J. Chem. SOC., Faraday Trans. I, 1982, 78, 2521-2528
`
`Potentiometric and Polarimetric Studies of the Reaction of
`Boric Acid and Tetrahydroxyborate Ion with Polyhydroxy
`Compounds
`
`BY J. G R A H A M DAWBER* A N D DAYANG HUSNI MATUSIN
`Department of Chemistry and Biology, North Staffordshire Polytechnic,
`Stoke-on-Trent ST4 2DE
`
`Received 16th November, 198 1
`
`Values of the association constant, K,, for the reaction of boric acid with sorbitol, mannitol, D-glucose,
`glycerol and ethylene glycol have been evaluated from a modified Antikainen equation using values of the
`dissociation constant, K*, obtained by the half-neutralisation method. This procedure gives values of K ,
`which are easily compared with each other, and which have trends which are compatible with other
`previously determined values. Measurements of p P at various temperatures for the complexes of sorbitol
`and mannitol with boric acid allow estimates to be made of AH* and AS* for complexation. Polarimetric
`studies of the sorbitol and mannitol complexes in solution indicate that the tetrahydroxyborate ion, B(OH),,
`is more effectively complexed than boric acid and do not suggest any major differences in complexing ability
`between sorbitol and mannitol.
`
`The reaction of boric acid and borates with polyhydroxy compounds (polyols) has
`been known for many years, particularly as a means of increasing the acid strength
`of boric acid for its analysis by volumetric titration., The relationship between the
`structural characteristics of the polyol and its influence upon the acidity of boric acid
`was reviewed by Boiseken2T3 and it was he who suggested that the formation of
`boric-acid-polyol complexes occurred in two stages, first the formation of a mono-
`chelated borate complex, followed by a bichelated complex. It has also been
`suggested4-' that it is the borate ion, rather than boric acid, which is complexed by
`the polyol. Because the stoichiometry of the complexes is not clearly defined8-10
`discrepancies occur among values derived for the association constants, since
`assumptions made about the complex stoichiometry lead to varying methods of
`calculation .5 9 1-13
`In order to compare association constants it has been suggested8 that the Antikainen"
`equation be used, i.e.
`K* = Kl K , C,, + K ,
`(1)
`where K* is the measured dissociation constant of the polyol+H,BO, solution, K ,
`is the association constant of the complex, K , is the dissociation constant of H3BO3,
`C, is the stoichiometric concentration of all species containing the polyol and n is the
`coordination number of the complex. However, for the complexes of mannitol and
`glucose with boric acid8 the value of K* varied with the extent of dissociation, a
`mixture of acidic complexes being formed, the composition of which varied as the ratio
`of undissociated boric acid to borate ions changed. Similar effects are also observed
`To overcome this problem, Davis and
`with complexes of mannitol and borate
`Matt* used a modified Antikainen equation (in its logarithmic form)
`p(K*-KJ = -nlogl,Ci+p(KIKn)
`2521
`
`(2)
`
`Exhibit 1099
`ARGENTUM
`IPR2017-01053
`
`000001
`
`

