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Journal of Research of the National Bureau of Standards Vol. 56, No.6, June 1956 Research Paper 2680
Calcium Hydroxide as a Highly Alkaline pH Standard
Roger G. Bates/ Vincent E. Bower/ and Edgar R. Smith
Th e National Bur ea u of Standards conventional activit y sca le of pH is de fin ed by a series of st andard buffer solution s prepar ed from ce rtified mat erials issued as N BS Stan dard Samples. Th e five st andard s thus far est ablished cover the pH rang e 1.68 to 9.18 at 25°. In ord er to increa e t he accuracy of m eas urem e nts at high pH , a highly alkaline st andard is needed. A so lu t ion of c al ci um hydroxid e sat urated at 25 ° C is recommended as the si xth pH sta ndard. K 0 weighing is necess ary, for the so lution is easily prepar ed by s haking fin cly granu l ar calcium hydroxide with wat er. Th e mat erial mu st not be contami n at ed with so lubl e alkal ies, but th e pre sence of insoluble carbonate is of no co nce rn. Th e filtered so lution s up ers aturat es re adily and can us ually be used from 0° to 60° C without the se para - t ion of solid pha se. E l ect romotive-force m eas ur em ents of 29 cells containing mixtur es of calcium h y dro xid e and pota ssi um chloride were mad e in the range 0° to 60° C, and st andard pH val ues were assigned to 0.0203-, 0.02- 0.019-, 0.0175-, and 0. 015-M solutions of calcium hydroxid e withou t added chloride. the sat urat ed so lut ion is about 0.0203 M and ha s a pH of 12. at 25 ° C. Th e buffer ca pa city is high (0.09 mol e/ pH ). Like mo st other alkaline solutions, how ever , thi s sta ndard ha s a rather larg e dilution va lue (- 0.28 pH unit ) and a lar ge tem- perature coeffici ent of pH (- 0.033 pH uni t/ deg C).
1. Introduction
Th e National Bur eau of S tandard s sta ndard pH
scale is defined in terms of several fix ed points in much the sa me mann er as the International Temper- ature Scal e. Th e primary st andard s ar e solutions
whose pH va lu e are only slightly affected by dilution
or by accidental contaminat ion of the solution with traces of acid or alkali from the walls of the container or from the atmosphere. The substances from which the standards ar e prepared are, in turn, stab le ma- terials; they are obtainable in the form of certified sampl es from th e Bur eau. Th e five st andard s thus
far established cover the pH range 1.68 to 9.18 at
25 ° C.1 It is the purpo se of th is paper to describe the establishment of a sixth standard, a solution of calcium hydroxide sat urated at 25 ° C, which will exte nd the s tandard scale to pH 12.45 at 25° C.
2. Need for an Alkaline pH Standard
In practice, mo st pH values are derived either directly or indirectly from thA Amf of th e ce ll
Pt; H2 (g) (or glass electrode), so lution X 13.5 M or satd. KCl , Hg 2 Clz; Hg , (1)
wh ere the vertical line marks a boundary between two liquid phases. Th e transfer of pos itiv e and nega- tive ions at different rates across this liqui.d jun ction gives rise to a potential differenc e. Inasmuch as the transference numbers of the ions vary through the boundary , as do the concentration gradients, the net charge transferred i rarely zero. Fmth ermore, the sign of the potential difference may be either positive or negative, and the magnitude can neither be meas- ured exactly nor calcu lat ed. If included in the measured emf, this potential would result in errone-
ous pH values.
1 Th e assignme nt of pH valn es to t bese standards has been described in earlier Bu reau {lapers: 'l'ctroxalate (p H 1. 68 at 25 ° 0) [I ]; ta rtr ate (p H 3.56) [21; ph t halate (p H 4.01 ) [3 1; phospbate (pH 6.86) [4] ; and borax (p H 9. 18 ) [5]. Figures in braek. ets indicate the Iiteratw'e references at tbe end of thi s paper.
Fortunately, the concentrated solution of po- tassium chloride that composes the salt bridge re- duces the liquid-junction pot ential to a small con- sta nt value for mo st so lu tion of interm ediat e
acidity, pH 3 to 11. Wh en solution X co ntain s ap-
preciable amounts of the highly mobile hydrogen and hydroxyl ions (PH less than 3 or greater than ll ), however, the liquid-jun ct ion potentials ma y differ considerably from the relatively constant va lu es maintained in the region of int ermediate pH. For
accurate pH meas ur ements in these r eg ions of hi O' h
acidity 01' high alkalinity, therefore, it is particularly important that reference stan dard s of lo w and hi gh
pH be availabl e.
