Buffer Standards for the Physiological pH of N-[2-hydroxy-1,1-bis(hydroxymethyl)ethyl]glycine (TRICINE) from T = (278.15 to 328.15) K

Abstract

The pH values of two buffer solutions without NaCl and seven buffer solutions with added NaCl, having ionic strengths (I = 0.16 mol·kg⁻¹) similar to those of physiological fluids, have been evaluated at 12 temperatures from T = (278.15 to 328.15) K by way of the extended form of the Debye-Hückel equation of the Bates-Guggenheim convention. The residual liquid junction potentials (δE_j) between the buffer solutions of TRICINE and saturated KCl solution of the calomel electrode at T = (298.15 and 310.15) K have been estimated by measurement with a flowing junction cell. For the buffer solutions with the molality of TRICINE (m₁) = 0.06 mol·kg⁻¹, NaTRICINE (m₂) = 0.02 mol·kg⁻¹, and NaCl (m₃) = 0.14 mol·kg⁻¹, the pH values at 310.15 K obtained from the extended Debye-Hückel equation and the inclusion of the liquid junction correction are 7.342 and 7.342, respectively. These are in excellent agreement. The zwitterionic buffer TRICINE is recommended as a secondary pH standard in the region for clinical application.

1. Introduction

Roy et al. [1] has reported the pK₂ values of N-[2-hydroxy-1,1-bis(hydroxymethyl)ethyl]glycine (TRICINE) at temperatures from T = (278.15 to 328.15) K, including 310.15 K. Various buffer substances recommended by Good et al. [2, 3] have proven very useful for the measurement of the pH of blood and the control of pH in the region close to that of physiological solutions. The structure of TRICINE is as follows:

For a routine calibration of the pH meter assembly, zwitterionic physiological pH standards are in need within the framework set-up by the NBS/NIST [4]. The phosphate buffer has been widely used as a physiological pH standard, but it is not an ideal primary pH standard buffer because of various limitations [4].

Roy et al. [5] has published the pK₂ and pH values of the biological buffer [bis[(2-hydroxyyethyl)amino]acetic acid (BICINE). This buffer has been recommended as a pH standard for use with in physiological applications. Feng and coworkers [6] have published the values of pK₂ and pH of the zwitterionic buffer N-(2-hydroxyethyl)piperazine-N-2-ethanesulfonic acid (HEPES). The HEPES buffer has been certified by the National Institute of Standards and Technology (NIST) as a primary reference standard. Bates et al. [7] recommended the buffer solution 0.06 m TRICINE + 0.02 m NaTRICINEate for use as a pH standard at T = (298.15 and 310.15) K.

In order to provide very accurate values of pH, we have undertaken a comprehensive study for the following compositions: (a) TRICINE (0.08 mol·kg⁻¹) + NaTRICINE (0.02 mol·kg⁻¹), I = 0.02 mol·kg⁻¹, (b) TRICINE (0.09 mol·kg⁻¹) + NaTRICINE (0.03 mol·kg⁻¹), I = 0.03 mol·kg⁻¹, (c) TRICINE (0.03 mol·kg⁻¹) + NaTRICINE (0.01 mol·kg⁻¹) + NaCl (0.15 mol·kg⁻¹), I = 0.16 mol·kg⁻¹, (d) TRICINE (0.03 mol·kg⁻¹) + NaTRICINE (0.03 mol·kg⁻¹) + NaCl (0.13 mol·kg⁻¹), I = 0.16 mol·kg⁻¹, (e) TRICINE (0.08 mol·kg⁻¹) + NaTRICINE (0.08 mol·kg⁻¹) + NaCl (0.08 mol·kg⁻¹), I = 0.16 mol·kg⁻¹, (f) TRICINE (0.05 mol·kg⁻¹) + NaTRICINE (0.05 mol·kg⁻¹) + NaCl (0.11 mol·kg⁻¹), I = 0.16 mol·kg⁻¹, (g) TRICINE (0.09 mol·kg⁻¹) + NaTRICINE (0.03 mol·kg⁻¹) + NaCl (0.13 mol·kg⁻¹), I = 0.16 mol·kg⁻¹, (h) TRICINE (0.06 mol·kg⁻¹) + NaTRICINE (0.02 mol·kg⁻¹) + NaCl (0.14 mol·kg⁻¹), I = 0.16 mol·kg⁻¹, (i) TRICINE (0.08 mol·kg⁻¹) + NaTRICINE (0.02 mol·kg⁻¹) + NaCl (0.14 mol·kg⁻¹), I = 0.16 mol·kg⁻¹

