAncon dung don
vi calo.Mot calo bAng 4,184 Jun
Theoquy ude, nhietco gia tri duong khi he thu nhiet vacogiatri Am khi hetoa nhiet
1.2.NGUYENLITHUNHATCUA NHIET DONG LUCHOC
Nguyen li thu nhatciia Nhiet dongluchoc (goi tAt la nguyen It I)hay con dupegoi la
nguyen Hbao toan nAng lupngkhAng dinh tmh bat diet ciia nang lupng Nguyen li dupe rut
ra tirviec tong ket kinh nghieinciia loai ngudi va khong chung minh dupe bAng con dudng
lithuyet.Tuy nhien,no dupe thira nhan khong phai chivi ban than no khong mau thuAnvdithuc nghiem,mil con vi moi liequaduperut ra tirdodAu phu hop vdi thuc nghiem
1.2.1. PHAT BIEU NGUYEN LII
Nguyen liI dupe phat bi6u dudi nhi6udang khac nhau.Cac dang naydeu tuongduong
va taco the tir dang nay suy ra nhung dang khac mot each hoan toan chat che Sau day lamot dangciia nguyen li.
Trang 16Khi mot he kin tlu / c hien mot chit tn ' nh , tong dui so nin cue cong W va nhiet Qmu he
truo doi vo ' i moi tnfdng ngoui hung khong
I(Qi + w ,) =o (1.5)
Hiennhien la tongnoibtrenkhongthe khac khong Vineu tong nay khac khong thi
cfingconghlalata co the thu dupenang lupngth hirvohoac bien nanglirongthanhhuvo,
vadieu nay hoantoan mauthuSnvoi thucte
Plurcmgtrinu(1.5)cho thayriing,khihe thirc hienmotchutrinh,neunhan congno se
nhubng nhiet,con neu nhan nhietno se sinh cong.Neu goimot dongco hoat dong tufin
hoan sinh congmakhongcan nhannhiet ladong covlnhcuuloaiIthico thekhang dinh
" khong the co dong co vTnh ciht loai/".Day cung lamoteachphat bieucuanguyen IfI
1.2.2.MAM TRANG THAINOl NANGU
Duratrdnnguyen IfI,chungtachung minhrangco tontaimothum noi nang
Gia sir mot he km thuc hien mot biendoi ABtheo hai con duong 1,2 roi sau do laiquay vd trang thai ban dau theo duong 3 (hinh 1.3).Nang luongma he traodoi voi moi
trubng ngoaitrongmoitrubng hppla:
Ap dung lan luot nguyen If Ivao
cac chu trinh 1-3va2-3tadupe:
Trang 17Nhu vay, gia tri cua tong W + Q doi vdi mot bien doi bat kl cua he km khong phuthuoc vao duPng bien doi ma chi phu thuocvao diem di va diem den. No bieu thi dp bienthien cua mpt ham cua cac thPng s6 trang thai cua he. Ham trang thai nay dupe goi la
noi nang U cua he
nang ltrpng cua cac electron, nang ltrpng hat nhan nguyPn tir Tom lai, do la tat ca cac
dang nang ltrpng, trir the nang do vitri cua he trong khonggian quydinh vadpng nangcuachuyendong toanhp
Khong the xac dinh dupe tri so tuyet doi cua noi nang mot he khi noavao mot trangthainaodo, ma chixac dinh dupe dpbiPnthiencua no khihe chuyen tir trang thainay sang
trangthai khac
Cache thtfc(1.5)va(1.6)lacacbieu thde toan hoc cuanguyen If I
Trongba dai lupng ahe thde(1.6)chicobien thien noi nangAU la dupe xac dinh boitrang thai dau va trang thai cuPi cua he va khong phu thuoc vao duPng bien doi. Hai dailupng con lai-nhiet vacPng-khong co tinh chatay.MPi dai lupng phu thuoc rieng re vaoeach thuc hien biPn doi,mac dii tdngcua chung thi khong.
Neusubien d6i cua he lavocimg nho thibieuthde toanhoccuanguyen li Ico dang :
C)day,dUlavi phan toan phan cua npi nangcua hp,8W va8Qla nhung lupng nhiet va
congvo ciing nho.