This need is readily demon st rat ed. A pH meas ur e-
ment is essentially a det ermination of the differen ce
between pHx, the pH of the unknown solution, and
pHs , that of the s tandard. If Ex is the emf of ce ll 1
and E s that of the sa me ce ll when the sta ndard is
substituted for solution X , and E jx and E js are the
corresponding liq uid-junction pot ential s, we hav e
•• T TT I Ex-Es E js- E jx
Pl.'f.. X= P.1.J..ST2.3026RTjF I 2.3026RTjF (2)
where R, T, and F are the gas constant, the absolute
temperature, and the faraday, respectively. There is no way to eva lu ate the l ast term of eq (2 ).
Hence, for th e usual pH meas ur ement the exper i·
mental conditions are cho sen so as to nullify the greater part of th e junction pot ential. Th e two
potentials, E js and E jx , are then ass umed to be
nearly equal and to cancel rather completely when the difference is taken (eq (2)). Hence the difference
of pH is assumed to be proportional to th e difference
of emf, Ex- Es. Evid ently th e r es idual liquid-
j unction pot ent ial will be small when the stan dard solution and the unknown so lution differ but littl e in pH , for the concentrations of th e free hydrogen or h yd roxyl ions (on which the liquid-junction potential largely depends) will be nearly the same in solution X as in so lution S.
383 6 2-56--1 (^) 305
3. Calcium Hydrox i de as a pH Standard
Th e ideal pH stan dard is a sta bl e so lu tion eas il y and reproducibly pr epared from pure materials. The pH of th e so lution should not be markedly affected by changes of te mp erat ur e. Th e buffer va lue [6] shou ld be high an d the dilution va lu e [7] low' in other words, the pH of the so lu tion shou ld
not 'be altered ap pr eciably by contamination wi~h
traces of acidic or ba sic impurities or by a change lD th e tota l conce ntration of the buffer substances. The ionization of water is strong ly affected by tem p erature chan ges, and hence the pH of most highly alkaline aqueous so lution s is also sensitive.to al teration of temperature. Th e pH falls wIth increasing temperature by as much as 0.033 unit /deg C [8]. This imposes, of course, an unfortunate linlitation on the use of an alkaline pH standard. It should be noted, however, t ha t a certain degree of te mp erature control is necessary for pH measure- ments in the highly alkaline region , not only becau se th e pH of the standard is sensiti ve to temperature chang es but also because the " unknown s," in general, are simil ar ly affected... Th e buffer va lu e, or buffer ca pa cIty, of so lu tIOns contain in g appreciable concent ration s of h ydro~ide ion is uniformly lar ger than that of buffer solutIOns of co mpar able conce ntr ations in th e pH range 3 to 11 but these same solutions usually undergo a lar ger
pI-I chan ge on dilution [8]. A high buffer ca pa city
is particularly impor~ant in an alka~ine pH sta~da~d, for contamination wIth atmosphenc carbon dIOXIde during storage and use can never b e co mpl ete ly avoided. In principle, a so lution of a str ong or moderately strong ba se will serve as an alkaline standar d. In view of th e hi gh buffer ca pa city of aqueous solu tions of even incompletely ionized bases at high pH, the addition of a sa lt of the ba se is unn ecessary. How - ever it is very difficult, if not impossible, to find a
str o~ g ba se, eith er inorga,nic .01' organic, t h at is a
stab le solid. Th e determmatIOn of the concentra- tion of the so lution by a ti trat ion with stan d ard acid is not only inconvenient and time-consuming but co mpound s the er rors of three se para te analytical operations. Buffer so lu tions of trisodium pho s pha te are subj ect to the same objections for , owing to the difficulty of preparing a sa mpl e of th e pho s pha te sa lt of the c orr ect composition , they must be mad e from the secondary phosphate a nci standard alkali. A pH g reat er than 11.2 at 25° C ca nn.ot readily be obtained with s olut ions of the alkalI car bona tes. To b e mo st useful, an alkaline sta ndard should have a pH of 12 or above. Sub stances that form highly alkaline so lution s usually become contam inat ed gradually with car- bonate from exposure to the atmosphere when t~e co ntain er is opened. Many are also hygroscopIc, and the moisture they acquire is not easily remov ed by s impl e drying procedure s. If the car ~onate were insol uble in water, however , the contanunant could be easily r emoved by filtration of the ~o lution , an.d later contamination would be clearly eV Ident when It occurred. If , in addition , the allqtline material were