2. Experimental

TRICINE was purchased from Sigma Chemical Co. (St. Louis, Missouri). It was subjected to recrystallization from 75% ethanol-water and assayed by titration with a carbonate-free standard solution of NaOH. The analyses of the unpurified and purified TRICINE averaged 99.72% and 99.98% pure, respectively. The substance TRICINE, NaCl (ACS reagent grade dried at T = 383.15 K), CO₂-free doubly distilled water, and a standard solution of NaOH were used to prepare NaTRICINEate. Air buoyancy corrections were made for all masses using a vacuum correction factor of 1.00106 for dilute buffer solutions.

The preparation of the hydrogen electrodes, thermal electrolytic type silver-silver chloride electrodes, the design of the all-glass cells, control of the temperature, use of digital voltmeter, and other experimental set-ups have been reported previously [8, 9].

The cells investigated were the following:

$$\text{Pt}(\text{s})\mid {\text{H}}_2(\text{g}),p=101.325\text{kPa}\mid \text{TRICINE}(m_1)+\text{NaTRICINE}(m_2)+\text{NaCl}(m_3)\mid \text{AgCl}(\text{s})\mid \text{Ag}(\text{s})$$ (A)

$$\text{Pt}(\text{s})\mid {\text{H}}_2(\text{g}),p=101.325\text{kPa}\mid \text{TRICINE}(m_1)+\text{NaTRICINE}(m_2)+\text{NaCl}(m_3)\mid \mid \text{KCl}(\text{satd})\mid {\text{Hg}}_{\text{2}}{\text{Cl}}_2(\text{s})\mid \text{Hg}(\text{l})$$ (B)

$$\text{Pt}(\text{s})\mid {\text{H}}_2(\text{g}),p=101.325\text{kPa}\mid \text{phosphate}\text{buffer}\mid \mid \text{KCl}(\text{satd})\mid {\text{Hg}}_{\text{2}}{\text{Cl}}_2(\text{s})\mid \text{Hg}(\text{l})$$ (C)

where the double line in cells (B) and (C) indicates the liquid junction.

The residual liquid junction potential is given by δE_j = E_j(s) − E_j(x), where E_j(s) and E_j(x) indicate the liquid junction potentials for the standard physiological phosphate solutions and the experimental buffer solutions of TRICINE, respectively. From cell (B), these values were obtained using the following equation [4, 6, 8]:

$$E_{\text{j}(\text{s})}=E_{(\text{s})}+E_{\mathit{SCE}}^{\circ }-k\text{pH}(s)$$ (1)

In equation (1) $E_{\mathit{SCE}}^{\circ }=-0.2415\text{V}$ (standard potential of the saturated calomel electrode), k = 0.059156 V, for the physiological phosphate buffer solution, pH(s) = 7.415 [4, 6, 8] at T = 298.15 K; pH(s) = 7.395 [4, 6, 8] at T = 310.15 K, k = 0.061538 V and $E_{\mathit{SCE}}^{\circ }=-0.2335\text{V}$ at 310.15 K. We have attempted to estimate values of the liquid junction potential for four out of nine buffer solutions. The difference in δE_j between the phosphate standard and each experimental buffer solution is an important factor when different standards are selected to obtain the operational pH for an unknown medium. This error can be estimated by the operational definition of pH using equation (2).

$$\text{pH}(\text{x})=\text{pH}(\text{s})+\frac{E_x-E_s+\delta E_j}{k}$$ (2)

where the subscript “x” refers to the unknown buffer TRICINE + NaTRICINE. If δE_j = 0, then equation (2) takes the form:

$$\text{pH}(\text{x})=\text{pH}(\text{s})+\frac{E_x-E_s}{k}$$ (3)

3. Methods and Results

The pressure corrected cell potential data for cell (A) containing two buffer solutions with varying chloride ion concentration in the ionic strength range I = 0.025 to 0.05 mol·kg⁻¹, and seven buffer solutions with NaCl at I = 0.16 mol·kg⁻¹ are listed in table 1. The uncertainty of duplicate cells, on average, lies within (0.02 ± 0.01) mV in the temperature range T = (278.15 to 328.15) K.