He thde (1.7) la bieu thurc vi phan cua nguyen li I. Trong he thirc nay, 8W la cPng
chong lai cac luc ben ngoai,baogom congchPngapsuat ngoai hay conggian nP-PngdV
vacongchPngcaclucdien,luctir goichung lacongco ich8W
8W= - PngdV+8W’
Trong Nhietdong luc hoc, nguPi tathuong chi xet nhung he khong chiu tacdung cuadien truong, tirtruPng ..., khi do8Wchilacong gian novabieu thde vi phdn cua nguyenli
Ico dang:
Trang 18dU=6Q- PngdV
Sau daylamdts6trudng hop dac bietcanphaichuy.
1.Bien doi doqn nhiet
Trong bien doidoannhietQ=0.Bieu thdctoan hoccuanguy6n liIco dang : AU=WDacbiet vdi chutrinh: AU=W=0
MotMn nuachung talai thay:mdthe chay theochu trinh khdng traoddinhietvdi benngoaikhong the sinhcdng.
2.Bien doi dang tich
Trong biendoidangtich AV=0.Dodo, nd'
u5Wchilacdnggian nd thi 8W= - PngdV =0
vataco:
dU=8Q
V=const
Nhuvay,Qv bang do bien thien cua mot ham trang thai ( AU ) va khong phu thuocvao
diicmg bien doi.Can chu y rang,Qv khdng phailamdtham trangthai nhungcothe giuvai
trocuaham trang thai trongdieu kien nay.
3 Giannorvao chan khong
Qua trinh gian nd cua khl vao chan khdng didn ra ra'
t nhanh nen co th^ coi la doannhiet, Q=0 Apsuatcua chan khdng bang khdngndnhekhdng sinhcdng,W=0.Dodo:
AU =0
Khi gian nd vao chan khdng,noi nang cua he khong thaydSi
4 He thuc hien chu trinh
Khihe thuc hienchu trinh AU= Uj-U!=0.Dodo W+ Q =0. Nhuvay, khi he nhan
nhiet , thinose sinh cdng va tro thanh dongconhiet.
5 He co lap
Khi mot he nhiet ddng la cd lap , no khdng th£ trao ddi nang luong vdi mdi trudng
ngoaiW=0va Q=0.VayAU=0.Noi nangcuamot he cd lap la khdng doi
Trang 196 Noi nang cua mot khiHtuang
NguPitadachung minhduperingnoi nangcuakhi litirdng chiphuthupcvaonhietdp :
Uk „ =U(T)
Dodo, trong mot bien doi dang nhipt cua khilituang, khong kem theophan ting hoahoc,bienddinoinang AUblngkhdng.
1.2.3 HAMTRANGTHAIENTANPIH
Xetmpt hekhongcothethuc hipncongcoich.
dupegoilaentanpicua hp.Hla mpt ham trangthaiviUvaPVdeula hamtrangthai
DPivPikhi lituongthiPV=nRT,dodo:
Nhuvay:
5QP =dH
GiPng nhu Qv , Qp khong phai la mpt ham trang thai, nhung co the giti vai tro ham
trangthai trong difeukien nay.
1.2.4.NHIET DUNG
Nhiet dung trung binh Ctb cua mpt he trong khoang nhiet dp tuT[ dPn T2dupe dinhnghTa bang hpthticsau :
Trang 20T2- TJ AT
Q lanhiat lupng phaicungdpcho he da’nangnhiat d6cuanoturTjda'n T2.
KhiT , - »•T2,nghialaAT- >dTvaQ- » 5Q,taco nhiet dungthucC cuaha tai nhiet doTj
C _ 6Q
Neu qua trinh nau nong he lading tich va he khPng lam cdng co ich thi taco nhiet
dung dang tichCv
Cv = 6 Qv
C5 day,tadungdao ham riengvakihieu d vi Ulaham khdngphaichi cuam6t bie'
ns<5
Na'u xet mot molchat nguyen chat thi nhiat dung trong diaukianthe tich khdng doi la
nhiatdungmol Cv
5T ' v
Khi ha duqc nlu nong trong diau kien ap suit khdng d6i vi chi co cPng gian nor la
dangcong duynhat dupe thuchian,thitaco nhiet dung dang dpCp
Nhiet dung dang ap Cplu6n lu6n lorn horn nhiat dung dang tich Cv, vi su nlu nong
trongdiau kianap suit khongd6icokern theo c6ng giannor.D6'ivorikhi lituongcothitim
phuorng trinh lienhagiua Cpva Cy nhu sau:
Trongtruomghop khi lituomg: H= H(T)vaU=U(T)
19
Trang 21n thien noinangAU va bie'
n thien entanpiAHtrongcacbie'
nd6i sau dayduorc tie'
nhanhthuannghich nhiet d6ng.
