V O L U M E 2 3 , NO. 8, A U G U S T 1 9 5 1 calibrated iii 0.3 nini. The drop time and drop weight values are based on measurements of 20 drops collected in 0.1 AV potassium chloride solution. The apparent pressure of mercury as measured as the difference bet\{-een the tip of t,he capillary : ~ n dthe level of mercury in the reservoir. Tho radius of the orifice was calculated by multiplying W by 4.11 ( I ) . The back pressure was read off from Figure 2; P is Pa,,,, P b a e k . Tho calculated value for the Irngth of t.he capillary was obtained on the basis of Equation 7 . By ineans of the nomogram (Figure 3) values cannot hc read closer than to one dccim:tl unlcss the length of the capillary is less than 1.5 ciii. It may be Seen t,hitt there is a satisfact,ory agreement between directly determined and calculated I values. Thc two capillarice C22 and C23 uerc cut froni the same piece o l marine barometer tubing; their p values, which should be identical, illust,rate the error of the drop-weight method. Capillary C20 was first sealcd t o an ordinary piece of glass tubing and then cut to t,he sinall length. It is essential that square cuts bc made; efforts to grind off R smooth enough surface have so far been t,o no avail. On the basis of the above relationships it is possible to dctcrmine the exact size of a capillary to perform according to specifications. However, the product actually obtaincd will depend on t h c available bore sizes and the accuracy with xhich t,he capillary :i rulc
-
1177
can he cut to size. esample :
Thii; m:iy
11:s
illust,ratetl by the following
A piece of the capillar). tul)ing used for i*upillaries C22 :riicl C23 was sealed into a regular piece of glass tubing. The seal was ni:tile as ahrupt, as possible, so that there would he a sharp b r r a k from the nwrow capillary bore to the wider dimension. The. c*apill:iry was espec%ed to produc-e a drop time of 2.0 second. in 0.1 .V pottmiuin chloride at, an effective pressure of 60 cm., thcwfow /'t = 120. From the nomogram (Figure 3) it was fonntl that thil lvrigth of thr capillary should be slightly grritt,er t!i:in 3.0 em. After cutting, the capill:uy length \vas fourid to bca actu:illy 3.10 cm. In 0.1 .V potassium chloride solution the drop time \\-it.< 2.1 1 seconds whcn the applird pressurc was 61.6 cm. (effectivr prctssurc 60.0 cm,). The small deviation from the int,endrcl tlrop tirnth r u i r:t*ily l)r ovcrconi(' l)y r:iisiny t,hr mercury p r e ~ u r r I)? 3.3 rni. 4CKNOWLEDGMENT
This work was support,ed in part by a research grant froin the Ilivision of Research Grants and Fellowships of the Xat,ional Instit,utes of Health, U. 9. Public Health Service. LITERATURE CITED
(1) MuIIer, 0. H., J . A m . C'heni. Soc.. 66,1019 (1944) I?.ECL.II.k:D
SOVCrltbCr
24, 1950.
Acidic Behavior of Concentrated Boric Acid Solutions DEWITT s r w - r w , J R . Public Health Research Institute of t h e C i t y of .leu. Ebrk, .Yew York, A'. use of aqueous boric acid for the quantitative collection I 'HE and subsequent titration of ammonia appears to have been
introduced by Winkler ( 17 ) ; there are numerous reports in t.hc litrrature of the application of this reagent i n the quantitative d&ermination of ammonia produced in various analytical procedures. Thus, boric acid is widely employed for the collection of ammonia generakd in the Kjeldahl nitrogen method ( 1 , 4, 6, 9-13, 16) and in other analytical procedures (15). The titration of solutions of ammonia in boric acid with standard hydrochloric acid is usually carried out to a mcthyl red end point, often in the presence of methylene blue, and by the use of color-matching techniques gives entirely satisfactory results ( 7 ) . Recently in this lahorntory it was noted that after significant quantities of ammonia vapor were delivered into 4% aqueous horic acid containing methyl red-methylene blue indicator, the expected change in color (purple --+. green) did not occur until after the mixture had been diluted with distilled water. Only after considerable dilution had been effected could the ammonia be satisfactorily titratcd with hydrochloric acid. I t thus appeared that in concentratrd solution boric wid behaved as a stronger acid than in dilute solution and the following experiments were designed to investigate this effect.