of moderate solubility, th e saturate d sol ution would serve as a standa rd. Under these conditions, the presence of carbonate would cause no concern; fur- thermore, no weighings would be necessary. Because of its ease of preparation , a saturated solution of slak ed lime, calcium hydroxide, has often been employed as a reference solution of high alka- lini ty [9, 10 , 11]. Tuddenham and Anderson [11] saturated calcium chloride solutions with calcium hydro)"'ide to achieve pH values from 11 to over 12, as desired. The concentration of the saturated so- lution of calcium hydroxide in pure water is about 0.02 M and the pH about 12.4 at 25° C. A few measurements made in an earlier study [12], however, suggested that the saturated so lu tion, like that of the more soluble barium hydroxide, might not be suffi- ciently reproducible to serve as a primary standard. Later work has shown that the solubili ty of samples of calcium hydroxide free from soluble alkalies and sa lt s is indeed reproducible within 1 percent. Th e solubili ty of cal cium hydroxide decreases with rising temperature, being about 4 percent higher at 20° than at 25° C, and 4 p ercent lower at 30 °. Nevertheless, a separation of solid phase does not usually occur at 50° or even at 60 ° C when a solu tion saturated at 25 ° is filtered and subsequently h eated to those temperatures [13, 14]. A solution of calcium hydroxide that ha s been saturated at or near 25 ° C can accordingly be employed as a pH sta ndard over a co nsiderable range of temperature. The properties of a solution of calcium hydroxide saturated at 25 ° C are co mpar ed with those of the phthalate and borax pH stan dard s in the following summary:
Calcium Potassium hydroxide (^) phthahydrogen l ate^ Borax
Mo l ar coneen tration __ O. (^0203) 0. 05 0. Den si ty (25^0 0) ------. 9991 1. (^0017) - - - -- Buffer va lue ({3), mole / pH unit ___________ (^) ca. 09 0.016. 020 Dilution va lue (~P HI /2), pH units for 1:1 dilution _____ (^) ca-.28 (^) + .05 +. 01 dpH / dl, pH un i ts /deg C. - .033 (^) +. 0012 -. 0082
It is seen t hat the pH chan ge, in absolute measure, on dilution of the calcium hydroxide standard is more than 5 times t ha t on dilution of th e phthalate so- lution of pH 4.0,2 whereas the te mp eratu re coefficient is 4 tim es that of the borax stan dard (pH 9.2). It a pp ears t hat any highly alkaline stan d ard will be subj ect to th ese limitation s in much the sam e degre e.
4. Method of Assi gni n g pH
Th e emf method by which standard pH valu es were assigned to solutions of calc ium hydroxide has b een described [1, 2, 8 ]. It will b e summariz ed briefly here, but certain novel features of the present treatment will b e ex plained in detail. 2 At low pH, the dilution va lu e attains large positive values. For the 0. 05 M potassium tetroxal ate sta nd ard (pH 1.7), apR.12 IS + 0. 19.
I
~
!
has made an extensive study of the solubility from
0° to 100° °and lists two va lu es over a considerable
range of temperature; his "true solubili ty" is from 6 to 15 percent lower than the solubili ty of very small crystals. The true solubili ty at 25° 0 , in moles per kilogram of water (molality ), was found by Bassett to be 0.02018, in reasonable agreement with 0.0205 found earlier by Moody and Leyson [20], but significantly lower than 0.0209 obtained by interpolation between the data at 10° and 42° as determined by Haslam, Oalingaert, and Taylor [21]. For the solubili ty of large crystals at 25° C, how- ever, Johnston and Grove [13] found a value of
0 .01976 m, and quite recently Peppler and Wells [19]
have concluded that the solubility of large, we11-
formed crysta ls is 0.0184 m at 30°. Inasmuch as
the solubility of calcium hydroxide appears to be only about 4 pe rcent lower at 30° than at 25°, there remains a discrepancy of about 2.5 percent between these two determinations of the solubility of large crystals. In the present study , the solubility of several sa mples of calcium hydroxide prepared in various way s was determined by shaking th e material vigorously with about 15 times its volume of water in a glass-stoppered bottle. Between periods of shaking, the bottle was maintained at a controlled temperature by immersion in a water thermostat. Th e excess of solid was r emoved on a sintered-glass funnel of medium porosity, and the concentration of the filtrate was determined by titration with a standard solution of hydrochloric acid to the endpoint of phenol red. Weight burets were used in the titra- tions. Th e solubility determinations were repro-
ducible to ± O. 5 percent or better.