1.Nung nong dangtich toriapsua'
tbang1,5atm ;
2.Giandang aptori thetichgapd6ithe tich ban dau ;
3.Gian dangnhiettori the tich 200 1;
4.Gian doannhietcho torith£tich 200 1.
Cha'pnhanrang niter lakhi lituomgva nhietdungdang ap khongdoi trongqua trinh thi
nghiem vabang29,1 J K-1.mol-1
Trang 2313 APDUNG NGUYEN LI THl / NHAT CUA NHI $ T D 0 NG LUC HOC VAO HOA HOC
1.3.1.HIEU UNG NHIET CUA PHAN UNG HOA HOC
Phan ting hda hoc thircmg c6 kem theo hi6n tircmg thu nhidt hay phat nhidt Nhi6tcua
mdtphan ting or nhidtddTla nhidtluqngQmah6phan ung trao d6ivdi m6itruting ngoaikhicacchat phan lingduqc lay theo ti16 hop thtic, tacdung hoan toan vdi nhau taothanh
cac san phdm cung theoti16 hop thtic.Lucrng nhi6t nay phu thudc vao each ti6n hanh cuaphan ung vino lamdt ham qua tnnh.D6’cho nhi6t phan dngco gia tri xac dinh, ngucri ta
phai quy dinhthdngnhatcacdi6u ki6n ti6n hanh phanung Dola:
1.Phan tingduorc thuchi6ntrongdi6u ki6n th6?tfch hayapsua'
Khi cac di6u ki6n tr6nduqc thoa man, nhi6t phan ting se co gia tri hoantoan xacdinh
vaduqcgoilahieutingnhiet cua phantinghod hoc.
Khi phan tingdi6n ra trongdi6u ki6n th^tfchkhdng d6i, tacohieu ting nhiet dang tichQv ,
controng di6u ki6n apsua'
tkhdngd6itacohieu ting nhiet dang dpQP.
Nhu da trinh bay a muc 1.2,Qv bangbi6'
n thi6n ndi nang cua phan ting,con QPbang
bi6'n thi6n entanpi cua phanting.
Trudc khi nguydn If I ra dcri, tinh chat co ban vtia duqc tiinh bay d tr6n da duqc
G.Hess1- phat hi6n bang thuc nghidm vio nam 1841.Phat ki6n niy la" dinh luat Hess"
-mdtdinh luatquan trongcuanhidthoahoc.
Nha hoi hoc Nga
Trang 24Hieu ling nhietcuampt phan ling hoa hocphu thudcvaolupng,trang thai cuacacchatphan lingva cacdiPu kien diPnbien cuaphan ling DP thuPn tien va tranh dupecac saisot
khisirdung cac hieuling nhietcuacac phanlingkhacnhau,ngudita thudng tinh hieulingnhiet doi vPi mot mol san phPm cua phan ling va cha'
p nhan viec quy chung ve cacdieukientieuchuPnxacdinh dudi day :
1.Phan ling dupe thuc hiengiua cac chat riengbiet (nguyenchat) b vao cac trang thaitieu chudnxacdinh.Cac trang thai tieuchudncuacacchat ranva long lacactrangthaiben
cua chungadieu kien thuemg khi apsua'
tbang 101,325kPa hay 1atm.Thf du: i6t-iot ran,brom-brom long, cacbon-than chi, luuhuynh-luu huynh truethoi, nude-nude long.
Trang thai tieu chuan cua khi la trang thai cua khinguyen chat b 101,325 kPa hay latm.
Dd'
ivdi chat tan trongdungdichthindngdocuano bang 1mol/1.