>-.
ml. After addition oi 3 tlrop.; 01 indicator, each sample \?as titrated with 0.0200 -V sodium hydroxide. At the end of titrittion, the p H of each solution WRP read on the glass talcrtrode a n d :dl were found to lie between 5.2 and 5.4
0.7H
0.6-
.
.-c
05-2 0 I
.I
Qa I
450
c'
$460 - 3
-0 -80
= 1100
EXPERIMENTAL
Materials and Apparatus. Twenty-five grams of recrystall.zet1 orthoboric acid were dissolved in water to a final volume of 500 nil.: this solut,ion was employed in subsequent titrations. Sodium hydroxide solution was prepared with carbon dioxide-free water and standardized against sulfamic acid ( 3 ) . The indicator employed contained 1 part of 0.1 yo methylene blue in 95y0 ethyl alcohol and 2 parts of 0.1% methyl red in 80% ethyl alcohol. The end point selected was a virtually colorless one lying h t w e e r i the purple (acid) and green (basic) tints. IZeasurements of pH were obtained with a Heckman Ilodctl H-2 glasv electrode instrument and all readings were madr at :i room temperature of 30" * 1 C. Titration of Boric Acid to Indicator End Point. To 20.00-ml. (oquivalent t o 1.00 gram) aliquots of horic acid solution werc added various quantities of distilled water ranging from 0 to i.5
Boric A c i d
Miliimolr NoOH per Mol
0.I
J
0 Figure 1.
I
2
3
4
5
6
T i t r a t i o n of Boric Acid to Methyl Red End Point
Titration Curves of Boric Acid a t Constant Volume. To 20.0ml. (equivalent to 1 gram) portions of boric acid solution were added quantities of 0.0200 S sodium hydroxide varying from 0 to 5 ml. The final volume was t,hen adjusted by the measured addition of water to a value of 25.0 ml. in one series, and 50.0 ml. in another. The final total concentration of borate plus boric acid was thus 0.647 mole per liter in the first writ)*, 0.323 in thr
1178
ANALYTICAL CHEMISTRY
second. The pH of the contents of each beaker was read on the glass electrode. Titration of Boric Acid with Water. The p H of aqueous solutions of pure boric acid was read on the glass electrode over a range of concentrations from 0.808 to 0.0311 M .
the relationship between pH and concentration of pure boric acid in water has been explored (Figure 3). This relationship in the case of an ideal neak acid is given by the equation,
DISCUSSIOS
It is apparent from the values in Figure 1 that in concentrated solution as much as 0.005 equivalent of alkali may be required to bring boric acid t o the turning point of the indicator. This quantity falls off rapidly as the solution is diluted, and virtually diaappears when the concentration falls to 0.1 M or below. In procedures like the Kjeldahl nitrogen method the recommended quantity of boric acid is in enormous excess, often 50 to 100 fold the amount of ammonia collected, on a molar basis. As usually conducted, the Kjeldahl distillation effects sufficient dilution of the boric acid to minimize the error which would otherwise result. In procedures, however, in which ammonia is delivered into concentrated boric acid by aeration rather than by distillation, proper dilution should precede titration of the ammonia if error i3 to be avoided. The concentration recommended by Van Slyke et al. (16),approximately 2% boric acid, would appear to tie too high for greatest ease of titration.
/I\
pH 4.0
where K =
‘HzE-l.