TABLE 1.

Electromotive force E (V) of Cell A: Pt(s); H₂(g, p° = 101.325 kPa) | TRICINE (m₁), NaTRICINE (m₂), NaCl (m₃) | AgCl(s), Ag(s)

m/mol·kg−1			T/K
m1	m2	m3	278.15	283.15	288.15	293.15	298.15	303.15	308.15	310.15	313.15	318.15	323.15	328.15
0.08	0.02	0.005	0.79915	0.80080	0.80236	0.80352	0.80464	0.80567	0.80636	0.80677	0.80729	0.80786	0.80842	0.80898
0.08	0.02	0.010	0.78265	0.78394	0.78511	0.78594	0.78670	0.78751	0.78792	0.78825	0.78855	0.78888	0.78914	0.78947
0.08	0.02	0.015	0.77286	0.77388	0.77479	0.77546	0.77608	0.77676	0.77694	0.77724	0.77741	0.77762	0.77776	0.77784
0.08	0.02	0.020	0.76593	0.76683	0.76747	0.76797	0.76840	0.76902	0.76910	0.76943	0.76949	0.76965	0.76958	0.76975
0.09	0.03	0.005	0.80442	0.80572	0.80716	0.80841	0.80954	0.81062	0.81163	0.81216	0.81275	0.81359	0.81431	0.81530
0.09	0.03	0.010	0.78838	0.78948	0.79058	0.79157	0.79243	0.79321	0.79391	0.79428	0.79466	0.79526	0.79557	0.79610
0.09	0.03	0.015	0.77900	0.78000	0.78085	0.78176	0.78246	0.78307	0.78358	0.78383	0.78408	0.78444	0.78459	0.78474
0.09	0.03	0.020	0.77260	0.77350	0.77436	0.77518	0.77569	0.77619	0.77653	0.77670	0.77684	0.77708	0.77707	0.77696
0.03	0.01	0.15	0.72560	0.72569	0.72583	0.72557	0.72556	0.72506	0.72460	0.72451	0.72423	0.72364	0.72308	0.72243
0.03	0.03	0.13	0.75394	0.75449	0.75490	0.75528	0.75551	0.75556	0.75574	0.75571	0.75563	0.75545	0.75520	0.75487
0.08	0.08	0.08	0.76742	0.76818	0.76889	0.76930	0.76990	0.77017	0.77061	0.77075	0.77082	0.77103	0.77115	0.77121
0.05	0.05	0.11	0.75961	0.76027	0.76083	0.76130	0.76162	0.76181	0.76205	0.76207	0.76201	0.76195	0.76183	0.76164
0.09	0.03	0.13	0.72956	0.72968	0.72972	0.72968	0.72966	0.81054	0.81141	0.72847	0.72816	0.72762	0.72697	0.72624
0.06	0.02	0.14	0.72763	0.72776	0.72776	0.72766	0.72750	0.79260	0.79320	0.72652	0.72622	0.72569	0.72518	0.72446
0.08	0.02	0.14	0.72096	0.72091	0.72077	0.72059	0.72029	0.76793	0.76826	0.71927	0.71897	0.71836	0.71764	0.71673
E°Ag-AgCl (V) =			0.23416	0.23147	0.22863	0.22562	0.22244	0.21913	0.21572	0.21429	0.21214	0.20840	0.20455	0.20064

Conventional pa_H values have been evaluated by the method of Bates et al. [7, 10–11] and other investigators [12–13] for two buffer solutions without NaCl and seven buffer solutions in the presence of NaCl.