2. Trang thai tieu chudn co the ling vdi mdt nhiet dp bat ki, nhung thudng ling vdi
298K(chinh xacla298.15K)hay25°C.
Hieu ling nhiet ling vdicac dieu kipn tieu chudn trendupe goi la hipu ung nhiet tieuchu<£n vadupeki hieu bang AH°98, AU°98.
Trongthuc te,cacphanling hoahocthudngdienraddieu kipndang ap,do dohPunhu
ngudi ta chi dung hieu ling nhiet dang ap va goila bien thien entanpi cua phan ting , haydcfn gian hon-entanpi cua phan ting .
Tuy nhien, khi bietentanpicua phan ling, chung taco thetinh dupe de dang hieulingnhietdangtichcuaphan lingdcung diPu kipn vPnhipt dd.
Quavay, vdi phanling viPt d dang:
VA[,VA', lathPtich molcua cacchPt A;, A{.
Nhuthe,khi phan ling diPn ragiua cacch&'
t ranhoac cha'
t long, thi viAUP» AUV va
AY«0nen:
23
Trang 25AHp= AUV (1.20)
D6'
i v6i nhung phan ting co chat khf tham gia thi 6 ap suri'
t tha'
p (latm chang han)
nhung khf nay co th£ dirge coi la khf If tubng Khi do, AUP = AUV (n6i nang cua khf If
tubng chi phu thubcvao nhietd6) vaPAV = AnRT;An-bie'n thien s6 mol khf trong phan
AHP = AUV+AnRT (1.21)
Khi An = 0 thi hieu ting nhiet dang ap bang hieu ring nhiet dang tfch ; Khi An *0
chung khacnhau m6tgiatri la AnRT.
De do hieu ring nhiet cua phan ring hoa hoc, ngubi ta dung nhifit lugng k6'
Dang ph6 bi£n nha't la dang co phan ring xay ra trong m6t budng phan ring (bom nhidtlugngke).D6tangnhietd6 dugcdobangm6t nhi6t k6'
nhay.Tren hinh(1.4)cotiinhbayso
d6cuam6tnhifit lugngkedongian.
Tfch s6'
giua bid'
n thien nhiet d6 vdi
nhiet dung chung cuanude vanhiet
lugngke'
bang lugng nhiettoara.
Phuong phap xac dinhtruetie'
phieu ring nhiet thubng phire tap va
cung chi dung dugc trong trucmg
hgp chi co m6t phan ring xay ra
nhanh va hoantoan. Vi vay, de’xac
dinhdugc hieu ring nhiet cua nhi£u
phan img khac nhau, ngoai viecdo
truetie'
p, ngucri tacon phai dungca
phuong phap tfnh dua vko cac du:
kienhoa hocda bie'
t.
Phuongtrinh cua phan ringhoa
hgc,maddo coghihieu ring nhiet
cua phan ring,trang thaicuacaccha'
t (trri nhiingtrucmg hgpqua ro)va dieu kien thuchienphan ring, dugcggilaphuong trinhnhiethoahgc.
1.3 2 PHUONG PHAPTINH HIEUUNG NHIET
Coscrcua phuong phap tfnh hieu ring nhietladinh luStHess.Chringtaxet m6tthf du :
Timhieu ring nhietcua phan ring
Hinh 1.4 So d 6 m 6 t nhiet luqng ke don gi^in
( 1 ) Bom nhiet luong ke ,
(2) Nhiet ke , (3) May khuay , (4) Nu6 c
Trang 26Khong the do dirge AHj cua phan ufng nay vi khi cacbon tac dung vdi oxi ludn ludncho cacbondioxit hoacmdth6n hop cacbon oxit va cacbon dioxit.Tuy nhien,cothe do dddangAH cua cacphan ling :
naode sau khicong va rut gon nhiing so hang gidng nhau ta thu duoc phuong trinh phan
ungc3nthiet.Doi vditrudnghoptidn:
Trang 27I 3.2 I Entanpisinh
Entanpi sinh cua mot chat la hieu vtng nhiet cua phdn img tqo thdnh mot mol chat ay tit cac dan chatavdo trqng thdi ben vffng nhd '
t trong nhutng dieu kien dd cho ve nhiet do vd dpsudt.
