LI CM N

Kha lun c hon thnh ti B mn Ha Phn tch- Khoa Ha hc- Trng i hc S phm H Ni.

Bng tm lng trn trng, em xin by t lng bit n su sc ti Ths.Nguyn Th Thanh Mai, PGS.TS o Th Phng Dip v Ths.V Th Tnh tn tnh hng dn em trong sut qu trnh hon thnh lun vn.

Em xin trn trng cm n cc Thy C gio trong B mn Ho Phn tch-Trng i hc S phm H Ni gip v to mi iu kin thun li cho em trong sut qu trnh lm thc nghim.

Cui cng, em xin chn thnh cm n bn b v ngi thn ng h v ng vin em hon thnh kha lun ny.

H Ni, ngy 03 thng 04 nm 2015Sinh vin

Trn Th Thu HngDANH MC CC T VIT TT

BPTT : Bnh phng ti thiu.H : n hnhCE

: in di mao qun.

CE-MS: in di mao qun- khi ph.

DAD: it quang.

KP : iu kin proton.

T : im tng ng.

HSCB : Hng s cn bng.

LC

: Sc k lng.

LC- MS: Sc k lng- khi ph.

I

: Lc ion.

[i]

: Nng cn bng ca cu t i.

h

: Hot ca ion H+.

pH

: Gi tr pH ca dung dch.

pHLT: pH l thuyt.

pHTN: pH thc nghim.

TPGH : Thnh phn gii hn.

UV-Vis: Ph t ngoi kh kin.

KX: khng xc nh c.

M UTrong Ha hc phn tch, hu ht cc qu trnh xy ra trong dung dch u lin quan n qu trnh cho nhn proton, tc l lin quan n phn ng axit baz, v vy hng s cn bng (HSCB) axit baz c ngha rt quan trng trong lnh vc nghin cu cn bng ion, c bit khi trong cc ti liu tra cu hin nay vn cha c s thng nht v cc gi tr hng s cn bng, trong c hng s cn bng axit baz.

Trong nhng nm gn y, nhm nghin cu cn bng ion ca b mn Ha Phn tch, khoa Ha hc, trng i hc S phm H Ni tp trung nghin cu phng php tnh lp theo thut ton bnh phng ti thiu (BPTT) v thut ton n hnh (H) kt hp vi vic ng dng cng ngh thng tin lp chng trnh tnh theo cc ngn ng lp trnh khc nhau nh Pascal, Matlab nh gi hng s phn li axit ca mt s cc n, a axit khc nhau.

M u cho hng nghin cu ny, cc tc gi s dng thut ton BPTT kt hp vi gi tr pH tnh ton theo l thuyt xy dng phng php tnh lp nh gi cc HSCB ca cc n axit, n baz [15], a axit, a baz [1] v hng s to phc hiroxo ca mt s ion kim loi [9]. V cng tng t, t ga tr pH l thuyt, s dng thut ton n hnh, tc gi trong [14] bc u xy dng c phng php xc nh HSCB axit baz bng cch tnh lp lc ion.

khng nh tnh ng n ca phng php nghin cu, ng thi kim tra s ph hp gia gi tr l thuyt v thc nghim, ln u tin tc gi trong [2] tin hnh thc nghim o pH v chun in th o pH cc dung dch a axit (axit oxalic) c nng khc nhau bng dung dch NaOH. T cc gi tr pH thc nghim thu c, tc gi s dng phng php BPTT vi vic tnh lp lc ion xc nh cc hng s phn li axit tng nc ca a axit oxalic. Kt qu thu c t thc nghim kh ph hp vi cc s liu c cng b trong cc ti liu tham kho tin cy [8].

khai thc kh nng ng dng thut ton tnh lp theo phng php BPTT, trong [7] cc tc gi cng tin hnh thc nghim o pH v chun in th o pH ca dung dch hn hp gm hai n axit c HSCB tng ng nhau: axit axetic v axit benzoic. Khc vi [2], y cc tc gi s dng mui tr KCl khng ch lc ion m khng phi tnh lp lc ion. Kt qu xc nh ng thi HSCB ca hai axit ny t cc gi tr pH thc nghim kh ph hp vi kt qu c cng b trong cc ti liu [8].

tip tc m rng kh nng ng dng ca phng php BPTT trong vic xc nh HSCB axit baz, ng thi i chiu kt qu nghin cu, trong [14] v [2], cc tc gi s dng song song 2 thut ton: BPTT v H nh gi HSCB ca 2 axit c hng s phn li axit chnh lch nhau nhiu: axit axetic v amoni t gi tr pH o c bng thc nghim chun in th trong cc trng hp khc nhau: pH ca dung dch hn hp hai n axit ny [5], pH ca dung dch tng n axit ring r (dung dch axit axetic, dung dch amoni), hoc pH ca dung dch n baz lin hp (NH3), trong cc tc gi u khng ch lc ion bng dung dch mui tr KCl. Kt qu thu c theo 2 phng php khc nhau kh ph hp vi nhau.

tip tc hon thin hng nghin cu trn vi vic s dng thut ton BPTT v khng ch lc ion trong dung dch nghin cu, chng ti chn ti: S dng phng php bnh phng ti thiu xc nh hng s cn bng (HSCB) ca axit cacbonic t kt qu chun in th ca h cacbonat

Trong khun kh ca mt kha lun tt nghip, chng ti t ra cc nhim v nh sau:

1. Tng quan cc phng php xc nh HSCB axit, baz.

2. Xy dng thut ton v chng trnh tnh theo phng php BPTT xc nh HSCB ca axit cacbonic t gi tr pH o bng thc nghim, trong h s hot ca cc ion c tnh theo phng trnh Davies [12], cn h s hot ca cc phn t trung ha c chp nhn bng 1.

3. S dng s liu thc nghim o pH ca dung dch mui cacbonat CO32- v chun in th o pH dung dch mui cacbonat CO32- vi cc nng khc nhau nh gi cc HSCB ca axit cacbonic bng phng php BPTT, theo cc h sau:

H mui cacbonat Na2CO3 (k hiu l A2-).

H mui hirocacbonat HCO3- (k hiu l HA-).

H m 1 gm: mui cacbonat v mui hirocacbonat (A2- v HA-).

H m 2 gm: mui hirocacbonat v kh CO2 (HA- v H2A).

4. Kt lun v kh nng ng dng ca phng php nghin cu trong vic khai thc d liu o pH.

nh gi kt qu nghin cu, chng ti s dng phng php i chng so snh gi tr HSCB ca a axit xc nh c t gi tr thc nghim o pH vi cc gi tr HSCB tra trong ti liu tham kho [8]. S ph hp gia gi tr HSCB tnh c t d liu thc nghim o pH vi gi tr HSCB tra trong ti liu [8] c coi l tiu chun nh gi tnh ng n ca phng php nghin cu v tin cy ca chng trnh tnh.

Chng trnh tnh c vit bng ngn ng lp trnh Matlab. Trong cc php tnh chng ti chn hi t nghim l = 1.10-9CHNG I. TNG QUAN

I.1. Cn bng v hot

I.1.1. nh lut tc dng khi lng [8].Hng s cn bng l i lng c trng cho trng thi cn bng ca qu trnh thun nghch. cc iu kin xc nh i vi mi phn ng thun nghch hng s cn bng K l i lng khng i. N khng ph thuc vo nng cc cht phn ng, m ch ph thuc vo nhit , bn cht ca cc cht nghin cu v dung mi.