`

`2522
`REACTIONS OF BORIC ACID WITH POLYOLS
`where Ci is the total stoichiometric concentration of polyol at half-neutralisation of
`the acid with NaOH, and K* is the dissociation constant of the polyol-boric-acid
`complex at half-neutralisation. pK* was obtained from the pH of the solution using
`the well-known Henderson-Hasselbalch equation, for which pH = pK* at
`half-neutralisation.
`The purpose of this work was to extend the studies made by Davis and Mott8 to
`other polyols and also to study the effect of temperature upon pK*. In addition, the
`formation of complexes of mannitol and sorbitol with H3BO3 and with tetrahydroxy-
`borate ion have been compared by polarimetric measurements.
`
`EXPERIMENTAL
`
`MATERIALS
`The materials used and their grades of purity were as follows: boric acid (AR), sodium
`chloride (AR), sodium hydroxide (AR), D-glucose (AR), glycerol (AR), ethylene glycol (GPR),
`mannitol (GPR) and sorbitol (GPR). The materials were used without further purification.
`
`POTENTIOMETRIC T I T R A T I O N S
`Solutions of 0.05 rnol dm-3 H,BO, in 0.1 mol dm-3 NaCl were prepared containing a range
`of concentration of polyol from 0.01 to 0.5 mol dm-3. 50 cm3 aliquots of these solutions were
`titrated with 0.1 mol dmV3 NaOH. The pH titration curves were obtained using an EIL (model
`7050) expanded-scale pH-meter. This model has a 2 pH-unit expanded-scale facility enabling
`pH readings to be estimated to 0.005, and includes both automatic and manual temperature
`compensation and also a fully adjustable isopotential facility. A combined glass/Ag/AgCl
`electrode was used to measure the pH. The values of p P were interpolated from the pH-titration
`curves at the half-neutralisation point.
`C H A N G E OF pK* W I T H TEMPERATURE
`The effect of temperature on pKy was studied for the mannitol and sorbitol complexes.
`Solutions of
`containing various amounts of polyol were prepared and standardised
`NaOH added to each solution corresponding to the half-neutralisation point. The pH of each
`solution was measured at 50, 40, 30, 25 and 20 OC, making appropriate adjustments to the
`temperature and isopotential controls of the pH-meter. The temperatures were maintained at
`- +0.5 O C over a period of ca. 2-3 min while the pH was measured.
`
`POLARIMETRIC MEASUREMENTS
`Solutions were made up containing 0.25 mol dm-3 mannitol plus H,BO, in amounts varying
`from 0 to 1 .O mol dm-3. The optical rotations of the solutions were measured with a Bellingham
`and Stanley model A photoelectric polarimeter using a 200 mm polarimeter tube. Angular
`rotations could be estimated to O.O0lo. The measurements were made at a wavelength of
`435.8 nm using a low-pressure Hg lamp with other wavelengths filtered out by a cobalt glass
`filter plus a solution of NaN0,.14 This wavelength was used rather than the sodium D-lines
`since it gave larger differences in angular rotation between successive solutions. The measure-
`ments were repeated with the
`neutralised with NaOH to give B(OH),, in amounts
`again varying from 0 to 1.0 mol dm-3.
`The whole series of polarimetric measurements was then repeated using sorbitol instead of
`mannitol. Thus the measurements were monitoring the changes in optical rotation of the polyol,
`with its total stoichiometric concentration kept constant, as it complexed with increasing
`amounts of added H3BO3 or B(OH),.
`
`RESULTS A N D DISCUSSION
`The pH-tritration curves for each solution were plotted and the values of pK* at
`half-neutralisation obtained from these graphs. The curves for sorbitol and ethylene
`
`000002
`
`

`

`J. G. DAWBER A N D D A Y A N G H U S N I MATUSIN
`
`2523
`
`1
`I
`I
`10
`30
`25
`20
`15
`35
`5
`volume of 0.1 mol dm-j NaOH/cm3.
`FIG. 1 .-Potentiometric titrations of 0.05 mol dm-3 H3BO3 + x mol dm-3 sorbitol where x = (a) 0, (b) 0.01,
`(c) 0.05, (d) 0.1, (e) 0.2, cf, 0.3, (g) 0.4 and (h) 0.5.
`
`1
`
`I
`
`I
`
`I
`
`I
`
`I '*I
`
`11
`
`l o t
`
`1
`I
`I
`I
`I
`30
`25
`20
`15
`10
`volume of 0.1 mol dm-3 NaOH/cm3
`FIG. 2.-Potentiometric titration of 0.05 H3B0,+x mol dm+ ethylene glycol where x = (a) 0, (b) 0.05, (c)
`0.1 (d) 0.2, (e) 0.3,
`0.4 and (g) 0.5.
`
`I
`35
`
`I
`5
`
`000003
`
`