Neu nhungdiPu kien nay la diPu kien tieu chu&i thi entanpi sinh dupe goi la entanpi
sinh tieu chuanvadupekihieubang AH°298
Thi du, d latm entanpi sinh tieu chudn cua canxi cacbonat (canxit) bang entanpi cuaphan ting:
Ca(r)+CthancW +-02( k ) >CaC03(canxit) AH°98 = -1207,68kJ
Chi co the do true tiep dupe entanpi sinh trong mot so it truerng hop (C02, HC1,
H20 . .),conthiphai tinh bang phuemg phap gian tiep.Hiennay,nguoita da xacdinh dupe
entanpisinh tieuchudncuachtmg8000cha't.Motsocac giatrido dupeghiabang 1.1.
Trang 29tieu chuan deu bang khbng .
Co the tfnh entanpi cua mot phan umg hoa hoc bang each dung entanpi sinh cua cac
chat phan umg theo quy the sau day : "Entanpi cua mot phan ting hod hoc bang tong
entanpi sinh cua cac sdnphdmtrti tong entanpisinh cuacacchat phan ting Quy tac duorc
rut ra tir sor do tinh toan chung sau day :
Cac don chat (
Trang 30Apdungdinh luatHessta duqc :
A^ S ^ ^s( chatphanuTig ) ~S ^A^s ( sanphim )
A^ — J A^s( sanpham ) S ^^s ( cha ' tphanting )
Thidu: Doi vdi phanling
CH2=CH2(k) + H20(1 ) > CH3CH2OH(1)
AH298- AHS( CH3CH2OH(1)) [AHs( CH2=CH2
(k ) )+AHs( H20( 1 ) )]
= -277,6-(52,2 -285,6)= -44,2kJ.mol" 1
Entanpi sinhnguyen tiit
Khi mot mol hop chat khiduqc tao ra tircac nguyen t£r thi do bie'n thien entanpi cuaqua trinh nay duqc goi la entanpi sink nguyen tit. Chico thetinh duqc dai luqng nay Cothe dungentanpisinhnguyen titdetfnh nangluqngcuacaclien ket hoa hoc
Entanpi sinh cua chat tan
Entanpi sinh cua chat tan la hieu vtng nhiet cua qua trinh hinh thanh mot mol chat a
trqng thdi tan tit cac dctn chat avao trqng thdi ben vitng nhd '
t trong cac dieu kien da cho ve nhiet do vd dp sud ' t .
Canchu y rang, vi entanpi hoa tan toanpMncuacacchat (bien thien entanpi trongquatrinh hoa tanmot molchat vao n mol dung m6i)phu thuoc vao sdmol dung mdi,cho nen
m6i khi noi de'n entanpisinh cua m6tchat tan naodoc^n phaichiroso'
mol dung moi.Thi
du, 6298 K entanpi sinh cua HC1 trong 100 mol H20, 200 mol H 20 va QO H2013n luqt
bang-166,15;-166,51 va-166,82kJ.Kihieu oo H 20 chi rluigsdmol nude larat Ion.Khikhong cosu chi din rorangnhu tren, chung ta duqcphephie’u rang so'mol nude la ratldn.
Trong tinh toan,co the boqua entanpisinhcua nude khi d ca hai ve'cua phuerng trinh hoahoccosdmol nude nhu nhau.Noi mot eachkhac,chungtada chapnhan rang, trongnhfingtrudng hqp nay, entanpi sinh cua nude trong dung dich nude bang entanpi sinh cua nudenguyenchat,
Entanpisinh cuamotsdchattanddivdi bandngdd duqctrinh bay trong bang1.2
29
Trang 31Bang 1.2 Entanpi sinh625°C , AH“ (kJ mol 1 ) cua cac chat tan trong dung djch nude Chat tan Trong 100 mol H2O Trong 200 mol HjO Trong oo H20
1 .Tinhentanpi hoa tan cua 1 mol HQ ( k ) trong 200 mol nuded25 ° C .