Tht vy, gi s xt cn bng trong dung dch:

(I.1)

Hay vit di dng tng qut:

(I.2)

Trong : i< 0 vi i t 1 ( p

i> 0 vi i t p + 1 ( s

Ha th cu t nm trong dung dch c biu th nh sau:

(I.3)

Trong :

(i l ha th hay nng lng mol ring phn ca cu t i khi nhit , p sut v s mol cc cu t khc hng nh.

l th ha hc ca cc cu t i trng thi chun (trng thi quy c m ).

ai l hot ca cc cu t i, l hm s ca nng , nhit , p sut. N lin h vi nng phn tch nh h thc:

ai = fi . Ci (fi 1 th ai Ci)

Khi h t trng thi cn bng th tng ha th ca cc cu t tham gia phn ng bng tng ha th cc cu t l sn phm phn ng:

(I.4)

(I.5)

Qua bin i cn thit ta c:

(I.6)

Vi iu kin T, p, ... khng i th khng i v ton b v phi ca (I.6) khng i.

Do :

(I.7)

Hay

(I.8)

Hoc c th vit di dng:

(I.9)

vi

Trong : i< 0 vi i t 1 ( p

i> 0 vi i t p + 1 ( s

K l hng s cn bng nhit ng ca phn ng (I.1) ch ph thuc nhit . F(f) trong biu thc (I.9) l tham s bt nh gy sai s cho K. F(f) ph thuc vo: lc ion ca dung dch, bn cht ion, mi trng ion.

nh gi chnh xc h s hot l iu kin cn thit tnh HSCB nhit ng K.

Hng s cn bng nhit ng biu din mi lin h gia hot ca cc ion tham gia vo cn bng. Khi s dng nh lut tc dng khi lng, nh lut bo ton in tch v cc HSCB nhit ng c th tnh ton c nhng cn bng trong dung dch nhng tnh ton cn phi bit h s hot ca tng ion ring bit cc lc ion khc nhau. Tt c nhng phng php nh gi chng cho n nay vn c xem nh mt s gn ng. Kt qu ca n c s dng i vi lc ion thp ngha l c xem nh mt dung dch l tng. Thc t, hu ht cc h l nhng h thc c sai lch so vi h l tng, v th khi biu din nhng tnh cht nhit ng ca h nht l khi xc nh nhng iu kin din bin ca qu trnh v iu kin cn bng ca h ngi ta khng th dng nng m nng c thay th bng hot .

I.1.2. Hot v h s hot [8].I.1.2.1. nh ngha, ngha ca hot v h s hot

H s hot l i lng cho bit s sai lch gia trng thi l tng v trng thi thc ca dung dch nghin cu, ng thi cho php thc hin c cc php tnh nhit ng cho h thc khi gi nguyn cc phng trnh nhit ng dng cho h l tng.

Hot thng c k hiu l a. Hot lin h vi nng C bi h thc: a = f.C, trong f l h s hot c dng nghch o l (f = -1), n xc nh mc nh hng ca tng tc gia cc ion vi nhau. Trong dung dch long ca cht in ly yu, tng tc khng ng k, h s hot f = 1 v hot bng nng (a = C).

H s hot phn nh lc tng tc tnh in gia cc ion trong dung dch. V vy h s hot khng ch ph thuc vo nng v in tch ca mt ion cht in li trong dung dch m cn ph thuc vo nng v in tch ca mi ion c trong dung dch (bi v mi ion c trong dung dch u tham gia vo tng tc tnh in).

S ph thuc ca h s hot vo lc ion ca dung dch rt long ca cht in li c biu din bng cng thc sau y ca Debye Huckel [12] :

.

Trong : Zi l in tch ca ion i, I l lc ion.

Lc ion biu din tng tc ca cc ion trong dung dch. [i] l nng ca cc ion i trong dung dch, lc ion xc nh bng h thc:

(I.10)

Trong cc trng hp khc nhau, hot thng c chun ha nh sau:

- Trong cc dung dch long, hot ca cc ion v cc phn t u bng nng mol ca chng (mt cch nghim ngt th hot ch bng nng trong dung dch v cng long).

- Trong cc dung dch long, hot ca dung mi bng phn s mol ca dung mi v bng n v.

- Cc cht rn hoc lng nguyn cht nm cn bng vi dung dch u c hot bng n v.

- Cc cht kh nm cn bng vi dung dch u c hot (hot p) bng p sut ring phn ca mi kh.

- Hot ca mi cu t trong hn hp cht lng gn bng phn s mol ca tng cu t.

- Chp nhn h s hot ca cc phn t trung ha in bng 1.

V coi hot ca cc phn t khng tch in bng nng cn bng nn sau y chng ti ch trnh by cc phng php kinh nghim nh gi cc h s hot ca cc ion.

I.1.2.2. Cc phng trnh kinh nghim nh gi h s hot ca ion [12].

Mi ion u c h s hot ring bit nhng khi nim h s hot ca tng ion ring bit thng c coi l khng c ngha vt l, cho nn chng ta thng dng khi nim h s hot trung bnh. Khi gii quyt cc bi ton c lin quan ti cn bng trong dung dch, trong nhiu trng hp do khng th hoc khng c iu kin o h s hot tng ion, ngi ta thng tnh h s hot cc ion theo cc phng trnh gn ng sau y: Phng trnh Debye Huckel. Phng trnh BGS. Phng trnh Danielle. Phng trnh tng qut. Phng trnh Pitzer. Phng trnh Davies.I.1.2.2.1. Phng trnh Debye Huckel

Phng trnh nh lut ti hn ca Debye Huckel c p dng cho cc h lc ion thp (I < 0,001):

lg fi = - A . . (I.10)

hay lg i = A . .

vi

Trong : A l hng s ph thuc vo bn cht ca dung mi v nhit . Trong dung dch nc 250C th A = 0,5115.

Lc ion I c tnh theo cng thc:

Vi lc ion ln hn (10-3 I 10-1) th p dng phng trnh Debye Huckel m rng:

Vi: ai l bn knh ion hirat ha n v l A0

Trong dung dch nc, 250C th A = 0,5115 v B = 0,3291

Vy mun tnh c hng s cn bng nhit ng Ka ta phi tnh hng s cn bng nng Kc, sau ngoi suy v lc ion bng 0. i lng c nhp vo phn ngoi suy theo Debye Huckel.

I.1.2.2.2. Phng trnh BGS

(I.14)

Nm 1926 Guntelberg dng Ba = 1 v p dng c tnh h s hot cho cc ion in li 1:1 cho n I = 0,1. Nm 1935, Bronsted b sung thm s hng th hai (b). Sau ny Scatch v Guggnheim pht trin tng ny trong m hnh BGS:

(I.15)

Gi tr Ba = 1,5 c dng cho cc ion khc nhau, y coi nh tham s c t ph vo lc ion trong khu vc I = 0,5 ( 3,5M

I.1.2.2.3. Phng trnh Danielle

Danielle v cc tc gi ngh b sung thm s hng th ba:

(vi Ba = 1) (I.16)

(vi Ba = 1,5) (I.17)I.1.2.2.4. Phng trnh Debye Huckel 4 tham s

Trong trng hp tng qut nht vi lc ion trong khong ln hn na, cn c th m rng thm s hng th t:

(I.18)

Nhng trong nhiu trng hp cc i lng th ba, th t thng t nh hng ti s ph thuc ca h s hot theo I.

gim bt sai s, tc gi khng c nh hng s Ba. y l phng trnh tng qut hn c so vi cc phng trnh ca cc tc gi khc, tuy nhin c nhc im ln l vic gii ra cc h s l ht sc phc tp.I.1.2.2.5. Phng trnh Davies

Khi gii quyt cc bi ton xc nh thnh phn cn bng trong dung dch, tnh h s hot ca cc ion, c th p dng phng trnh Davies:

(I.13)

Nm 1938, Davies ly gi tr trung bnh b = 0,2. n nm 1962, sau nhng nghin cu b sung, ng ngh dng gi tr b = 0,3. Davies khuyn co rng phng trnh ch l gn ng, ch nn p dng cho nhng nng cht in li di 0,1M v khng nn dng nng cao. Theo Davies th vi b= 0,2 c th p dng phng trnh n lc ion I = 1,5 vi b = 0,3 c th p dng phng trnh n lc ion I = 0,8.