The calculation of pa_H values for two buffer solutions without NaCl and seven buffer solutions in the presence of Cl⁻ were made in the temperature range T = (278.15 to 328.15) K using the cell potential (E) listed in Table 1, as well as the molality of the chloride ion. The acidity function [7, 9] is given by:

$$p(a_H{\gamma }_{Cl})=\frac{E-E^{\circ }}{k}+{log}_{10}{m}_{\text{Cl}}$$ (4)

where k is the Nernst slope, and E° is the standard potential of the silver-silver chloride electrode listed in table 1.

Values of the acidity function p(a_Hγ_Cl) for Cl⁻ free buffer solutions were derived at each temperature and were plotted as a function of m_Cl⁻. Straight lines with small slopes were obtained. The values of the intercepts, p(a_Hγ_Cl)° are entered in Table 2 for two buffer solutions without the presence of NaCl. The acidity function, p(a_Hγ_Cl), for seven buffer solutions are listed in Tables 2 and 3 from T = (278.15 to 328.15) K, including 310.15 K. The uncertainty introduced in this type of graphical extrapolation is usually less than 0.002. The equation for the calculation of pa_H is given below:

$${\text{p}a}_{\text{H}}=p{(a_{\text{H}}{\gamma }_{\text{Cl}})}^{\circ }+{log}_{10}{\gamma }_{Cl}^{\circ }$$ (5)

where the single-ion activity coefficient, ${\gamma }_{Cl}^{\circ }$, cannot be measured experimentally. Thus, a non-thermodynamic convention [7, 8] is normally adopted for the estimation of the ion activity coefficient of a single species, chloride. The pH values obtained from the liquid junction cell are indicated by the “operational” pH, whereas the “conventional” pH calculated from equation (5) is designated as pa_H.

TABLE 2.

p(a_Hγ_Cl) of (TRICINE + NaTRICINE) buffer solutions from (278.15 to 328.15) K, computed using equation (4), and values of p(a_Hγ_Cl)° estimated from the plot of p(a_Hγ_Cl) at m_Cl = 0 for two Cl⁻ free buffer solutions

T/K	m/mol·kg−1
	0.08 m TRICINE + 0.02 m NaTRICINE + 0.00 m NaCl	0.09 m TRICINE + 0.03 m NaTRICINE + 0.00 m NaCl	0.03 m TRICINE + 0.01 m NaTRICINE + 0.15 m NaCl	0.03 m TRICINE + 0.03 m NaTRICINE + 0.13 m NaCl	0.08 m TRICINE + 0.08 m NaTRICINE + 0.08 m NaCl
	I = 0.02 m	I = 0.03 m	I = 0.16 m	I = 0.16 m	I = 0.16 m
278.15	7.937	8.024	8.081	8.532	8.564
283.15	7.834	7.912	7.973	8.424	8.456
288.15	7.738	7.809	7.873	8.319	8.353
293.15	7.638	7.709	7.771	8.220	8.250
298.15	7.545	7.615	7.681	8.125	8.156
303.15	7.453	7.524	7.587	8.032	8.064
308.15	7.363	7.437	7.499	7.946	7.978
310.15	7.329	7.407	7.467	7.912	7.946
313.15	7.280	7.359	7.418	7.861	7.895
318.15	7.197	7.280	7.338	7.780	7.816
323.15	7.119	7.203	7.263	7.702	7.740
328.15	7.043	7.136	7.190	7.626	7.666

TABLE 3.

p(a_Hγ_Cl) of (TRICINE + NaTRICINE) buffer solutions from (278.15 to 328.15) K, computed using equation (4)

T/K	m/mol·kg−1
	0.09 m TRICINE + 0.03 m NaTRICINE + 0.13 m NaCl	0.06 m TRICINE + 0.02 m NaTRICINE + 0.14 m NaCl	0.08 m TRICINE + 0.02 m NaTRICINE + 0.14 m NaCl	0.05 m TRICINE + 0.05 m NaTRICINE + 0.11 m NaCl
	I = 0.16 m	I = 0.16 m	I = 0.16 m	I = 0.16 m
278.15	8.090	8.088	7.967	8.562
283.15	7.982	7.980	7.858	8.454
288.15	7.878	7.876	7.754	8.350
293.15	7.780	7.777	7.656	8.251
298.15	7.688	7.684	7.562	8.156
303.15	7.351	7.534	7.425	8.064
308.15	7.442	7.445	7.338	7.977
310.15	7.469	7.470	7.352	7.943
313.15	7.419	7.420	7.303	7.891
318.15	7.339	7.341	7.225	7.810
323.15	7.262	7.266	7.148	7.733
328.15	7.186	7.191	7.073	7.658