2 . TinhAH298 cua phan ling
HQ trong 100 mol H20+ NaOH trong 100 mol H20 >NaG trong 200 mol H20+ H 2OQ
Gia tri entanpi cua cac chat duocl& '
Entanpi sinh cua ion
Entanpi sinh cua ion trong dung dich nude Id bien thien entanpi cua phan ring hinh
thdnh 1 mol ion bi hidrat hoa tit cac don chat
l
Trang 32- bi hidrat hoa. Khong th£
xacdinh dupe bangthuc nghiem hay bangeach tinh gia tri tuyet d6'i cua entanpi sinh cua
ion, machico thd tinh dupegia tri tuong dp '
i cuachung bang each chapnh&n ring entanpisinhcuaH+trong nudebang khong.Thidu,entanpi sinh cua Cl”
Entanpisinhcuamot soion dupeghiofbang1.1
Bietentanpi sinh cuacac ion va cac chatco mat trong phuefng trinh phan ling, tatinh
dupe hi6uirngnhidtcuaphanling theo quytac da dupetrinh bayoftren
Bdi tap 1.4.
Tinh hieuling nhietcuaphanling
3Fe(N03)2 (aq)+4HNO-(aq) >3Fe(N03)
Trang 33AH=3 AH° + AH ° , + 2AH ° „ n , - 3AH ° - AH °
s, 298 ( Fe3 , aq ) s,298 ( NO(k)) s, 298 ( H20( 1 ) ) s,298 ( Fe2+, aq ) s , 298 ( N03, aq )
= -3.47,7+90,25-2.285,6+3.87,86+206,57= -153,9kJ.
I 3.2.2.Entanpi chay
Entanpi chay cua mot chat la hieu ting nhiet cua phan ting dot chay mot mol chat toi
cdc dang oxi hod thick ting cua cdc nguyen to Nhttng dang'nay ducrcquygtdinh bdididu
kien dot chat trong buong phan tfng cuanhiet lucmgke.Thf du,hidro vacacbon thuong bioxi hoa den nude va khf cacbonic.Cacchat chua halogen tori halogen hay hidrohalogenua;luu huynh tori khf sunfuror ; niter toi demchat niterhay axit nitric .Trong cac bang tracuu
vdentanpi chay cua cac chat,banchatcungnhu trang thaicua cacsanph^m cuo'icungdeuduprechiro.
Entanpich£y cua cacchat dupre xacdinh bang thucnghiem va thuong duprequyvecac
dieu kien tieuchuan:Entanpi chaytieuchuan AH°h298•
Entanpichay tiduchuan cuametanla hieu ring nhidt tiduchudncua phantfng :
Trang 356day entanpi chay cua H20 bang khdng vi nolasan pham cudi ciing cua phan ting.
Didunaycung dtingdd'
ivoiC02khi no comattrongphuong trinh phan ting.
Khac voi trucmg hop cua entanpi sinh, trong trucmg hop nay chting ta khong thd lap
duoe sodo tmh hidu ting nhidt chung dd’ tfir dorut raquy tac tlnh hidu ting nhidt cua mot
phan ting tti entanpi chay cua cacchatcomat trong phuong trinh phan ting.Tuy nhidn,tCrvide phanrichnhuftgthldu ridnglenhu6trdnchung tacoquytac:
Trang 36" Hieu ling nhiet cua mot phan ling hod hoc bang tong cac entanpichay cua cac chat
phan ling true di tongcacentanpi chay cua cacsanpham "
AH= 2 lAHch( cMtphanting ) ^cMsan ph & n ) (l- 22 )
i va j la nhung he so hopthurctrong phiromg trinhphanutig
Trongthucte , ngucri ta dung entanpichayde xac dinh entanpi sinh cua cac ch & '
t hfiuco
va hieu ling nhiet cua cac phan linghuu ccr, vi cac dai liromg nay hoac khdng , hoac kho co
the xac dinh dime bangthucnghiem .
Bdi tap 1.6 Biet entanpi chay tieu chuan cua C2H2 ( k ) la -1298, 88 kJ-mol - 1 , tmh
entanpi sinh tieuchuancua no . Cac dtf kien can thiet dirge layorbang 1.1 .