Trong thc t, cc phng trnh vi h s 0,2 v 0,3 cho kt qu khng khc nhau r rt v mt thng k, cho nn trong cc chng trnh tnh phn sau, chng ti dng phng trnh Davies vi tham s 0,2. Chng ti s dng phng trnh ny v y l phng trnh tuy gn ng song n gin nht, khng cn n tnh phc tp nh cc phng trnh khc.

I.1.2.2.6. Phng php thc nghim nh gi h s hot ion Phng php Kamar [1]

Chng hn cn nh gi h s hot ca cc ion A- (dng phn li ca cc axit HA) hoc HA+ (dng proton ha baz A) ca cc axit HA, ngi ta chun b dung dch HA nng a0 mol/l khi c mt cht in li tr XY (v d NaCl) c nng bng lc ion cn thit lp I, bng Vi ml dung dch kim mnh XOH hoc axit mnh nng X mol/l v mui tr XY nng (I X) mol/l. y (trong dung dch HA); = I (trong dung dch XOH);

Vi qu trnh phn li ta c:

(I.21)

(I.22)

(I.23)

(I.24)

Hoc vi qu trnh proton ha baz A ta c:

T phng trnh trung ha in, sau khi t hp ta c:

[H+] = [OH-] + [A-] [X+] + [Y+]

vi h = 10-pH

EMBED Equation.DSMT4

Chia c hai v cho Ai c:

t:

Ta c: (I.25)

Mt khc theo nh lut bo ton nng ta c:

Thc t trong khu vc nng nghin cu s lin hp ca cc axit HA l v cng nh. Do :

(I.26)

Theo nh lut bo ton in tch, ta c:

[H+] [OH-] + [X+] [A-] = 0

Mt khc ta c: ; kt hp vi (I.26) ta c:

Ai = [HA] +

Thay vo (I.14) ta c:

(I.27)Kt hp vi (I.22) ta c:

Trong : K:l hng s ca phn ng.

: Gi tr nghch o h s hot ca ion ;

l h s hot ca axit HA;

h: hot ca ion hiro o c bng thc nghim o pH.

lc ion xc nh, bng cch o pH ca hn hp chun cc thi im khc nhau ta s c mt dy cc gi tr trung bnh

(I.28)

Bng cch ngoi suy K* cc lc ion khc nhau v lc ion I = 0 ta c:

v sau nh gi

Bng cch o trc tip ca cc cht khng in li (th d bng phng php o tan, o h s phn b) ta s nh gi c:

Hoc nh gi i lng tp hp cc lc ion khc nhau, sau ngoi suy t lc ion I = 0 nh gi hng s proton ha nhit ng ca cc baz nghin cu sau tm tch: . Bng php o trc tip h s hot ca phn t khng tch in (v d bng php o tan, o p sut hi, o hng s phn b cht tan gia hai dung mi khng trn ln, ...) c th nh gi h s hot i ca cc lc ion I cho .

I.2. Cc phng php xc nh hng s cn bng

c nhiu cng trnh nghin cu phng php xc nh HSCB ca cc phc cht, axit, baz ring l nh phng php o pH, phng php o trc quang. Cc phng php u xut pht t vic nh gi HSCB nng KC, sau ngoi suy v lc ion bng 0 nh gi HSCB nhit ng. Mt s phng php khc (phng php Kamar) nh gi tp hp cc HSCB iu kin ca cc n axit, n baz ri tnh ring l cc tham s cn bng. Bn cnh cn c nhng phng php thc nghim nh: phng php o dn in, phng php o in th, phng php quang hc kt hp vi nhng phng php tnh ton nh: phng php BPTT, phng php hi qui phi tuyn, phng php n hnh, thut gii di truyn c trnh by chi tit trong cc ti liu [1, 2, 3, 4, 5, 7, 10, 11, 13, 15]. I.2.1 Tnh hng s cn bng nng KC sau ngoi suy v lc ion I = 0 nh gi hng s cn bng nhit ng Ka

V nguyn tc, ta phi dng hot trong biu thc nh lut tc dng khi lng v s dng nng trong biu thc nh lut bo ton khi lng.

i vi ion kim loi Mn+ ta c:

Theo nh lut tc dng khi lng:

(I.29)

Trong :

(i): hot ca cu t i.

[i]: nng cn bng ca cu t i.

fi : h s hot ca ion i (tnh theo thang nng mol/l).

vy: (I.30)

Hay:

l tham s bt nh gy sai s cho .

ph thuc vo:

+ Lc ion ca dung dch

+ Bn cht ca ion

+ Mi trng ion.

Vy mun tnh c hng s cn bng nhit ng ta phi tnh hng s cn bng nng , sau ngoi suy v lc ion I = 0. i lng c tnh theo mt trong cc phng trnh kinh nghim trnh by trn.

I.2.2. Phng php Kamar nh gi hng s phn li axit

Xt axit HA:

Theo nh lut tc dng khi lng:

V

Vy nu xc nh c hng s cn bng nng Kc v hot ca cc cu t l v gi tr th ta s xc nh c hng s cn bng nhit Ka.

Vic o pH ca dung dch ch cho ta hot ca ion H+ do: pH=-lg(H+)

Ta c:

Nn nu thit lp c mt nng chnh xc ca ion H+ v o c pH ca dung dch th c th nh gi c h s hot . Cc phng php o c thc hin ring trc khi o hng s cn bng.

V mt thc nghim nh gi hng s cn bng Ka ngi ta chun W ml dung dch HA nng A0 mol/l khi c mt cht in li tr XY (v d NaCl) c nng bng lc ion cn thit lp I, bng V ml dung dch kim mnh XOH nng X mol/l v mui tr XY nng (I X) mol/l. V vy:

Theo nh lut trung ha in:

Mt khc:

Gi a = () ta c:

V

V vy:

t:

lc ion xc nh, bng cch o pH ca hn hp chun cc thi im khc nhau ta s c mt dy cc gi tr trung bnh . Bng cch xc nh cc lc ion I khc nhau sau ngoi suy v lc ion I = 0 ta c (v lc ion I = 0 th = 1, = 1) v sau nh gi (.)I = .

Bng cch o trc tip ca cc cht in li (bng cc phng php o tan, p sut hi, o h s phn b ) ta s nh gi c:

Nh vy, phng php Kamar c u th c bit v cho php nh gi ng thi tt c cc tham s cn bng trong dung dch Ka, , , mc d v mt thc nghim l kh cng phu. S liu tham s cn bng ca nhiu axit baz c cng b.

I.2.3. Phng php o dn in

Phng php da trn vic o dn in ng lng v nh gi in li ca cc axit da trn quan h ph thuc:

(I.31)

y:

o l gi tr gii hn ca c khi C = 0 (dng phng php nh gi ngoi suy).

l h s dn in

l in li.