In the initia l experiments with calcium hydroxide of reagent grade, solubilities as high as O. 0229 m at
25° ° were obtained, but this figure was lower ed
somewhat by repeated digestion of the hydroxide under hot water. This behavior could result from the extraction of soluble alkaline impurities or from a gradual stabilization of crystal form during the digestion. Ther eafter , the samp les of hydroxide were pr epared from "O P" low-alkali calci um car- bonate and the effect was no longer observed. The fine ly granular calcium carbonate was ignited
in platinum dishes at 1,000 ° ° for about 45 min ,
and the resulting lime, after cooling in a desiccator, was added with stirring to water. The mixture was heated to boiling with continual stirring and was then filtered. The calcium hydroxide obtained in
this way was dried at 1l0° °and powdered.
The solubility of five sampl es of hydroxide pre- pared in th is manner was found to be 0.02037 m, with a standard deviation of 0.0001l, and this figure was substantially unchanged after seven ex- tractions of the product with water. To test the effect of aging, the calcium hydroxide was stored under water in a polyethylene bottle and sampl es removed from time to time for solubility tests con- ducted as described above. After 1 month, the solubility of four samp les was found to be 0.02032 m, with a standard deviation of 0.00006 , and after 6
months had elapsed a figure of 0.02022 m was ob-
tained as the mean of two determinations. Th e
average solubility is 0.0203 m at 25° 0. At 20° °the
solubility was found to be 0.02ll m and at 30 ° 0 , 0.0196 m. Thes e figures are in excell ent agreement with the
true solubility of Bassett [18], who found 0.02ll m
at 20°, 0.0202 m at 25 °, and 0.0195 m at 30° 0. It appears t hat they represent satisfactorily repro- ducible concentrations achieved by shaking granular ca lcium hydroxide, prepared from low-alkali calcium carbonate, with water at 20°, 25°, or 30 ° C. How- ever, they do not preclude a so lubili ty lower by perhaps 1 to 3 percent for large well-defined crystals of the mat erial. It should be noted that a change of 1 per cent in the concentration of calcium hydrox-
ide corresponds to about 0.004 in the pH of the
nearly sat urated solution.
5 .2. Electromotive-Force Measurements
The calcium hydroxide solutions for the emf measurements were prepared by dilution of nearly sat urated stock solutions whose concentrations had been established by titration with standard acid. A weighed amount of potassium chloride was then added to each so lu tion flask, or a portion of a 0 .3 - M solution of the salt introduced from a weight bur et. The dilution and the addition of chloride in an at- mosphere of carbon-dioxide-free nitrogen were ac- complished with the aid of an arrangement very similar to that described by Bate s and Acree [22]. The potassium chloride was a bromide-free fused samp le prepar ed in the manner described in an earlier publication [23]. The cells were rinsed, flushed, and filled in the usual manner. So lution was admitted from the so lution flask, the cell emptied and flushed with pure hydrogen, and the cycle repeated before the final portion of solution was admitted. The preparation of the electrodes has been described elsewhere [8]. Each ce ll contained two pairs of electrodes, and the duplicate measurements were averaged. Initial measurements were mad e at 25 ° 0, those
from 0° to 30° °on the second day, and those from
30° to 60° ° on the third day. With these highly
alkaline so lu tions, the final measurements at 25° 0 , when they were obtained, did not agree as closely with the initial va lu es as those for so lu tions of low
or intermediate pH often do. Differences of 0.3 to
0 .5 mv were not uncommon. Th e emf data were corrected in the usual way to a partial pressure of 1 atm of hydrogen.
