3.5 Practical measurement of ph in nonaqueous and mixed solvents

Transcription

1 3.5 Practical meaurement of ph in nonaqueou and mixed olvent Introduction Procedure analogou to thoe on which a practical ph cale for aqueou olution have been baed can be ued to etablih operational acidity cale in certain nonaqueou and mixed olvent media. A univeral ph cale relating proton activity uniformly to the aqueou tandard reference tate i not poible, but eparate cale for each medium can be achieved and will fulfill mot of the requirement, uch that the notional definition i ph = - log (mh γ m,h), where γ m,h i referred to the tandard tate in each particular medium. The 'normal cale length of ph' in each olvent and olvent mixture i determined by the autoprotolyi contant (ee ection ) Notation and terminology The notation adopted i that ued by Robinon and Stoke for their dicuion of the effect of the medium on tranferring a binary electrolyte from water (w) to a nonaqueou or mixed olvent. Thu, lower-cae left-hand upercript indicate the olvent (w or ) in which meaurement are being made; lower-cae left-hand ubcript indicate the olvent in which the ionic activity coefficient γi i referred to unity at infinite dilution (w or ). Therefore, the potential of the hydrogen electrode (at Pa preure of H2) a a function of the activity ah of the H + ion in the olvent i expreed a: EH = E o H + k lg ( γ HmH/m o ) = E o H + k lg ( ah) = E o H - k( ph) 3.27 where k = (RT/F) ln 10, the concentration i on the molality cale m, and the ionic charge i omitted in the ubcript; and analogouly: w EH = w E o H + k lg ( w w γ HmH/m o ) = w E o H + k lg ( w wah) = w E o H - k( w wph) 3.28 in water. It i to be noted that E o H and w E o H are tandard electrode potential (or, in other word, potential determined with repect to an electrode of ideally invariant tandard potential in the variou olvent). Alo, the notation o w γ H (correponding to the notation m γ H ometime ued by Bate) will be ued for the primary medium effect (related to the tandard Gibb energy change) for the tranfer of the H + ion from water (w) to the olvent (nonaqueou or mixed). Thu the ph value meaured in the olvent relating to the ph cale pecific to the olvent might be expreed a wph on an "interolvental" cale with ultimate reference to the olvent water w, and be meaningfully compared with the latter by the following converion equation: wph = - lg ( w γ HmH/m o ) = ph lg ( o w γ H) = ph + ( w E o H - EH)/k o 3.29 where: w γ H = γ H x w γ o H and w γ o H 1 a w 3.30 Chapter 3-1

2 The feaibility of the ph cale i hindered by the indeterminability of the ( w E o H - E o H) term. In concluion, taking into account that imple and functional ymbol (e.g. EX, the e.m.f. of operational cell (XI) meaured on the ample olution at unknown phx; ES, ES1, ES2..., the e.m.f.' of operational cell (XII) meaured on tandard olution at known phs, phs1, phs2...) are currently in ue with the operational equation for ph meaurement in aqueou olution, any olvent indication ( and/or w) i better placed (a upercript and/or ubcript) on the left-hand of the relevant quantitie, a in Robinon and Stoke' notation. However, the imple ymbol γ t, and the related term "tranfer activity coefficient" propoed by Trémillon and Coetzee, can alo be recommended intead of the cumberome ymbol o w γ H, provided that γt i explicitly and unambiguouly defined each time. The quantity γt can alo be ued to repreent the analogou tranfer property for ion other than H + between olvent Operational cell and equation Jut a in the cae of aqueou olution, the notional definition of ph in a olvent i: ph = p( ah) = - lg ( γ HmH) 3.31 where ah i the activity of the ingle H + ion at the molal concentration mh and γ H i the correponding ingle-h + -ion activity coefficient, and the quantity γ H i, in trict thermodynamic term, immeaurable. For thi reaon, a for the aqueou w wph tandardiation, ph i defined operationally, namely, in term of the operation or method ued to determine it. Thi method conit of meauring the e.m.f. EX of the cell (XI), (compare cell (II)): Reference electrode Salt bridge in olvent ample olution at unknown phx in olvent H + -ening electrode (XI) (which i the operational cell). EX i a linear function of the unknown phx according to the Nerntian relation: EX = E o - k( phx) + EJX 3.32 where E o i a temperature dependent contant, and EJX i the liquid junction potential ariing at the junction between the ample olution and the alt bridge (which i aumed to be negligible if the alt bridge i a olution of an equi-tranferent binary alt in the ame olvent of, and at much higher concentration than, the ample olution at phx). Since E o i unknown, determining phx from the meaured EX require cell calibration by a tandard olution of aigned phs (ee for the determination of phs), which require replacing the ample olution at phx in cell (XI) by the tandard olution at phs and meauring the e.m.f. ES of the reulting cell (XII): Chapter 3-2