Php o dn in cho php nh gi ., nu bit c th nh gi v sau nh gi hng s cn bng theo cng thc:

I.2.4. Phng php o in th

Php xc nh hng s cn bng ca cc n axit HA da vo vic o E(s) ca pin khng cu ni:

V nh gi hng s cn bng da vo biu thc:

(I.32)

Trong : E0 l sc in ng ca pin chun:

l nng molan ca Cl-

Bit cc gi tr chnh xc [HA], , [A-] c th nh gi chnh xc , sau ngoi suy v lc ion I = 0 cho php nh gi K. i vi cc axit yu HA c th chp nhn [HA] = CHA, .

Cng c th da vo php o sc in ng ca cc pin c cu ni:

H2 (Pt) | dung dch nghin cu || KCl bo ha | in cc so snh (*)

Php o sc in ng cho php nh gi pH ca dung dch:

(I.33)

Gi tr pH c cha gi tr th khuch tn trong pin (*). c nh gi theo sc in ng ca pin vi dung dch c pH bit trc v cng gn vi gi tr pH o cng tt (chn mt lot cc dung dch m c pH bit).

Biu thc K c tnh theo cng thc:

Thay pH theo gi tr pH:

Thng thng ngi ta biu din theo cng thc Debye Huckel gii hn tin hnh ngoi suy v lc ion I = 0.

I.2.5. Phng php quang hc

Ni chung tnh cht quang hc ca dng axit khng phn li HA khc vi tnh cht ca dng phn li , v d nh tnh nhiu x, hunh quang, hiu ng Raman, hp th nh sng ... Nu c kh nng phn bit khc nhau ny xc nh nng ca cc dng HA v th c th dng phng php quang hc xc nh hng s cn bng K. Phng php o hp th nh sng l phng php chnh xc nht xc nh hng s cn bng K.

Cc phng php trc quang u da trn nguyn tc xc nh nng cn bng ca cc cu t [HA], [] da trn nh lut Bia:

Mt quang:

bc sng thch hp, bng php o trc v cng bc sng c th nh gi [HA], [] t nh gi hng s cn bng nng Kc. i vi aaxit khng mu ngi ta s dng vic o pH da vo mt cht ch th mu thch hp. Phng php da trn vic t hp o in th v trc quang cng thng c s dng.

Cc phng php k trn ch cho php nh gi gi tr hng s cn bng K ca cc n axit, n baz ring l v c p dng xc nh hng s cn bng K ca nhiu axit, baz.

I.2.6. Phng php n hnh nh gi hng s cn bng ca cc n axit, n baz [4]

Bi ton xc nh cc tham s ak trong hm s f(xi, yj, ak) = 0 m t mi quan h gia cc gi tr thc nghim yj vo cc bin xi (bit trc) thng c xc nh bng phng php bnh phng ti thiu, tc l tm b tham s ak sao cho: S = min.

Nh vy, bi ton hi quy thng a v bi ton tm cc tiu hm S vi cc ak l cc bin s ca hm s ny, cn xi, yj l gi tr bit trc. Phng php o hm l phng php n gin thng c s dng, tuy nhin trong nhiu trng hp rt kh hay khng th tnh o hm ca hm S khi m mi quan h gia hm s v cc tham s khng c biu din di dng tng minh. Mt s phng php khng s dng o hm c a ra, trong phng php n hnh l mt phng php hu hiu, n gin, c th s dng cho mi dng ca hm s S.

Phng php n hnh c a ra, s dng trong bi ton tm cc tiu ca mt hm s n bin bng cch tnh n + 1 im to nn mt n hnh trong khng gian n chiu. Sau tin hnh vng lp thay th im c gi tr hm s ln nht (trong n + 1 im ly trn) bng im i xng vi n qua mt phng cha cc im cn li, cho n khi thu c im c gi tr cc tiu. Nm 1965, Nelder v Mead m rng phng php ly im i xng, lm cho phng php c hi t nhanh hn (gi l phng php n hnh m rng). y chng ti trnh by ni dung ca mt phng php n hnh m rng.

Thut ton n hnh: Tm cc tiu ca mt hm s n bin gm hai bc: Tin hnh chn n hnh S0 bao gm (n + 1) im: P0, P1,, P2,.., Pn; ng vi mi im Pi (c cc ta l ak , k = 1) v gi tr hm s ti im ny l yi.

Tin hnh chn im i xng: gi yh = max(yi) v y1 = min(yi), tin hnh thay im Ph (im c gi tr y cc i) bng mt trong ba im sau: im i xng P*, im m rng P** hoc im rt ngn P***.

- Trc ht ta xc nh cc im ny nh sau:

+ im tm l im c ta c xc nh theo biu thc sau:

+ im i xng P* c xc nh nh sau: trong l h s i xng, mt hng s dng. im nm gia P* , v .

+ im m rng P* * c xc nh nh sau: trong 1: l h s m rng, nm ngoi im P*.

+ im P*** c xc nh: trong l h s rt gn 0 < < 1.

Cc tc gi Nelder v Mead cng tm ra gi tr , , ti u nh sau: = 1,0; = 0,5 v = 2,0.

V d: Hm hai bin f(x1,x2), v n = 2, n hnh S0 ly 3 im W, N, B v ba im m rng l P*, P**, P***.

Hnh 1.1. Phng php n hnh m rng ng vi n = 2-Cch xc nh cc im thay th P*, P** hoc P*** nh sau: Gi y*, y**, y*** l gi tr hm s ng vi ba im P*, P**, P***. Nu y1 < y* < yh th thay im Ph bng im P*, ta c n hnh mi v bt u li t u.

Ngc vi trng hp ny chng ta c hai trng hp sau:

-Nu y*< y1 tc l im i xng l mt im cc tiu mi, hay y l hng tin n cc tiu, chng ta tin hnh thm d bng im m rng P**, nu gi tr hm s ca im ny vn ln hn im P1(y**>y1) th thay im Ph bng im P*.

-Nu y* > yh khi thay th bng im rt ngn P***.

Vng lp thay th dng li khi phng sai , trong gi tr cho trc.I.2.7. Phng php chun in th [16].

Chun in th l mt phng php chun xc nh HSCB. Trong qu trnh chun in th, mt mu c chun bng axit hoc baz, in cc o pH c s dng ghi li cc gi tr pH trong sut qu trnh chun . Gi tr pKa c tnh da trn s thay i hnh dng ca ng cong chun khi chun mu tht so vi ng cong khi chun mu trng. Phng php phn tch thng thu c pKa t ng cong chun nh gin Grant [23], th o hm bc 2 (2pH/V2) [3] v ng hi quy BPTT khng tuyn tnh [19, 26]. Chun in th l phng php xc nh pKa ca cc cht c chnh xc cao. Phng php ny hay c s dng v tnh chnh xc, nhanh v c th dng cc thit b t ng ha. Tuy nhin, hn ch ca n l cn lng kh ln ha cht tinh khit (c 10-3g) v hn hp m [23]. Dung dch phi c nng thp nht khong 10-4 M mi pht hin c s thay i ng k trong hnh dng ca ng cong chun . trnh sai s, c bit khi o vng pH trung tnh v kim, cn chun b tht cn thn dung dch khng c cacbonat [19, 26].I.2.8.Phng php o quang [16]

Tin b hn phng php chun in th l phng php o quang vng UV-Vis bi phng php ny c th p dng cho nhng cht c tan thp v nhng mu c nng thp hn so vi phng php chun in th. u im chnh ca phng php ny l nhy cao (10-6 M) i vi nhng hp cht c h s hp th mol phn t () ph hp. Tuy nhin, nhng hp cht ny phi cha nhm gy ph UV gn vi nhm chc axit-baz.