( k ) ) =2AHs, 298 ( C02( k ) ) +AHs, 298 ( H20( l ) ) “ AHs, 298 ( C 2 H 2 ( k ) )
AHs, 298 ( C 2 H 2 ( k ) ) =2AHs, 298 ( C02( k ) ) +AHs, 298 ( H20( 1 ) ) “ AHch, 298 ( C 2 H 2 ( k ) )
=- 2.393 , 1 -285, 6 +1298, 88 =227 , 08 kJ . mol - 1
Canluu y la trong truemghopnay cung nhutrong cac truemg hop tuong tu , mot sai s6
nho cua entanpi chay cungdinden m 6t sai s 6 '
ldn veentanpi sinh . Gia sir sai s6trong viec xac dinh entanpi chay cua C 2 H 2 ( k ) la 0 , 1 % thi sai s 6 '
phamphai trong viec tmh entanpi sinh
1298 , 88.0 , 1
sela : =0 , 57 % .
227 , 08
I 3.2.3 Nhietchuyen pha
Qua trinh chuyen pha la qua trinh trong do mot chat chuyen tut mot trang thai tap hap nay sang mdt trang thai tap hap khac Qua trinh chuyen phac6 thela thang hoa , bay hoi ,
nong chay ,bieridoi dahinh,chuydntur trang thai v6 dinh hinh sang trang thai tinh the .
Hieu ling nhiet kem theo qua trinh chuyen pha la nhiet chuyen pha.
35
Trang 37Trong nhi6u trucmg hap, co the xac dinh nhiat chuyen pha bang thuc nghiem. Tuy
nhien,cung cotrucmghapphai tim bangeachgian tieptrenca sadp dungdinhluatHess
Thidu,d6timduqcnhietchuyen pha cuaqua trinh:
Qdmcircmg ^ Qhanchi
ta khong thadung phuong phapdoduavaonhiet luqngka'duqc, viadieu kien thuemgquatrinh nay xay ra v6 ciing cham. Vi vay, nguai ta thuc hian phan ting nhanh vci cahaidang :
Cthanchi + 02 >C02( k ) AH= - 393,51kj.mol-1
Ckim „», s + 02 — — > C02( k ) AH = - 395, 40kJ.mor1
Hieusohieu ling nhiatcuahai phan uengnay bangnhiat chuya’n phacSntim :
AHchuy ^n pha= -395,40-(-393,51)= -1,89kJ-mol" 1
1.3 2.4.Nang luqng lienket
Nang luang cua mot lien ket dinhvila ndng luang duac giai phong khi lien ket hod hoc duac hinh thdnh tvtnhvtng nguyentitcolap
Doi vdd cac phan tirdan gian loai AB thi nang luqng lian ka'
t va nang luqnglam durt
lifinka '
tcotrisotuyetdoibangnhauviphantirABchico m6tlianka '
t .
D6'i vdi cac phan tir loai khac thi diau noi cr tran kh6ng dung nua Thi du, phan tir
metan CH4 co bon lian ket C-H hoan toan tuang duang; nang luqng lian ka'
t cua chungphai bangnhau. Nhung ka'
t qua nghiancuu thuc nghiam cho thfiy nang luqnglam dut lianketthur nha't bang 426,8kJ.mol_1
; nangluqng lam dut caclian ket tia'ptheolan luqt bang
347,3;535,5;334,7kJ.rnol" 1
ViIf dotran,trongtrucmg hop chung,khinoi da'n nangluqng lianketchungtahieu do
landng luang lien ket trung binh.Thidu,tri s6'tuyatd6'i cuanangluqng lianket C-Hbang:
td cacha khac.
Trang 38Nanglugnglien ke'
Co th£tfnhdirgenang lirgng lienke'
tbang eachdungcacdukien nhiethoa hgc
Bai tap 1.7
Xacdinhnanglirgnglienke'
tcua lienke'tH-Cl.Chobie'
Trang 40Cac dtt kien con lai giong nhir 6 bai tap tr£ n .
Lapso< J6va thuc hien phep tinh giO '
ng nhu 6 trfin taduoc:
t duoc tnnh bay6bang1.4.
Bang 1.4 N3ngludng lien ket
Dung cac gia tri cuanang luong lien ket ta co the tinh duoc ang chimg hieu ling nhiet
cua phan ling hoa hoc theo quy tac sau day :
" Hieu ting nhiet cua mdt phan ling hod hoc bang tong cac nang luCctng lien ket cua cac
phan tutsan pham tritdi tong cac nang luong lien ket cua cac chat phan ling "
39