`

`2524
`
`REACTIONS OF BORIC A C I D WITH P O L Y O L S
`
`TABLE 1.-pP VALUES AT HALF-NEUTRALISATION FOR VARIOUS POLYOLS IN BORIC ACID
`SOLUTIONS
`
`p P with polyol
`
`[polyol]/mol dm-3
`
`sorbitol
`
`mannitol D-glucose
`
`glycerol
`
`0
`0.01
`0.05
`0.10
`0.20
`0.30
`0.40
`0.50
`
`9.15
`8.98
`7.50
`6.40
`5.52
`5.16
`4.90
`4.75
`
`9.15
`9.00
`7.94
`6.88
`5.99
`5.58
`5.22
`5.05
`
`9.15
`-
`8.60
`8.35
`8.05
`7.92
`7.80
`7.34
`
`9.15
`-
`8.90
`8.70
`8.36
`8.14
`8.00
`7.83
`
`ethylene
`glycol
`
`9.15
`-
`-
`9.04
`9.00
`8.97
`8.94
`8-90
`
`I
`
`I
`
`I
`
`1
`
`0.2 0.4 0.6 0.8 1.0
`
`I
`
`I
`
`1.2
`
`I
`
`1.4
`
`FIG. 3.-Antikainen plots for 0, ethylene glycol and A, sorbitol.
`
`glycol are shown in fig. 1 and 2. The p& of boric acid (pK,) was found to be 9.15,
`which is close to other reported
`l5? l6 The pK* values obtained for various
`polyol-boric-acid systems at half-neutralisation are given in table 1.
`The modified Antikainen equation [eqn (2)] predicts that graphs of p(K* -Kl)
`against log,, C;l should be linear; n, the coordination number, is obtained as the slope,
`and p(K, K,) is obtained as the intercept, from which K, can be evaluated. Linear
`plots were in fact obtained when the polyol concentration was greater than ca.
`0.1 mol dm-3, i.e. when the polyol concentration is high relative to that of the H3BO3,
`and for which eqn (2) is valid. The graphs for sorbitol and ethylene glycol are shown
`in fig. 3. The data derved from the Antikainen plots are summarised in table 2.
`
`000004
`
`

`

`J. G. DAWBER AND DAYANG HUSNI MATUSIN
`
`2525
`
`TABLE 2.-RESULTS FROM ANTIKAINEN PLOTS [EQN (2)]
`
`complexant
`
`sorbitol
`mannitol
`
`slope,
`(4
`1.95
`2.27
`
`~~
`
`~
`
`intercept,
`PKK,)
`
`~
`
`3.80
`3.99
`
`PK,
`-5.35
`-5.16
`
`D-glucose
`
`1.03
`
`7.24
`
`-1.91
`
`glycerol
`
`ethylene glycol
`
`1.25
`
`0.67
`
`7.32
`
`8.98
`
`- 1.83
`
`-0.17
`
`Kn
`
`other values of
`K?z
`
`81.3
`
`2.24 x lo5 -
`1.45 x lo6 1.38 x lo5"
`1 x lo4 and
`8.24 x 104b
`186"
`188 and 574*
`8 and 77OC
`36.4 and 81.3b
`16.0 and 41.2c
`1.85 and 0.lc
`
`67.6
`
`1.48
`
`ref. (11); ref. (5).
`a Ref. (8);
`TABLE 3.-pK* FOR HaBOa + SORBITOL AT VARIOUS TEMPERATURES
`pK* at [sorbitol]/mol dm+
`
`T/OC
`
`0
`
`0.05
`
`0.1
`
`0.2
`
`0.5
`
`50
`40
`30
`25
`20
`
`8.86
`8.94
`9.04
`9.09
`9.15
`
`7.50
`7.44
`7.35
`7.28
`
`6.54
`6.44
`6.28
`6.18
`
`5.76
`5.65
`5.50
`5.38
`
`4.98
`4.85
`4.70
`4.58
`
`The values of n when glucose, glycerol and ethylene glycol were used as complexants
`correspond to the formation of a 1 : 1 complex with boric acid. For sorbitol and
`mannitol, however, n is ca. 2, indicating the formation of a bichelated complex. The
`values of the association constants (K,) for the various complexants, evaluated from
`the Antikainen equation, are compared in table 2. There is broad agreement between
`the values of K , evaluated by this method and those determined by other methods
`for which certain association equilibria are assumed. However, the Antikainen
`method, based upon the p P at half-neutralisation,8 allows a comparison to be made
`between various complexants without assumptions having to be made concerning the
`association equilibria. The value of K , for sorbitol is only slightly larger than that
`for mannitol, indicating that there is not a major difference in the complexing abilities
`of these two polyols for boric acid. The values of K , for the other polyols studied
`(table 2) are considerably lower than those for sorbitol and mannitol and follow trends
`similar to those found in other st~dies.~,
`8 v l1
`The values of p P at various temperatures and at various concentrations of sorbitol
`and mannitol are given in tables 3 and 4. It can easily be shown from the van't Hoff
`isochore that
`p P = AH*/2.303 RT+constant.
`Thus the enthalpy of ionisation of the polyol-H,BO, complex, AH*, can be obtained
`from a graph of pK* against 1/T. The values of AH* obtained in this way are plotted
`
`000005
`
`