Cc d kin ph c ghi lin tc bi my ghi ph i-t trong sut qu trnh chun . Ph hp th ca mu thay i trong qu trnh chun cho thy s thay i nng ca cc cu t trung ha in cng nh cc ion c mt trong h. S thay i r nht ca mt quang s xy ra ti pH tng ng vi gi tr pKa. Nhng thay i ny c th thy r trn th o hm bc nht gia mt quang A v thi gian hoc thng qua vic chng ph ca cc mu. Xc nh pKa bng phng php ph hp th c ng cao, tuy nhin cng nh phng php in th, phng php ny i hi ha cht phi tinh khit v cc cht khc nhau phi c ph khc nhau. Thng thng, pKa c xc nh da trn kt qu ph hp th ti bc sng xc nh ca 1 dy mu cha cht nghin cu c chun b ti cc pH khc nhau (s dng dung dch m duy tr pH). s dng phng php ny, trc ht cc cht ring r phi c ph hp th c trng, thm na l cc cht khi proton ha hay proton cng phi c kh nng hp th khc nhau. Vic ghi ph s tr nn phc tp nu cn bng axit-baz c t 2 mc ion ha hoc cc hp phn khng bn trong khong 2 n v pH quanh gi tr pKa. V vy m phng php ghi ph ti nhiu bc sng khc nhau ca mu ti cc pH khc nhau ang c pht trin.

I.2.9. Phng php chun NMR [16]

Phng php chun pH-NMR l mt cng c rt hu ch trong vic xc nh pKa. S proton ha nhm baz s gy ra cc hiu ng trn lp v electron ln cn vi ht nhn mang ph NMR, dn n s dch chuyn trung bnh ca cc tn hiu ph NMR nh mt hm ca pH s phn nh s proton ha tng nc ca mi nhm baz trong phn t. S kt hp gia chun in th vi mt my ghi ph cng hng t NMR c gi l k thut chun NMR [20, 22].I.2.10. Phng php sc k lng [16]

Vic xc nh pKa bng phng php sc k lng (LC) da trn mi quan h gia h s mang v pH ca pha ng. i vi mi hp cht v mi thnh phn ca pha ng cng nh khi tnh n pH, thi gian lu tR l xc nh. H s mang c tnh t biu thc:

k =

(I.30)

vi tM l thi gian tr (c xc nh c th i vi mi pha ng ti pH khc nhau). i vi n axit, h s mang ti cc pH khc nhau c biu din di dng hm ca h s mang ca cht trung ha v anion ( v ) vi phn mol tng ng ca chng ( v ) [6]:

k = . + . hay k =

(I.31)

Phn mol c biu din theo hng s phn li v nng ca ion hiro hay theo pH v pKa.

hoc

(I.32a)

hoc

(I.32b)

Thay xi trong phng trnh (I.31) ta c:

hoc

(I.33)

Phng trnh trn lin quan n thi gian lu trong sc k ca n axit v pH ca pha ng, t tnh c gi tr pKa v cng d on c sc k ca cc cht.

n gin, s hiu chnh hot khng c cp n. H s hot ca ion trong dung dch long ti 250C c th c nh gi da trn phng trnh Debye-Huckel.

Sc k lng (LC) l mt phng php hu hiu trong vic xc nh hng s phn li, phng php ny ch cn mt lng nh ha cht, cht nghin cu khng cn phi tinh khit v do nu c tan thp trong nc th cng khng gy tr ngi g. Tuy nhin cc gi tr pKa c xc nh theo phng php ny thng cao hn so vi kt qu tnh theo phng php chun in th v ph UV-Vis [20]. Hn ch ca phng php ny l pH ca pha ng v do phm vi ca pKa c th xc nh c b gii hn. Thm na l i vi cc cht c thi gian lu ln th rt kh xc nh c pKa trong nc hoc trong hn hp dung mi nc-cht hu c.

I.2.11. Phng php in di mao qun [16]

Phng php in di mao qun xc nh pKa da trn vic quan st lc chuyn ng ca cc ion trong mt dy cc dung dch cht in li c lc ion c nh nhng pH thay i. trng thi khng mang in, cht tan c lc chuyn ng bng 0, trng thi ion ha hon ton th lc chuyn ng l ln nht. Do lc chuyn ng s l 1 hm ca cn bng phn li, i vi n axit yu, lc chuyn ng c biu din:

(I.34)

Trong : xi l anion do n axit phn li ra v ep,I l lc in chuyn ca 1 ion m. Khng c gii hn no v s cn bng ion ha lin quan v do lc chuyn ng tng qut c biu din nh sau:

(I.35)

Vi xi l phn mol ca cu t i c lc in chuyn ep,i. Thay phng trnh phn s nng hoc

(I.36)

ta thu c phng trnh biu din lc chuyn ng:

(I.37)

T y ta s xc nh c pKa khi bit pH v tnh c lc chuyn ng . Phng php ny c bit hu ch i vi nhng cht him v CE ch cn lng mu phn tch c vi nano gam hoc t hn. Trong phng php CE, ch cn xc nh pH- ph thuc linh ng nn c nhng thun li sau: Nng cht nghin cu ch cn s dng khong gii hn pht hin ca chnh cht . Qu trnh o khng cn xc nh nng ca cht tan nn khng cn dng ha cht tinh khit.

I.2.12. Phng php kt hp [16]

Trong nhng nm gn y, mt phng php kt hp gia LC, CE trong vic xc nh pKa ang c pht trin cng vi vic s dng thm detector dy i-t quang (DAD) o hp th. Trong trng hp ny gi tr pKa c xc nh t ph hp th ti nh ca sc k hoc nh ca dng in chuyn. u im ca php kt hp ny l tit kim thi gian phn tch, tng tin cy ca kt qu. Hng s phn li c xc nh d dng bng k thut LC-MS hay vic s dng CE-MS c th lm tng nhy cng nh tng tnh chn lc, t m bo rng s khng tinh khit ca ha cht s khng gy nhiu.

I.2.13. Phng php tnh ton [16]

pKa c th c xc nh bng cc phng php tnh ton nh SPARC [30] v ACD/Lab [17].

SPARC l th vin tra cu trc tuyn cho php nh gi gn ng gi tr ln hoc nh pKa ca bt k hp cht hu c ch t cu trc ha hc ca n.

ACD/Lab l mt chng trnh phn mm tnh ton chnh xc hng s axit- baz nhit 250C v lc ion I = 0 trong dung dch nc hoc ca bt k cu trc hu c no.I.3. Thut ton bnh phng ti thiu

xc nh gi tr pKa c nhiu phng php hin i c trnh by trong mc II.2, tuy nhin vi nhng iu kin v k thut, trang thit b phng th nghim, phng php chun in th l phng php ph hp v tin li, m vn m bo chnh xc cn thit, c bit i vi vic xc nh gi tr pKa trong dung mi nc. Trong nhng nm gn y c mt s cng trnh tp trung nghin cu cc phng php l thuyt kt hp vi vic ng dng cng ngh thng tin vo ho hc phn tch lp cc chng trnh tnh ton cn bng ion trong dung dch, trong c nghin cu cc phng php nh gi cc hng s cn bng t gi tr pH bit. Phng php BPTT v phng php n hnh l nhng phng php tnh ton kt hp vi d liu pH thu c t php chun in th c s dng rng ri trong vic xc nh HSCB nhit ng. Tuy nhin vic s dng phng php BPTT l n gin v ngn gn hn nn chng ti s s dng phng php ny tnh ton.