The convention is not subject to any proof but is reasonable for the purpose of assigning standard pH values. The equation (6) of a ‘pH convention’ [7, 11], based on an extended form of the Debye-Hückel equation, has been widely used. In the assignment of pa_H values and the establishment of NIST pH standard [4, 8], the calculation of ${log}_{10}{\gamma }_{Cl}^{\circ }$ for two buffer solutions without chloride ion was made using equation (6):

$${log}_{10}{\gamma }_{Cl}^{\circ }=-\frac{A\sqrt{I}}{1+{Ba}^{\circ }\sqrt{I}}+CI$$ (6)

where I is the ionic strength of the buffer solution, A and B are the Debye-Hückel constants [4, 5, 9] and are temperature dependent, a constant value of Ba° = 1.38 kg^½·mol^−½ used for experimental temperatures, and C is an adjustable parameter which can be calculated by the following equation [5]:

$$C=C_{298.15}+\alpha \{(T/T^{\circ })-298.15)\}+\beta {\{(T/T^{\circ })-298.15)\}}^2$$ (7)

where C_298.15 = 0.032 kg·mol⁻¹, α = 6.2·10⁻⁴ kg·mol⁻¹, β = −8.7·10⁻⁶ kg·mol⁻¹, T° = 1 K, and T is the thermodynamic temperature.

For the calculation of pa_H using equation (4) for seven buffer solutions with chloride ion, the equation (6) is also used where ${log}_{10}{\gamma }_{Cl}^{\circ }$ is replaced by log₁₀γ_Cl. This procedure does not involve any extrapolation.

The pa_H values of two buffer solutions of TRICINE without NaCl and seven buffer solutions with NaCl are calculated using equations (4) to (7) and are fitted as a function of the thermodynamic temperature:

$$\begin{array}{l}\text{For}\text{TRICINE}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.02\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.484-1.860·{10}^{-2}\{(T/T^{\circ })-298.15)\}+5.95·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (8)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.09\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.03\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.545-1.869·{10}^{-2}\{(T/T^{\circ })-298.15)\}+8.68·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (9)

where 278.15 K ≤ T ≤ 328.15 K. The values of the acidity function p(a_Hγ_Cl) for all buffer solutions were obtained from equation (4) whereas for the chloride free solution, the values of p(a_Hγ_Cl)° were calculated from the plot of p(a_Hγ_Cl) against the molality of the chloride ion (a linear function). The intercept is p(a_Hγ_Cl)° at m_Cl = 0. The values of pa_H listed in table 4 were obtained from equations (5)–(6). The standard deviations of regression are 0.0012, and 0.0018, respectively, for these two buffer solutions.

TABLE 4.

pa_H of (TRICINE + NaTRICINE) buffer solutions from (278.15 to 328.15) K, computed using equations (4)–(6)

T/K	m/mol·kg−1
	0.08 m TRICINE + 0.02 m NaTRICINE + 0.00 m NaCl	0.09 m TRICINE + 0.03 m NaTRICINE + 0.00 m NaCl	0.03 m TRICINE + 0.01 m NaTRICINE + 0.15 m NaCl	0.03 m TRICINE + 0.03 m NaTRICINE + 0.13 m NaCl	0.08 m TRICINE + 0.08 m NaTRICINE + 0.08 m NaCl
	I = 0.02 m	I = 0.03 m	I = 0.16 m	I = 0.16 m	I = 0.16 m
278.15	7.879	7.956	7.955	8.407	8.440
283.15	7.776	7.843	7.848	8.298	8.331
288.15	7.678	7.740	7.747	8.193	8.227
293.15	7.580	7.640	7.646	8.095	8.125
298.15	7.485	7.544	7.554	7.999	8.031
303.15	7.393	7.453	7.460	7.905	7.937
308.15	7.302	7.366	7.371	7.819	7.851
310.15	7.268	7.335	7.339	7.784	7.818
313.15	7.219	7.287	7.289	7.773	7.766
318.15	7.135	7.207	7.209	7.651	7.687
323.15	7.057	7.130	7.133	7.572	7.610
328.15	6.980	7.062	7.059	7.495	7.535