3 Reference electrode Salt bridge in olvent ample olution at unknown phs in olvent H + -ening electrode (XII) having the ame H + -ening electrode, reference electrode and alt bridge of cell (XI) at the ame temperature and preure. A the Nernt expreion for ES i: ES = E o - k( phs) + EJS 3.33 then phx i determinable in term of the aigned tandard phs by: phx = phs - ( EX - ES)/k 3.34 (which i the ph operational equation in the olvent ) ignoring the term: EJ = EJX - EJS 3.35 known a the reidual liquid junction potential. When there i a well-founded upicion that EJ cannot be neglected (e.g. for poible inappropriatene, or ineffectivene, of the alt bridge choen), the error in phx caued by EJ can be reaonably reduced by the procedure of bracketting unknown and tandard, namely, meauring two emf', ES1 and ES2 of cell (XII) with the two repective tandard, phs1 and phs2, one lower and the other higher than (and a cloe a poible to) the unknown phx. In uch cae the operational equation become: phx = phs1 + ( EX - ES1)( phs2 - phs1)/( ES2 - ES1) Aignment of the reference value tandard phs The RVS material elected for making up the phs tandard in the domain of the olvent mixture with water at 100 down to 10 wt per cent water i the 0.05 mol/kg potaium hydrogen phthalate (KHPh) buffer olution in. The procedure for the determination of the relevant phs value for the RVS, in general, follow the ame cheme ued for the RVS in water, and i baed on meauring the e.m.f. E of a cell without liquid junction, at fixed ms but varying m1: Electrode reverible RVS buffer (ms) + KX (m1) Electrode reverible to H + in olvent in olvent to X - in olvent (XIII) For mot aquo-organic mixed olvent (and alo for ome 100%-pure nonaqueou olvent) the cell (XIII) take the form: Pt H2 (101 3 Pa) KHPh (ms) + KCl (mcl) AgCl Ag Pt (XIV) Chapter 3-3

4 where ms i 0.05 mol/kg and mcl i varied. From the e.m.f. expreion (ee 3.16): - lg ( ah γ ClmCl/m o ) = ( E - E o )/k + lg (mcl/m o ) 3.37 where E i the tandard e.m.f. of cell (XIII), k =(RT/F)ln10, and the ubcript ion are indicated without charge to implify printing, it i clear that: (i) (ii) knowledge of accurate E value i eential; an extrathermodynamic aumption, i.e. a Debye-Hückel equation of the type (ee equation 3.09): lg γ Cl = AI½ /(1 + BaI ½ ) 3.38 i neceary to compute the ingle Cl - ion activity coefficient γ Cl in order to obtain the nonthermodynamic quantity ph from the thermodynamic quantity p( ah γ Cl). The equation (3.38), where I i the total ionic trength of the mixed electrolyte KHPh + KCl, introduce two feature: (iii) (iv) one can write I = IS + mcl, where IS i the ionic trength of KHPh alone, but IS ms depending on the ionization contant of the o-phthalic acid H2Ph: thi implie iterative calculation procedure to obtain IS, I and ultimately γ Cl; the ion-ize parameter a i aigned a value fixed by the Bate-Guggenheim convention extended to the general olvent by the relation, at each temperature T ( B a)t = 1.5 { w ε w ρ/( ε w ρ)} 1/2 T 3.39 where B i the Debye-Hückel contant of eq. (3.38), appropriate to the (ingle or mixed) olvent, w ε and ε are the relative permittivitie of pure water (upercript w ) and of the olvent (upercript ), and w ρ and ρ are the correponding denitie. If i water, equation (3.39) reduce to Ba = 1.5, which i the form of the Bate-Guggenheim convention which wa introduced originally for ph tandardiation in pure water. The equation (3.37) to (3.39) are combined into an extrapolation function Φ to determine phrvs a intercept at mcl = 0 of a linear regreion plot of Φ v. mcl, with optimization of phrvs through iterative calculation cycle. In thi context, another important point mut be outlined: (v) the above determination and optimization of phrvs mut be carried out at each ditinct compoition of the olvent, thi compoition being uually expreed a the mol fraction x of the nonaqueou component. Chapter 3-4

5 In fact, even a minimal change in x caue a change in the tandard tate "hyp. m = 1" for the H + ion (primary medium effect upon H + ), and alo a change in both the ph cale and it poition relative to the familiar aqueou ph cale. Therefore, each phrvs, o determined in a olvent, i only valid for the ph cale in that olvent. It wa hown that the above determination and optimization of phrvs at each compoition x of the olvent can be carried out by ingle-tage multilinear regreion of E a a function of mcl, x, and temperature T, giving final, moothed, recommended value. Thi i very important becaue there might be variou independent E et from different author with obviou problem of overlapping and reulting difficultie in extracting bet value. The ame applie for the determination of the tandard e.m.f. E of cell (XIV), required by eq. (3.37), which i currently carried out by the claical method of extrapolating to I=0 a uitable function of the e.m.f. of the cell: Pt H2 (101 3 Pa) HCl (m) in olvent AgCl Ag Pt (XV) Recommended value of phrvs and phs All the reference value tandard (phrvs) and primary tandard (phs) determined to date have been re-examined to enure compliance with the above IUPAC rule and to provide et of recommended data. Thee have been grouped in three Table, of which Table report the data (phrvs) which are relevant to the RVS buffer (the 0.05 m potaium hydrogen phthalate buffer) in variou aqueou organic olvent mixture. Table report value (pdrvs) that pertain to the pecial cae of the RVS buffer (0.05 m potaium deuterophthalate buffer (KDPh) for pd in heavy water, D2O, and Table collect thoe for uch other buffer a acetate, oxalate, carbonate, uccinate, phophate, Tri + Tri.HCl, etc, in ingle or mixed olvent (including heavy water, D2O) and at variou temperature. In the cae of ethanol/water and dimethylulphoxide/water mixture, the Celiu temperature range extend to ubzero. Chapter 3-5