I.3.1 Ni dung phng php bnh phng ti thiu

C s ton hc ca phng php BPTT l gii h phng trnh gm n n v m phng trnh vi n < m (s n nh hn s phng trnh).

(I.38)

Vi: x1i, x2i, , xni l cc gi tr cho trc.

yi : l cc gi tr thc nghim.

a1, a2, , an l cc gi tr cn tm.

V cc cp gi tr l cc gi tr cho trc, yi nhn c t thc nghim gi tr ny ch l nhng gi tr gn ng nn chng khng hon ton nghim ng phng trnh Ngha l:

(I.39)

Trong l cc sai s.

Phng php BPTT nhm xc nh sao cho tng cc bnh phng ca cc sai s l nh nht. Ngha l:

b nht. Nh vy phi tho mn h phng trnh:

(I.40)

(I.41)

Vy h phng trnh gm m phng trnh n n c a v h n phng trnh n n (gi l h Cramer nu ). Bi ton a v gii h phng trnh gm n phng trnh n n vi ma trn h s:

(I.42)

l mt ma trn vung cp n.

Dng ma trn ca h l: A.a = Bvi

H Cramer c nghim duy nht tnh bng cng thc tc l:

Trong A l ma trn h s, Aj l ma trn suy t A bng cch thay ct th j bi ct v bn phi B.

Vi n = 2, h phng trnh trn tr thnh:

(I.43)

H 2 phng trnh 2 n ny c gii theo phng php s dng nh l Cramer kt hp vi gii nh thc bc 2:

Ta c:

EMBED Equation.DSMT4

EMBED Equation.DSMT4

EMBED Equation.DSMT4 Nghim ca h l:

;

(I.44)

i vi trng hp tng qut, ta c th lp chng trnh tng qut gii h phng trnh tng qut theo phng php kh Gauss.

I.3.2 Tng quan v tnh hnh nghin cu s dng phng php bnh phng ti thiu nh gi HSCB axit-baz. [16]I.3.2.1 Trn th gii

Trn th gii, phng php xc nh HSCB ca axit, baz v phc cht da trn kt qu ca chun in th kt hp vi phn mm tnh ton trn my tnh c thc hin t nhng nm 90 v c cp n trong ti liu [19].

Cc tc gi trong [19, 20] s dng kt qu ca chun in th, phn mm tnh ton BEST v SPE (c cp n trong ti liu [19]) tnh c HSCB ca phc gia Cu(II) v 5 nguyn t h lantan vi aminoiaxetat trong dung mi nc v dung mi l hn hp gia nc v hiropeoxit v thu c kt qu tng i ph hp vi l thuyt.

Cc tc gi trong [20] xc nh hng s phn li axit ca 26 khng sinh trong c th ngi v ng vt bng phng php chun in th. Thuc khng sinh c la chn bao gm: sulfonamides, macrolides, tetracyclines, fluoroquinolones. Sau khi xc nhn phng php phn tch s dng axit photphoric nh mt cht mu, phng php o hm bc 2 (2pH/V2) c p dng ch yu xc nh pKa t ng cong chun cho hu ht cc khng sinh v s tin li v chnh xc. Tuy nhin vi tetracyclines phng php hi quy BPTT c pht trin xc nh pKa bi v phng php o hm bc 2 khng th phn bit tt gi tr pKa2 v pKa3 ca tetracyclines. Kt qu ch ra rng gi tri pKa xp x 2 v 5 - 7,5 vi sulfonamides; 7,5 - 9 vi macrolides; 3 - 4, 7 -8 v 9 - 10 vi tetracyclines; 3 4; 7,5 9 v 10 11 vi fluoroquinolones. Nhng kt qu ny c vai tr quan trng trong vic nghin cu, pht trin phng php phn tch v kim sot khng sinh trong cc hot ng iu tr sau ny.

I.3.2.2. Trong nc

Trong nhng nm gn y, nhm nghin cu cn bng ion ca b mn Ha Phn tch, khoa Ha hc, trng i hc S phm H Ni tp trung nghin cu phng php tnh lp theo thut ton bnh phng ti thiu (BPTT) v thut ton n hnh (H) kt hp vi vic ng dng cng ngh thng tin lp chng trnh tnh theo cc ngn ng lp trnh khc nhau nh Pascal, Matlab nh gi hng s phn li axit ca mt s cc n, a axit khc nhau.

M u cho hng nghin cu ny, cc tc gi s dng thut ton BPTT kt hp vi gi tr pH tnh ton theo l thuyt xy dng phng php tnh lp nh gi cc HSCB ca cc n axit, n baz [15], a axit, a baz [1] v hng s to phc hiroxo ca mt s ion kim loi [10]. V cng tng t, t gi tr pH l thuyt, s dng thut ton n hnh, tc gi trong [14] bc u xy dng c phng php xc nh HSCB axit baz bng cch tnh lp lc ion.

khng nh tnh ng n ca phng php nghin cu, ng thi kim tra s ph hp gia gi tr l thuyt v thc nghim, ln u tin tc gi trong [2] tin hnh thc nghim o pH v chun in th o pH cc dung dch a axit (axit oxalic) c nng khc nhau bng dung dch NaOH. T cc gi tr pH thc nghim thu c, tc gi s dng phng php BPTT vi vic tnh lp lc ion xc nh cc hng s phn li axit tng nc ca a axit oxalic. Kt qu thu c t thc nghim kh ph hp vi cc s liu c cng b trong ti liu tham kho tin cy [8].

khai thc kh nng ng dng thut ton tnh lp theo phng php BPTT, trong [7] cc tc gi cng tin hnh thc nghim o pH v chun in th o pH ca dung dch hn hp gm hai n axit c HSCB tng ng nhau: axit axetic v axit benzoic. Khc vi [2], y cc tc gi s dng mui tr KCl khng ch lc ion m khng phi tnh lp lc ion. Kt qu nghin cu cho thy: t gi tr pH thc nghim o c ca dung dich hn hp 2 n axit c HSCB tng ng nhau, cho php xc nh ng thi HSCB ca c 2 axit. Kt qu thu c t thc nghim kh ph hp vi kt qu c cng b trong ti liu [8]. Kt lun ny cng c khng nh mt ln na trong ti liu [11] khi tc gi tin hnh xc nh ng thi HSCB ca 2 axit c lc axit tng ng nhau: axit axetic v axit fomic t gi tr thc nghim o pH ca dung dch gm hn hp 2 n axit ny. tip tc m rng kh nng ng dng ca phng php BPTT trong vic xc nh HSCB axit baz, ng thi i chiu kt qu nghin cu, trong [5] v [4], cc tc gi s dng song song 2 thut ton: BPTT v n hnh nh gi HSCB ca 2 axit c hng s phn li axit chnh lch nhau nhiu: axit axetic v amoni t gi tr pH o c bng thc nghim chun in th trong cc trng hp khc nhau: pH ca dung dch hn hp hai n axit ny [5], pH ca dung dch tng n axit ring r (dung dch axit axetic, dung dch amoni), hoc pH ca dung dch n baz lin hp (NH3), trong cc tc gi u khng ch lc ion bng dung dch mui tr KCl. Kt qu thu c theo 2 phng php khc nhau kh ph hp vi nhau. Tuy nhin, t gi tr thc nghim o pH ca hn hp 2 n axit c hng s phn li axit chnh lch nhau nhiu, ch cho php xc nh c HSCB ca axit mnh hn.