6. Determination of pwH and pwH o
A value of pwH was computed from each co rr ected
emf value by eq (4), and the co n stants a and b of eq
(5 ) were obtained for each of the three molalities of potassium chloride (m2 equal to 0.015, 0.01 , or 0.005) in the ce ll so lutions. The data are summarized in tab le 1. The third co lumn gives the number of ce lls studied, and the sixth column lists rr , the standard
deviation of a single pwH value from the line defined
by the constants a and b. Th e last five columns give
J \
r
pwH at fi ve se lected va lu es of ml, the molali ty of
calcium h ydr oxid e. Th ese :fi g ur es were compu ted by eq (5) with the values of a an d b gIven in the
t abl e. F or each ml, the limiting va lu e of pwH ,
namely , pwH o, as Lhe molali Ly (m2) approached ze ro, ob ta ined by eq (6), is entere n on Lhe fo ur th lin e at each te mp er at ur e. Th e La nda rd devintion, IT i, of this in tercep t (pwH O) is li sLccl on Lhc fifth line.
TARLE 1. pwH and pwH o fOI' mixtures of calcium hydroxide (0.015 < m1 < 0.0203) and potassium chloride (m 2) Jr om 0° to 60 ° C; constants oj the equation pwH = a + b log 1n
° C
5
10
15
20
25
30
35
40
45
50
55
60
711 2
l _ O ~ ~L
1
. 015
--~ ~~ --
1
. 015
--~ ~ --
1
. 01 5
-.~ ~ --
1
. 01 5
--~ ~ --
1
.
--~ ~ --
1
. 015
--~ ~ --
1
. 015
--~ ~ --
{
. 01 5 . . 005 . 000 l -- _____ _
1
.0 1.
)~ --
1
. 015 . 010
--~ ~~ --
1
. 015
--~ ~ --
1
. 015
--~ ~ --
- Standard deviation of pwR.
Number of cell s
II 10 8
II 10 8
)l 10 8
11 10 8
11 10 8
II 10 8
II 9 7
11 9 7
11 9 7
10 7 7
11 9 7
10 7 7
11 9 7
121
137
1 5. 095
901
70 5
838
714
495
606
47
300
331
139
124
967 1 3. 975 14.0:1O
830
817
82 5
658
682 13 .5 86
323
226
269
081
9450 . 9548 . 9432 . 9480 I. 0578
. 9463 I. 0258
. 9360 I. 0093
.
. 9746 . 9533 . 9312 . 9502 . . 9268 . 9354 . 9707
.93 87
. 9366 . 9441 . 9276 . 9444 . 8924
.
. 9492 . 8978 . 8995 . 8549 . 9016 . 9150 . . 8832
.
8945
. 002 . pwR o= bU i =
- 005 . OM . 004 pw H o= Ui =
- 004 . 004 . 00 5 pwlJO = 0' ;=
- 003 . 004 . 004 pwll o= (T i=
- 004 . 004 . 006 pwH o= U j=
- 002 . 003 . 007 pwR o= CT i =
- 004 . 003 . 004 pwR o= 0' ;=
. . 003 pwR o= 0' ;=
- 006 . 004 . 005 pwH o= U j-
. 004 . pwH o= CTi=
- 007 . 009 . 008 pwH o= CT i =
. 002 . 010 pwH o= CTi=
- 006 . 005 . 008 pwH o= CTi=
- Standard deviation of t he intercept, pw H o.
0203
513
294
29 1
006
103
1 02
004
729
727
717
712
00 5
563
537
398
392
387
381
002
23 2
227
088
0.