6 TABLE Value of ph Reference Value Standard (phrvs) for the 0.05 m potaium hydrogen phthalate (KHPh) buffer in variou aqueou organic olvent mixture (mol fraction x) at different temperature t/ C, with overall etimated uncertaintie δ. Weight percent of the nonaqueou olvent in mixture with water METHANOL x t/ C δ ±0.003 ETHANOL x δ ±0.002 ±0.003 ±0.002 ± PROPANOL x δ ±0.005 ±0.002 ±0.006 ±0.013 ACETONITRILE x δ ± ,4-DIOXANE x δ ±0.002 DIMETHYLSULPHOXIDE x δ ± Chapter 3-6

7 TABLE Value of pd Reference Value Standard (pdrvs) for the 0.05 m potaium deutero phthalate (KDPh) buffer in deuterium oxide (D2O) at variou temperature t/ C, with overall etimated uncertainty δ = ± t/ C pdrvs t/ C pdrvs Chapter 3-7

8 TABLE Value of primary tandard (phs) for ph meaurement in different olvent or aqueou organic olvent mixture at variou temperature. Value not fully complying with the IUPAC criteria are quoted in parenthee (); value not atifying F-tet are quoted in brace {}. All % value for mixed olvent with water are by weight. Methanol 50% t/ C Acetate Succinate Phophate Tri+Tri.HCl AmPy+AmPh.HCl a b c d e 10 (5.518) (5.720) (7.937) (5.506) (5.697) (7.916) (5.498) (5.680) (7.898) (5.493) (5.666) (7.884) (5.493) (5.656) (7.872) (5.496) (5.650) (7.863) (5.502) (5.648) (7.858) Oxalate Succinate Oxalate Succinate Salicylate Barbiturate g h f h i j %(m/m) Methanol at C Ethanol at C 0 {2.145} {4.119} {2.374} {5.398} 70 {2.771} {6.289} 90 {3.729} {7.147} (5.79) (8.75) (8.31) (13.23) Acetate k Phophate l Ethanol Ethanol t/ C H2O 10% 20% 40% t/ C H2O 10% 20% 40% Chapter 3-8

9 TABLE (continued) Citrate n Phophate o Carbonate p Phophate l t/ C D2O* D2O* D2O* t/ C H2O DMSO 20% DMSO 30% Phophate m t/ C H2O DMSO 20% DMSO 30% Te + NaTe q t/ C H2O DMSO 20% DMSO 30% a: Acetic acid (0.05 m) + Sodium acetate (0.05 m) + NaCl (0.05 m) b: NaHSuccinate (0.05 m) + NaCl (0.05 m) c: KH2PO4 (0.02 m) + Na2HPO4 (0.02 m) + NaCl (0.02 m) d: Tri = Tri (hydroxymethyl)aminomethane (0.05 m); Tri.HCl = TRIS hydrochloride (0.05 m) e: AmPy = 4-Aminopyridine (0.06 m); AmPy.HCl = 4-Aminopyridinium chloride (0.06 m) f: Oxalic acid (0.01 m) + Lithium oxalate (0.01 m) g: Oxalic acid (0.01 m) + Ammonium oxalate (0.01 m) h: Succinic acid (0.01 m) + Lithium uccinate (0.01 m) i: Salicylic acid (0.01 m) + Lithium alicylate (0.01 m) j: Diethylbarbituric acid (0.01 m) + Lithium diethylbarbiturate (0.01 m) k: Acetic acid (0.05 m) + Sodium acetate (0.05 m) l: KH2PO4 (0.0 m) + Na2HPO4 (0.0 m) m: KH2PO4 ( m) + Na2HPO4 ( m) n: KD2C6H5O7 (0.05 m) o: KD2PO4 (0.0 m) + Na2DPO4 (0.0 m) p: NaDCO3 (0.0 m) + Na2CO3 (0.0 m) q: Te = N-tri(hydroxymethyl)methyl-2-aminoethane ulfonic acid (0.07 m) +NaTe = Sodium alt of TeES (0.03 m). For the buffer a,b,c,d,e the original work give phs value from 0.005, 0.005, 0.002, 0.01, 0.02 m to 0.05, 0.05, 0.02, 0.10,0.10 m at 0.005, 0.005, 0.002, 0.01, 0.02 interval, repectively. * The tandard value in heavy water (D2O) are in term of pds. Chapter 3-9