m rng kh nng ng dng phng php BPTT trong vic nh gi hng s phn li axit tng nc ca a axit, cc tc gi trong ti liu [3] tin hnh o pH v chun in th o pH ca dung dch axit tactric. T pH ca cc h khc nhau thu c trong qu trnh chun , cc tc gi xc nh kh chnh xc gi tr hng s phn li axit tng nc ca axit ny. kim tra kt qu tnh ton theo BPTT, tc gi trong ti liu [10] s dng b s liu thc nghim o pH ca dung dch axit tactric nh gi HSCB ca axit ny, nhng theo phng php n hnh. Kt qu thu c theo 2 phng php khc nhau kh ph hp vi nhau. T kt qu nghin cu, cc tc gi rt ra nhn xt: thng ch xc nh c gi tr hng s cn bng ca qu trnh no nh hng trc tip n pH ca h. iu ny cng ph hp vi ti liu [2]. CHNG II: THC NGHIM

V nhng l do nu trong phn m u nn trong kha lun ny chng ti tin hnh chun in th o pH ca dung dch mui natri cacbonat c cc nng khc nhau bng dung dch HCl. xac inh HSCB cua axit cacbonic chung ti a xac inh gi tr pH ca cc h sau: H mui cacbonat Na2CO3 (k hiu l A2-).

H mui hirocacbonat HCO3- (k hiu l HA-). H axit cacbonic H2CO3 (k hiu l H2A) H m 1 gm: mui cacbonat v mui hirocacbonat (A2- v HA-). H m 2 gm: mui hirocacbonat v kh CO2 (HA- v H2A).

T kt qua thu c nh gi s ph hp gia l thuyt v thc nghim cng nh khng nh tnh ng n ca phng php nghin cu.II.1. Ha cht, dng c Na2CO3 (M = 105,99), xut x Trung Quc, tinh khit 99,5%.

HCl, xut x c, tinh khit 100%.

KCl (M = 74,55), xut x Trung Quc, tinh khit 99,5%.

Na2B4O7.10H2O (M = 381,32), xut x c, tinh khit 99%.

Phenolphtalein, metyl da cam, metyl .

Cn phn tch (c chnh xc 0,0001 gam)

Bnh nh mc loi 100 mL, 250 mL, 500 mL v 1000 mL.

Cc thy tinh.

Buret, pipet, bnh hnh nn.

My o pH meter SCHOTT 850 ca c.

II.2. Tin hnh thc nghimII.2.1. Pha ch dung dch

Ht 8,3 mL dung dch HCl pha vo bnh nh mc 2000 mL bng nc ct hai ln. Cn chnh xc 5,31 g Na2CO3 sau pha vo bnh nh mc 500 mL bng nc ct hai ln, c dung dch gc Na2CO3. Cn chnh xc 149,129 gam KCl, ri pha vo bnh nh mc 1000 mL bng nc ct hai ln.

CKCl = = 2,0 (mol/L)

II.2.2. Chun th tch xc nh nng cc dung dch Na2CO3II.2.2.1. Chun ha dung dch HCl bng Borax:

chun ha dung dch HCl thng dng cc cht gc baz trng thi rn nh borax, natri cacbonat, natri oxalat Trong phn ny chng ti s dng borax chun ha HCl. Phn ng chun :

B4O72- + 2H+ +5H2O 4H3BO3 K=2,7.1015

K rt ln nn phn ng xy ra gn nh hon ton. H3BO3 c coi nh mt n axit yu c pKa =9,24 (s phn li ca nc 2 v nc 3 v cng yu).

Gi tr pHt = 5,12 gn trng vi pT ca ch th metyl , v vy chn ch th metyl , ch th i mu t vng sang hng da cam (pT = 5,0).

Cn mt lng ph hp (khong 0,095 g) Na2B4O7.10H2O bng cch: Cn chnh xc khi lng cc G1: mcc Cn chnh xc cc v ha cht c G2: mcc + mNa2B4O7.10H2O Khi lng Na2B4O7.10H2O l a = G2 G1 Ha tan bng nc nng hon ton Na2B4O7.10H2O trong cc sau chuyn ton b dung dch ny vo bnh tam gic ra v trng sch bng nc ct hai ln.

Thm 2 git metyl , lc u. Chun bng dung dch HCl cho ti khi dung dch chuyn t mu vng sang mu hng da cam, ngng chun v ghi gi tr VHCl trn buret. Lp li php chun nh trn 6 ln v ly gi tr trung bnh 6 ln o, t xc nh chnh xc nng dung dch chun HCl.II.2.2.2. Chun xc nh nng ca dung dch mui natri cacbonat:

Mui cacbonat co Kb1 /Kb2 > 104 nn c th chun ring nc 1 v nc 2 ca CO32- c vi sai s khng vt qu 1%.

Phng trnh ca phn ng chun :

CO32- + H+( HCO3

Kb1

HCO3 + H+( CO2 + H2O

Kb2 Ht 5 mL dung dch gc Na2CO3 vo bnh hnh nn. Thm 2 git ch th phenolphtalein, lc u Chun t t bng dung dch chun HCl v lc u cho n khi dung dch mt mu hng hon ton. Ghi gi tr V1(ml) HCl trn buret. Thm tip 2 git metyl da cam vo hn hp chun .

Chun tip bng dung dch HCl cho n khi dung dch chuyn t mu vng sang mu hng da cam. Ghi gi tr V2(ml) HCl trn buret.

Lp li th nghim 2 ln na xc nh th tch trung bnh ca HCl tiu th , .

Kt qu ca php chun c trnh by trong bng 2.1 v 2.2:Bng 2.1: Kt qu xc nh nng dung dch HCl theo phng php chun th tch

LnKhi lng Na2B4O7.10H2O (g)VHCl (ml)

10,09511,85

20,09511,9

30,09511,9

40,09511,85

50,09511,85

60,09511,9

= 11,875

= 4,196.10-2 M

Bng 2.2: Kt qu xc nh nng Na2CO3 bng HCl theophng php chun th tch.LnTh tch Na2CO3 (ml)Th tch HCl (ml)

V1V2

1511,923,75

2511,9523,8

3511,9523,8

= 11,93= 23,78

= 1,0012.10-1 M= 0,09978 M

= 0,09995 M

II.2.3. Chun b cc dung dch mui Na2CO3 c nng khc nhau.

- Ly chnh xc tng th tch xc nh dung dch mui natri cacbonat cho vo 10 bnh nh mc 100 mL; thm tip vo mi bnh chnh xc 50 mL dung dch KCl 2M v nh mc bng nc ct 2 ln n vch c 10 dung dch mui natri cacbonat vi nng khc nhau.

Nng ca cc dung dch Na2CO3 c tnh theo cng thc sau:Ci = QUOTE

Trong : C0 l nng ban u ca dung dch Na2CO3 gc; Vi l th tch dung dch Na2CO3 ly, Ci l nng ca mui thu c sau khi pha long. V CKCl c tnh nh sau:

CKCl = = 1M

II.2.4. o pH cc dung dch Na2CO3 v chun in th o pH ca dung dch mui Na2CO3 bng HCl.

II. 2.4.1. o pH ca cc dung dch Na2CO3:- Tin hnh o pH trn my o pH ca cc dung dch mui. Kt qu thu c, c trnh by trong bng 2.3.

Bng 2.3: Kt qu o pH ca dung dch mui Na2CO3 c nng khc nhau.