- 944
- 005
- 807 II. 796 II. 790
- 677
- 673
II. 661
- 002
- 553
1.1. 540
pw R for "" equal to
005
298
006
096
086
006
905
904 12 .8 92
004
723
711
706
004
552
539 12.53 1
3R
375
235
226
221
213
077
070
0. 002
938
933
926
920
803
791
786
004
672
667
002
548 1 1. 546
538 II. 534
019
48 5
482
004
277
274
267
002
07 6
0 65
060
003
884
881
8 72 12 .8 67
703
699
690
684
003
537
531 12 .5 J 12 .5 11
004
372
3 59
352
002
214
205
200
192
062
000
918
906
900
000
783
78 1
771
766
651
646
528
1 1. 518
513
002
0175
460
452
004
246
237
233
226
003
0' 12 1 3. 036
024
12 .8 51
- 84 5
- 832
- 664 1 2. 656
- 649
- 002
- 503
- 497 J2. 485
- 477
12 .3 39
- 332
- 324
- 317
- 172
- 166
12.0 18
- 012 0. 002
- 884
- 878 1l. 876
- 871
- 003 II. 751
- 750 1 1. 739
- 735
- 006
- 619 1 1. 612
- 603
I I. 486
480
003
396 1 3. 389
003
I SO
166
169 1 3.1 61 O.Oll
979
967
966
9~~
006
7 88
778
776
769
007
607
599 1 2. 592 12 .58 4
002
441
423 12.4 14
277
259
2 50
002
118
109
09 5
966
959 1I.9 59
954
00 5
822 1 1. 814
814
809
00 5
691
693
678
674
011
557
549 1l .5 50
54 5
006
435
421
426
418
012
8. Standa r dization in the Ra n ge pH 9to 12.
As has been pointed out ea rlier in this pap er, a plot of the e mf of cell 1 as a function of pH is a stra ight lin e of slop e 2. 3 026RT/F when the pH is neither too low nor too high. At high alka linities a v olta ge d epartur e or c hang e in slop e is to be ex- p ecte d. Th er e will be an accompanying aberration
of the pra ct ical pH scale neal' it s upper end, operat-
ing to yield pH values that are too low. It is
a pp ro priate to consi der next the probabl e magni- tu de of the enor and m e an s of minimizing or elimi- nating it by prop el' standardization of the p H asse mbl y. The error ha s it s origin in an exp erimenta l def ect
of the pH m et hod, nam ely the changing liquid-
junction potential with alteration of the concentra- tion of highly mobil e hydroxide ion s. It is oft en
not notic('able below pH 11 , but ea rli er work with
car b on a te buffer solu tions [12] ha s indicated that it m ay b e detectable at pI-I 10. Thi s ea rli er st udy suggested fmther t hat t h e magnitud e of the discr ep-
ancy at 25° C is about 0.01 unit at pH 10,0.02 unit
at pH 11.1 , and about 0.05 unit at pH 12.6. Th e
error t hu s appears to incr ease in a fairly r eg ul ar
manner with the pH of the test so lution.
It is of s om e impor tance, therefore, to d eter min e wh et h er this apparent r eg ularity exten ds to solu- tions of calcium hy droxid e. Th e difference of pot e n- tia l betw een one hy drog en el ectr od e dipping in a s olution sa turat ed with ca lc ium hy droxide at 25° C and another dipping in the sta ndard 0.025 ]Y[ pho s- phate buff er (p H (^) s = 6.860 at 25° C) wa s therefore determined. A cell consisting of two hydrog en- electrod e co mpar t ments [12] was u se d. Contact b e- tween the so lu tions wa s es tablish ed through a sat u- rated so lu t ion of po tass ium chloride. TIl e ob serve d difference of poLential was 0. 328 v at 25 °, corre- s ponding to a pH of 12.420for the s olution of ca lcium hydroxide. Thi s s olution wa s assigned a pHs of 12.454 from measurements of cells withou t a liquid junction (c ompar e table 2). Th e discrepan cy of
0.03 4 unit at pH 12.45 is reasonably co nsis te nt with
a lin ear progression of th e e rror from pH 9.18 (t h e
pH of the borax standard), whieh li f\R in the upp er
end of the err or-free region of the practi ca l pH
scale [12], to pH 12.88, wher e an error of about 0. 05
unit ha s been found [24].
As a co nse qu ence, a pH m ete r sta ndardiz ed at
pH 9.18 will y ield ii , slightl y low reading b et wee n
pH 9.18 and 12 .45, and a m eter sta ndardiz ed at pI-I 12.45 will yield a slightl y hi gh r ea din g in the sa me region of the scal e. Th e e rror evid e ntly will be (0.034/3.27) (pH x - pH s) unit. B ence, we have from eq (2)
1.0105 (E x - E s) (13) PH^ x = pH^ s +^ 2.3026 RT/F (at^ 25°^ C)
pHx = pH s+ 17.08(Ex - Es) (at 25° C) (14 )
Inasmuch as the liquid-jun ction potential is some - what depe nd e nt upon the st ructme of the liquid-
liquid boundary , it is advi ab le to d etermin e the error for the parti c ular a se mbly that is b ein g used. Fresh ly pr epar ed bor ax and cale ium hy dro xide so lu - tions should b e u se d for this purpo se. If the error differs much from 0.03 or 0.04 uniL, Lh e num e ri cal coefficients of eq (13) and ( 14 ) s hould be actju ted accordingly. Th e difference as indi cated b y a p~l meter may b e influen ced som e what by e rrors ll sc al e length and in the temperature co mp en sat or , if these hav e not b een calibrated.
