Buffer Solutions of Tris(hydroxymethy1)aminomethane for pH Control in 50 Weight Per Cent Methanol from 10' to 40' C. SIR: Recent e.m.f. measurements by the authors (7) which have led t o a determination of the dissociation constant of t h e protonated form of tris(hydroxymethyl) aminomethane ("tris") in 50 wt. % methanol solvent can also yield conventional p H values for the buffer mixtures included in the study. Tris buffers composed of the amine and its hydrochloride in equal molal amounts are then suitable for pH control in 50 wt. yomethanol and to a limited extent for the standardization of pH equipment in this solvent medium. From the e.m.f. ( E ) reported in t h e earlier paper, together with the standard e.m.f. (,Eo) (6) values of the acidity function ps(aHycJ were calculated by t h e equation PS(UHYCI)
=
E - ,E" -___(RT In 10)/F
+ log mcl
(1)
They are summarized in Table I. T h e subscript s preceding t h e symbol in Equation 1 identifies the standard state to which the quantity is referred, in this case, the mixed solvent 50 wt. % methanol.
Table 1.
Conventional hydrogen ion activities can be derived from the acidity function ps(aHycl) only by adopting a nonthermodynamic formula for the estimation of numerical values of y c ~ . T h e convention chosen for this purpose should be consistent with t h a t on which aqueous p H standards are based ( 9 ) ; this is in essence the Debye-Huckel formula with ion-size parameter of 4.56 A. For other solvents, the form of the equation and the same ion size have been preserved, b u t the Debye-Huckel constants have been modified in a manner appropriate to t h e dielectric constant ( E ) , the density (do), and absolute temperature ( T ) of the medium:
where a = 4.56 A , Z is in terms of moles per kilogram of solvent, A = 1.825 X 106 (tT)-3l2 &1'2, and B = 50.29 ET)-^/^ & 1 / 2 , This formula is intended to apply t o solutions of ionic strength ( I ) of 0.1 or less. T h e ionic strength of buffers of tris and its hydrochloride is equal to the molality of the hydrochloride. The conventional value
Values of p.(aHycl) for Buffer Solutions Composed of Tris(hydroxymethy1)aminomethane and Its Hydrochloride, Both at Molality m
-
Temperature, 15" 20" 25O 8.415 8.258 8.108 7.966 8.468 8.310 8.162 8.020 8.505 8.348 8.200 8.059 8.535 8.379 8.230 8.090 8.560 8.404 8.256 8.115 8 582 8 426 8 277 8 137 8 601 8 445 8 296 8 157 8 618 8 313 8 462 8 174 8 634 8 477 8 328 8 189 8.647 8.490 8.342 8.203 c 61.2 59.5 57.9 56.3 do, g.ml.-1 0.9222 0.9187 -0.9155 -0.9125 A , kg.'I2 mole-l'z 0.7681 0.7791 0.7895 0.8015 10-8 B , kg.1'2 mole-1'2 cm.-l 0.3668 0.3682 0.3693 0.3708
m 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Table 11.
m 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.05 0.09 0.10
O
10"
C. 30" 7.831 7.885 7.924 7.955 7.981 8 003 8 023 8 040 8 055 8.069
5.4 . ~ 8
35 7.702 7.758 7.797 7.828 7.854 7 877 7 896 7 913 7 929 7.942 O
53.2
.
40" 7.580 7.637 7.677 7.708 7.735 7 757 7 777 7 794 7 810 7.824 51 8
0.9805 -019045 -0:9005 0.8122 0.8268 0,8381 0.3719
0.3736
0.3747
Values of paH* for Buffer Solutions Composed of Tris(hydroxymethy1)aminomethane and Its Hydrochloride, Both at Molality m
10" 8.349 8.380 8.402 8.420 8.436 8.448 8.460 8.470 8.480 8.488
15" 8.191 8.221 8.244 8.262 8.277 8.290 8.302 8.312 8.321 8.330
Temperature, 20° 25 8.041 7.897 8.072 7.929 8.094 7.952 8.112 7.970 8.128 7.985 8.140 7.998 8.152 8.010 8.162 8.020 8.171 8.029 8.179 8.038
O
C.
30" 7.761 7.793 7.816 7.834 7.850 7.863 7.874 7.884 7.894 7.902
35O 7.631 7.663 7.686 7.705 7.720 7.734 7.745 7.755 7.764 7.772
40" 7.509 7.541 7.565 7.584 7.599 7.613 7.624 7.635 7.644 7.652
of 4.56 A. for the ion-size parameter of the chloride ion is not to be confused with the ion-size parameter a = 4.3 -4. used in determining the standard potential of the silver-silver chloride electrode ( 5 ) . T h e latter is the mean diameter of the hydrogen and chloride ions, sometimes called the "closest distance of approach of the ions." The conventional value of -log aH calculated by combining Equations 1 and 2 is designated parr*; here the asterisk signifies that the activit'y is referred to the standard state in 50 wt. % methanol rather than to pure water. The paH* of buffer solutions composed of tris (molality m) a t seven temperatures is summarized in Table 11. Tris buffers have proved very useful for control of the pH of aqueous solutions in the physiologically important region p H 7 to 9 ( 1 ) . They can now be utilized to determine the p K values of weak acids and bases in 50 n t . yo methanol by spectrophotometric methods (3, 6) when the strength of the acidic species is from 0.1 to 10 times t h a t of protonated tris. There is some evidence, however, that the residual liquidjunction potent,ial is abnormally large when tris buffers are used in the glasscalomel pH assembly. For this reason, therefore, the paH* values given in Table I1 are not recommended for the standardization of the pH meters unless a n uncert'ainty of 0.05 unit can be tolerated. For standardization purposes the reference solutions already described (4) should preferably be employed. LITERATURE CITED
(1) Bates, 92, 341 (IJVI,. (2) Bates, R. G., Guggenheim, E. A., Pure A p p l . Chem. 1, 163 (1960). (3) Bates, R. G., Schwarzenbaich, G., Helv. Chim. Acta 37, 1069 (1954) (4)Paabo, M., Robinson, R. A,, Bates, R. G., J . Am. Chem. SOC.87,415 (1965). (5) Paabo, M., Robinson, R. A , , Bates, R. G., J . Chem. Eng. Data 9, 374 (1964). (6) Robinson, R. A., Biggs, A. I., Trans. Faraday Soc. 51, 901 (1955). (7) Woodhead, M., Paabq M., Robinson, R. A., Bates, R. G., J . Res. l\~atl. Bur. Std. 69A, 253 (1965). LIAURICE WOODHE.4D1 MAYAPAABO R. A . ROBINSON ROGERG. BATES National Bureau of Standards Washington, D. C. On leave from Makerere University College, Kampala, Uganda. VOL. 37, NO. 10, SEPTEMBER 1965
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