`

`2526
`
`REACTIONS OF BORIC A C I D WITH POLYOLS
`TABLE 4.-pK* FOR H3B03 +- MANNITOL AT VARIOUS TEMPERATURES
`
`p P at [mannitol]/mol dm-3
`
`T/OC
`
`0
`
`0.05
`
`0.1
`
`0.2
`
`0.5
`
`50
`40
`30
`25
`
`8.86
`8.94
`9.04
`9.09
`
`7.92
`7.86
`7.84
`7.82
`
`7.08
`7.00
`6.83
`6.75
`
`6.20
`6.10
`5.96
`5.87
`
`5.30
`5.20
`5.08
`4.98
`
`I,,,,,,,,,,,,,
`2
`
`4
`
`8 1 0 1 2
`6
`mJmt
`FIG. 4.-Enthalpy of ionisation of H,BO, complexes with 0, sorbitol and x , mannitol.
`
`as a function of polyol concentration for mannitol and sorbitol in fig. 4. Although
`the AH* values will not be very precise, they do show the trends occurring as
`complexation takes place. The values of AH* level out at a ratio of ca. two moles of
`complexant per mole of H,BO,, i.e. rn,/rn, x 2, which is consistent with the formation
`of a bichelated complex, with AH* for sorbitol being slightly more exothermic than
`for mannitol.
`Assuming that AGe* = -RTln P, it is possible to calculate the corresponding
`values of AS,*,, for formation and ionisation of the complex, and these values for
`sorbitol and mannitol are given in table 5. The As&, values will only be very
`approximate, but nevertheless the large negative values do indicate the large loss of
`vibrational and rotational freedom of motion of those groups in the polyol which
`become involved in the complexation with the boron atom.
`
`000006
`
`