Becaus e th e pH met er read s pH unit s dil'ectly , it
may be convenient to apply a correction to th e indi-
cated pH, rath er than to comput e the c orr ect figure
by eq (13) or (14) from a m e asur em e nt of the emf. The temperatur e compensator of th e m eter is, how - ever , de signed to permit the se lecti on of differe nt valu es of the slope pH /emf, corresponding to the valu e of F / ( 2.3026RT ) at differ e nt te mp eratur es. H e nce , t hi s d evice p ermit s pH to b e read dir ect ly from the sc al e of the in st rum ent, eve n though the fun ct ional r elation ship b et w een the e mf of the cell and the pH value varies rather wid el y, as it ma y do wh en the temperature of the cell c han ges. Wh en the Lemperature c omp en sator indi cates 25° C, the in st rum e nt conve rt s emf differ ences into pH dif- ferences according to the relation hip ApH = 16.90AE; at 20° C , the convers ion is mad e according to ApH = 17.19AE. It is evi d ent ly possible, th en, to c omp en sate the liquid-jun ct ion e rror at th e hi gh end of the sca l e, p ermittin g cor r ect values at 25° C to b e r ead dir ect ly from the m eter, if the tempera- ture compensator is et at 22 ° C , for at t hi s te mp er- ature F / (2. 3026R T ) is not far from 17 .08 (co mpar e eq (14 )). Th e values of this quantity at other te mp erat ures are:
°C
10 17 .8 0 15 17. 20 17. 25 1 6. 90 30 16. 63
The allmline error of t,h fl la ss el ecL rod e m ade from Corning 015 glass is very much low er in so lution s of calcium sal ts than in solutions of lithium or so dium sal ts [25]. How ever, in a sat ura ted so lution of ca l- cium hydrm..'ide, this so ur ce of error ma y be of con- ce rn at temperatures from 40° to 60° C. M any of the newer co mm ercial el ectro d e g la sses conta in no calcium, and hen ce the voltage departur es in ca l cium s olutions are probab ly n egligibl e.
9. A St andard Solution of Cal c ium H y-
d roxide
A sol ution of cal cium hydro:A'ide sat urat ed at room temperatme is recommend ed as a pH stan dard for the highly al ka line rang e. A conside rabl e excess of pure, finely granu l ar h y droxid e is s hak en vigorously in a stoppered bottle with wat er at room tempera- ture. The gross exces of so lid is allowed to settl e,
the temperature recorded to the nearest degree Cel- sius, and the suspended material remov ed by fi l tra- tion with suction on a sintered-glass funnel of medium porosity. It has been re co mm ended that a slurr y containing excess calcium hydroxide be used for standardization purposes [11]. However, larg e errors are sometimes
in curred in pH m eas urement s of suspensions [26],
and it seems best to rul e out this uncertainty by r e- moval of the solid pha se. For the saturation, a pol yethylene bottle is very satisfactory; in faqt , it may be found convenient to keep th e solid continuously under wat er in a well- st oppered polyethylene bottle ready for final sat ura- t ion and filtration when a fresh so lution is needed. Contamination of the so lution with atmospheric car- bon dioxide prior to filtration is obviously of little concern. Contamination of th e filtered standar d solution render s it turbi d and is a cause for replace- ment. Th e tem p erature coefficient of so lubili ty is nega- tive, but the solution supersaturates readily and no precipitation of solid is ordinarily obse rved at 60 ° C. Unfortunate ly, however, the change of so lubili ty with te mp erature is sufficiently l arge to require t ha t th e saturation temperature be noted and the pH s valu es (c olumn 2, tabl e 2) adjusted by the appropriate amount. Th ese values for s aturation temperatur es of 20 °, 25°, and 30° Car e:
Satura- pHs at (0 C )- (^) Corr ection t ion Solubi l- te mp- ity (m) to co^ lumn^ 2, erat ur e 20 25 30 ta^ ble 2
°C
20 0.0211 12. 64 12. 47 12 .3 1 + 0.
- 0203 12. 63 1 2.45 12 .3 0 0 30 .0195 12. 61 12. 44 12. 28 -.