Dung dch(ml).103(M)pHTN

130,00295710,52

240,00398410,59

35,50,00549810,67

46,50,00650410,7

580,00810,84

690,00900910,85

710,50,01051710,87

811,50,01143110,89

9130,01296710,92

10140,01395510,94

II.2.4.2. Chun in th o pH ca dung dch mui Na2CO3 bng HCl.

c c d liu pH ca cc h khc nhau, tc gi tin hnh chun in th o pH ca 10 dung dch mui cacbonat c nng khc nhau (V0 = 25,00 mL) bng dung dch axit mnh HCl (VHCl (mL) l th tch HCl tiu th). Kt qu chun c ghi trong bng 2.4:

Bng 2.4:Kt qu chun in th o pH ca 10 dung dch mui Na2CO3STTHn hp 1Hn hp 2Hn hp 3Hn hp 4Hn hp 5

VHCl(ml)pHVHCl(ml)pHVHCl(ml)pHVHCl(ml)pHVHCl(ml)pH

1010,52010,59010,67010,70010,84

20,2010,280,809,991,0010,091,0010,211,0010,33

30,4010,111,209,832,009,582,009,792,009,98

40,859,791,509,732,509,252,709,483,009,56

51,209,421,809,182,709,053,109,254,009,12

61,409,172,008,922,808,923,408,994,208,95

71,508,872,108,652,908,683.508,894,308,86

81,558,712,158,513,008,673.558,814,408,75

91,608,632,308,613,108,443.608,724,458,66

101,658,592,358,513,208,313,658,624,508,58

111,708,422,408,393,257,893,808,614,608,49

121,758,112,457,823,307,593,858,554,708,51

131,807,732,607,623,357,513,907,524,758,39

141,907,662,806,893,507,253,957,444,808,29

152,007,173,206,574,006,915,006,674,857,89

162,406,623,606,295,006,127,005,425,007,64

172,606,343,905,855,505,827,505,198,006,15

182,806,124,105,746,005,617,654,888,805,84

193,006,064,205,656,205,267,704,779,005,48

203,205,664,305,506,405,027,753,909,205,18

213,255,584,405,486,504,857,803,759,304,88

223,305,524,505,386,554,398,003,419,454,75

233,355,374,605,236,604,168,503,139,504,68

243,405,074,704,976.653,9710,52,879,553,98

253,454,974,754,926,803,5412,02,569,603,82

263,504,164,803,977,003,3610,003,72

273,603,854.853,8111,003,58

283,803,315,003,23

294,003,10

STTHn hp 6Hn hp 7Hn hp 8Hn hp 9Hn hp 10

VHCl(ml)pHVHCl(ml)pHVHCl(ml)pHVHCl(ml)pHVHCl(ml)pH

1010,85010,87010,89010,92010,94

21,0010,351,0010,381,0010,412,0010,362,0010,38

32,009,953,009,772,0010,224,009,965,009,77

43,009,515,009,565,009,686,009,796,009,56

54,008,926,009,476,009,537,009,537,009,12

64,808,826,109,136,508,957,408,918,008,95

74,908,766,208,816,708,467,508,308,108,86

85,008,696,258,746,758,387,658,218,258,54

95,108,626,307,366,808,317,707,718,308,48

105,308,516,357,216,858,267,757,638,357,61

115,358,436,406,956,907,858,007,578,407,50

125,407,646,606,826,957,728,357,468,507,37

135,457,547,006,7710,006,319,007,329,007,29

145,607,489,006,1113,006,5011,006,1712,006,67

155,807,2811,005,0513,505,8714,006,0413,006,38

166,206,7912,004,9113,655,1215,005,7815,006,18

177,006,4212,304,8613,705,0115,305,4516,005,61

188,006,1612,404,8313,753,9515,405,9616,205,37

1910,505,1412,454,7614,003,8515,455,8716,405,11

2010,604,8312,503,7414,503,7615,504,0616,504,98

2110,654,7712,553,6416,553,9616,604,94

2210,704,6812,603,7317,004,6616,654,77

2310,754,5812,803,6918,004,4316,703,59

2410,803,8612,903,5516,753,44

2510,903,7817,003,38

2611,003,3218,003,66

2720,003,23

CHNG IIIXC NH HNG S CN BNG TNG NC

CA AXIT PHOTPHORIC T GI TR THC NGHIM O pH

III.1. Xy dng thut ton tng qut tnh lp HSCB axit trong dung dch cc a axit, a baz bt k theo phng php BPPT kt hp vi KP

Gi s c dung dch hn hp cc a axit, k hiu chung l HnA (c hng s phn li axit tng nc Kai, c nng tng ng l Ca) v cc a baz, k hiu chung l Bm- (c hng s phn li axit lin hp l Kai, nng tng ng l Cb).

n gin, khi thit lp phng trnh tnh chng ti ch xt trng hp h gm 1 a axit v 1 a baz.

Cc qu trnh xy ra trong dung dch:

HnA ( iH+ + Hn iA i-

(i = 1 n)

Bm- + iH+(HiB(m-i)-

(i = 1 m)

H2O ( H+ + OH-

KwKP vi mc khng l HnA, Bm- v H2O:

- = -

.-..=

EMBED Equation.DSMT4

(III.1)Trong :

1/

(III.2)

2/

(III.3)

3/ =..

(III.4)

4/

(III.5)

5/ i , m-i , m l nghch o h s hot ca cc ion ha tr i, ha tr m-i v ion ha tr m tng ng. Chp nhn h s hot ca cc phn t trung ha bng 1. Cc gi tr c tnh theo phng trnh Davies:

(III.6)

Vi I l lc ion, c xc nh theo lng mui tr cho vo. Trong trng hp nghin cu I = 1.

5/ [HnA] = Ca.

, vi Ka0 = 1

(III.7)

6/ [Bm-] = Cb.

, vi i = 0 m

(III.8)

Coi =

EMBED Equation.DSMT4 =

T m gi tr pH o c ca m h hn hp cc a axit, a baz kt hp vi KP, chng ta thit lp c h m phng trnh n n (h phng trnh quy c):

H phng trnh trn tng ng vi h:

(III.10)

Vi:

yi =

EMBED Equation.DSMT4 - (i=1( n; aj= (j= 1( iak = (j= 0 ( i-1); xj=

EMBED Equation.DSMT4 (i=1( nxk = (i=1( n

Dng nguyn l BPTT chng ta a h phng trnh quy c trn v h phng trnh chun:

(III.11)

Gii h phng trnh trn tm cc n s chnh l cc HSCB Kaj (j = 1(i), (j= 0 (i-1)Cc bc tnh lp

Bc 1: Chp nhn [HnA]1 = Ca, [Bm-]1 = Cb, kt hp h = 10-pH, thay vo h phng trnh chun tnh cc hng s Kaj, Ka(m-j) ln 1T cc gi tr Kaj, Ka(m-j) tnh c tnh li nng cc cu t [HnA]2, [Bm]2 theo phng trnh (III.7), (III.8)

Bc 2:

Thay cc gi tr [HnA]2, [Bm-]2 va tnh c vo h phng trnh chun ta tnh li c Kaj, Ka(m-j) chnh xc hn. Tip tc tnh lp nh th cho ti khi t sai s cho php:

(III.12)

EMBED Equation.3 ( l hi t nghim)

Trong :

Kaj(m+1), Kaj(m), Ka(m-j)(m+1), Ka(m-j)(m) l hng s phn li axit nc i cc ln lp th (m+1) v (m) v ( l hi t nghim.

Nh vy ng vi mi gi tr hng s axit phn li tng nc s c mt gi tr sai s tng ng. Qu trnh tnh lp s dng khi tt c cc gi tr qi