`

`J. G. DAWBER AND DAYANG HUSNI MATUSIN
`
`2527
`
`TABLE 5.-VALUES OF AS* FOR SORBITOL AND MANNITOL COMPLEXES
`
`AS,*,,/J K-l mol-l
`
`rnz/mla
`
`sorbitol mannitol
`
`0
`1
`2
`4
`10
`
`-115
`-195
`-210
`-197
`-183
`
`-115
`-173
`-206
`-192
`-172
`
`a Moles of polyol per mole of H,BO,.
`
`TABLE 6.--EFFECT OF BORIC ACID (a) AND BORATE ION (b) ON OPTICAL ROTATION OF SORBITOL
`(mz = 0.25 mol dm-3) AT 436 nm
`
`mla/mol dm-, ml/m2
`
`0
`0.02
`0.04
`0.10
`0.20
`0.30
`0.40
`0.50
`0.60
`0.70
`0.80
`0.90
`0.96
`1 .oo
`
`0
`0.08
`0.16
`0.40
`0.80
`1.20
`1.60
`2.0
`2.4
`2.8
`3.2
`3.6
`3.84
`4.0
`
`a/lO-, O m2 mol-I
`(4
`- 5.75
`-
`- 1.20
`+ 6.64
`15.70
`24.98
`30.18
`33.1
`35.6
`37.3
`38.3
`39.8
`40.1
`40.2
`
`(a)
`- 5.75
`- 5.50
`- 5.04
`- 4.00
`- 2.52
`- 1.26
`- 0.02
`+ 0.82
`1.76
`2.66
`3.44
`3.94
`-
`4.84
`
`a Moles of (a) boric acid and (b) borate ion.
`
`by
`The optical rotation results were converted to molar optical rotation, a!,,
`a, = a/cl, where a is the measured rotation, 1 the path-length of the polarimeter tube
`(in m) and c the total polyol concentration which for these measurements was
`250 mol m-3, i.e. 0.25 mol dm-3. The units of a, are thus O m2 mol-l. The experiments
`were conducted with the polyol concentration (m,) kept constant and with increasing
`amounts of boric acid or tetrahydroxyborate ion, m,, added up to a maximum
`concentration of 1 mol dm-3 (i.e. ml/m2 = 4 for the most concentrated solutions). The
`optical rotation results are compared in tables 6 and 7. The results suggest that the
`B(0H); ion, rather than boric acid, complexes with the polyol. The configuration of
`B(0H); will be tetrahedral and this will involve rather less change in symmetry on
`complexing with the polyol compared with H3BO3, for which the bond angles are likely
`to be ca. 120°. The data show that the formation of the mannitol-borate complex is
`accompanied by larger changes in optical rotation than in the case of the sorbitol-borate
`complex, which suggests the mannitol complex as having the greater asymmetry. The
`
`000007
`
`

`

`2528
`
`REACTIONS OF BORIC A C I D W I T H POLYOLS
`
`TABLE ?'.-EFFECT OF BORIC ACID (a) AND BORATE ION (b) ON ROTATION OF MANNITOL
`(m, = 0.25 mol dm-3) AT 436 nm
`
`~c/lO-~ O m2 mol-l
`
`mla/mol dm-3 ml/m2
`
`(a)
`
`0
`0.04
`0.10
`0.20
`0.30
`0.40
`0.50
`0.60
`0.70
`0.80
`0.90
`1-00
`
`0
`0.16
`0.40
`0.80
`1.20
`1.60
`2.0
`2.4
`2.8
`3.2
`3.6
`4.0
`
`-2.1 10
`- 1.080
`+ 0.860
`3.740
`6.100
`8.72
`10.96
`13.34
`15.44
`17.28
`19.32
`21.76
`
`- 2.14
`+7.10
`24.02
`53.9
`80.1
`93.4
`100.7
`106.7
`11 1.0
`113.6
`117.2
`120.0
`
`a Moles of (a) boric acid and (b) borate ion.
`
`changes in optical rotation as a function of mJm, do not show any major differences
`between sorbitol and mannitol in the effectiveness of complexation with H3BO3 and
`B(0H);.
`
`The helpful comments of a referee are gratefully acknowledged.
`
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`l2 S. J. Angyal and D. J. McHugh, J. Chem. SOC., 1957, 1423.
`l 3 J. J. Kankare, Anal. Chem., 1973, 45, 2050.
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`l6 Handbook ofChemistry and Physics, ed. R. C . Weast (C.R.C. Press, Columbus, Ohio, 60th edn, 1980).
`(PAPER 1 / 1776)
`
`@
`
`000008
`
`