Line B , Figure 3, is the plot of this equa-
tion for the situation p K = 9.2. Whereas in dilute solution (AI < 0.05) the experimental points fall close to this ideal line, a t higher concentrations (M> O . l ) , the points deviate markedly on the side of unexpectedly high acidity, falling close to a straight Line (line a t left, Figure 3). In the succeeding analysis advantage is taken of the fact that the ionic strengths of the aqueous solutions of boric acid are low (maximum = 10-3.1 mole per liter). From the limiting law of Debye and Huckel activity coefficients have been estimated as ranging from 0.98 for the most concentrated to 1.00 for the most dilute solutions of boric acid employed. Consequently it is felt that no important error is introduced by the use of concentrations in lieu of activities in the following equations. If the reaction, nH.4 is (HA4)n,is assumed to occur, where
then ((HA),] = K I [HBI”
0.647 Molar
That the abundance of complex is a t all times low compared with that of monomeric boric acid is indicated by the failure to detect its occurrence from studies of the colligative properties of boric acid solutions (5, 8). Hence as a first approximation the quantity [HA] in Equation 3 can be taken as equal to the concentration of orthoboric acid introduced. If it further be assumed that only one species of complex exists, that it dissociates as a monobasic acid with an acidic dissociation constant K?, and
5.5
10 mM. 1NaOH 2per
6.5’
I
Figure 2.
Mol Boric Acid 3 4 5
6
Electrometric Titration Curves of Boric Acid a t Two Concentrations
Sensitibe range of rnethll red-meth,lene blue indicator
The titration of concentrated solutions of boric acid in the presence of met,hyl red gave indistinct end points, whereas in dilute solution (-44 < O.l), sharp end points were obtained. The reason for this difference is found in Figure 2, where are plotted the initial segments of titration curves of 1 gram of boric acid mnducted a t two different volumes. The block in this graph wpresents the range of turning of the indicator. =it the higher roncentration abont 5 to 6 me. of sodium hydroxide are required to bring the acid into the sensitive range of the indicator whereas halving the concentration reduces this quantity to about 1 me. Furthermore, dietinct buffering is evident in the indicator range pH 5.2 to 5.4 when the more concentrated solution is titrated. The first pK of orthoboric acid is generally given as approximately 0.2 ( 2 ) and one would not anticipate any extensive buffering effect of a weak acid a t p H = pK - 4. The evidmce presented thus far fits the hypothesis that in concentrated solutions ( J I > 0.1) of boric acid there exists a molecular species more highly dissociated than orthoboric acid. On the assumption that t h i 3 nprv Fpecies represent? a complex of boric acid with itself,
Figure 3. Relationship between Concentration of Boric Acid and pH 0 Present experimental points
0 Caloulated from data of Thygesen
(14)
V O L U M E 2 3 , N O . 8, A U G U S T 1 9 5 1
1179
that a t high concentrations essentially all the H' ions arise from this dissociation of the comples acid, the relationship
(4) van be shown to apply. On the coordinates selected in Figure 3 this also becomes the equation for a straight line, with the following characteristics:
LITERATURE CITED
.4t the intercept, log [HA] = 0 PH =
'/* (PKI
+ P&)
(6)
For line A these quantities may be evaluated as follows:
- n3
= -1.6
n = 3.2 l,'~
at a lower temperature, 18" C. Thygesen interprets his data on the assumption of a doubly dissociated tetramer rather than a singly dissociated complex. He further elects to assign dissociation constants to his complex acid in the same ratio as the two dissociation constante of glutaric acid. Inasmuch as both of these judgments appear to be arbitrary to the present writer, it is deemed preferable to describe concentrated solutions of boric acid as behaving as if they contained a far stronger complex acid than orthoboric acid of an average molecular weight 3 2 times that of the monomer.
+ pKt) 3.43 + pKz = 6.86
(pKi pKi
Bearing in mind the assumptions which have been made it may be concluded that the complex is made up, on the average, of 3.2 monomeric molecules and that the product of polymerization and dissociation constants of this complex, Kl.Kz = 10-6.8". The undue acidity of concentrated boric acid solutions ha< previously been investigated by Thygesen ( 1 4 ) n ho, on the basiq of electrical conductivity measurements, collpcted data indirating the occurrence in concentrated solution of a complex borate made up of approximatelv 3 monomeric molecules. Calculations f i om his data give rise to points included in Figure 3. These points