The calcium hydroxide should be prepared from well-washed calcium carbon ate of low-alkali grade. The carbonate is h eated slowly to 1 ,0 00 ° C and ignited for at l east 45 min at that temperature. After cooling, the cal ci um oxide is added sl ow ly to water with stirri ng and the suspension h eated to boiling, cooled, and filtered on a sintered-glass funnel of m e dium porosity. Th e solid is dried in an oven and crushed to a uniform finely granular state for use. It is advisable to determine the concentration of a sat urat ed solution of one portion of calcium hy droxide prepared from each particular lot of calcium car- bonate, as described earli er in this paper. The
molality (m ) and molarit y (M ) of the saturated solution are practi cally identical, differing by only 0.3 percent. If the concent ration of the so lu tion
s aturated at 25 ° C appears to exceed 0.0206 Ai, th e
presence of so luble alkalies is indicated. If calcium carbonate of a high er grade cannot readily be obtained, the impurity in the avai lable ca rbonate or hydroxide should be extracted by car eful washing with water.
10. References
[1] V. E. Bower , R. G. Bat es, a nd E. R. Smith , J. R esearch N BS 51, l S9 (19 53 ) RP. [2] R. G. Bat es, V. E. Bower , R. G. Miller, a nd E. R. Smith , J. R esea rch NBS 47, 433 (1951) RP. [3] W. J. Ham er, G. D. Pinching , a nd S. F. Acree, J. R e- sea rch N BS 36, 47 (1946) RP. [4] R. G. Bat es a nd S. F. Acr ee, J. R esea rch N BS 34, 373 (1945) RP. [5] G. G. Ma nov , N. J. D eLollis, P. W. Lindvall , and S. F. Acree, J. R esearch NBS 36, 543 (1946) RPl72l. [6] D. D. Va n Sly k e, J. BioI. Chem. 52, 525 (1922). [7] R. G. Bat es, Anal. Ch ern. 26, 871 (1954). [8] R. G. Ba tes, E l ect rom et ric pH d ete rmination s, chapters 4, 5, and 7 (John 'Wil ey & Sons, Inc ., New York , N. Y ., 1954). [9 ] E. P. Flint and L. S. 'W ell s, BS J. R esea rch 11, 163 (1933) RP. [10] G. G. Manov , N. J. D eLolli s, and S. F. Acree, J. R esearch NBS 34, 115 (1945) RP. [11] W. M. Tudd e nham and D. H. Ander son, Anal. Cbem. 22, 1146 (1950). [12] R. G. Bates, G. D. Pinching , a nd E. R. Smith , J. Re- sea r ch NBS 45,41 8 (1950) RP. [ 13] J. J ohnston a nd C. Grove, J. Am. Ch em. Soc. 53, 3976 (1931). [14] T. N oda and A. Miyo shi, J. Soc. Chem. Ind ., Jap an 35, 3173 (1932). [ 15] H. S. H arned a nd R. W. Ehlers , J. Am. Ch em. Soc. 55, 1350, 2179 (1933) ; R. G. Bat es a nd V. E. Bower, J. R esea rch NBS 53, 283 (1954) RP2546. [16] G. A. Ma nov , R. G. Bat es, ,y. J. Ham er, and S. F. Acree, J. Am. Chern. Soc. 65, 1765 (194 3). [17] R. P. Be ll a nd J. E. Pm e, J. C hem. Soc., 362 (1949). [18] H. Ba ssett, J. Chem. Soc., 1270 (1934). [19] R. B. P e ppl er and L. S. Well s, J. Re sea rch NBS 52, 75 (1954) RP. [20] G. T. Mood y and 1,. T. Leyso n, J. Ch em. Soc. 93, 1767 (190S). [21] R. T. H aslam , G. Calingaert, a nd C. M. T ay lor , J. Am. Ch em. Soc. 46" 308 (1924). [22] R. G. Bat es and S. F. Acree, .J. R esea rch NBS 30, 129 (1943) RP. [23] G. D. P inch ing and R. G. Bate s, J. R esea rch NBS 37, 3 11 (1946) RP. [24] R. G. Bat es and V. E. Bow er, Anal. Ch em. (publica tion p e nding ). [25] M. D ole, Th e glass el ect rod e, ch. 7 (John Wiley & Sons, In c., New York, N. Y. , 1941). [26] H. Je nn y, T. R. Nielsen , N. T. Colem an, a nd D. E. William s, Science 112, 164 (1950).
WASHINGTON , February 6, 1956.