For the seven buffer solutions with an ionic strength I = 0.16 mol·kg⁻¹, the values of pa_H listed in tables 4 and 5 are given by the equations:

$$\begin{array}{l}\text{For}\text{TRICINE}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.01\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.15\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.552-1.865·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.40·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (10)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.13\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.999-1.888·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.07·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (11)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.08\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=8.031-1.883·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.86·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (12)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.05\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.05\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.11\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=8.030-1.887·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.06·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (13)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.09\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.13\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.558-1.887·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.04·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (14)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.06\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.14\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.558-1.887·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.04·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (15)

$$\begin{array}{l}\text{For}\text{TRICINE}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaTRICINE}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.14\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.436-1.884·{10}^{-2}\{(T/T^{\circ })-298.15)\}+7.21·{10}^{-5}{\{(T/T^{\circ })-298.15)\}}^2\end{array}$$ (16)

where T is the temperature in K. The standard deviations for regression from equations (10) to (16) are 0.0012, 0.0013, 0.0011, 0.0014, 0.0012, 0.0012 and 0.0010, respectively.

TABLE 5.

pa_H of (TRICINE + NaTRICINE) buffer solutions from (278.15 to 328.15) K, computed using equations (4)–(6)

T/K	m/mol·kg−1
	0.09 m TRICINE	0.06 m TRICINE	0.08 m TRICINE	0.05 m TRICINE
	+ 0.03 m NaTRICINE	+ 0.02 m NaTRICINE	+ 0.02 m NaTRICINE	+ 0.05 m NaTRICINE
	+ 0.13 m NaCl	+ 0.14 m NaCl	+ 0.14 m NaCl	+ 0.11 m NaCl
	I = 0.16 m	I = 0.16 m	I = 0.16 m	I = 0.16 m
278.15	7.965	7.962	7.841	8.437
283.15	7.856	7.854	7.732	8.328
288.15	7.753	7.751	7.628	8.224
293.15	7.655	7.652	7.531	8.126
298.15	7.562	7.557	7.435	8.029
303.15	7.465	7.463	7.346	7.937
308.15	7.375	7.374	7.258	7.849
310.15	7.341	7.342	7.224	7.815
313.15	7.391	7.291	7.175	7.763
318.15	7.210	7.211	7.095	7.681
323.15	7.131	7.136	7.018	7.603
328.15	7.055	7.060	6.941	7.526

The potential difference of the cells (B) and (C) for four buffer solutions at T = (298.15 K and 310.15) K are given in table 6. The values of the residual liquid junction potential, δE_j, listed also in table 6 were estimated by using equation (1). From the pH data at T = (298.15 K and 310.15) K from table 6, there is excellent agreement between the calculated value obtained from the extended Debye-Hückel equation and the value obtained from the δE_j correction. The experimental method for determining the single-ion activity coefficient, ${log}_{10}{\gamma }_{Cl}^{\circ }$, is not possible. Partanen and Minkkinen [14] and Covington and Ferra [15] both used the Pitzer theory to estimate the single ion activity coefficient at ionic strengths higher than 0.1 mol·kg⁻¹ in the calculation of the pH standards of the phosphate buffer solutions. Camoes et al. [12] and Buck et al. [13] recommended the use of Pitzer formalism [16] for the estimation of ${\gamma }_{Cl}^{-}$ because of the consistency of the improvements of the pH measurements. Work is under progress in this laboratory for the calculation of the single ion activity coefficient γ_Cl using Pitzer theory [17] for I = 0.16 mol·kg⁻¹. The results of pH for various buffers by applying this value of γ_Cl will be reported in a separate publication. The total uncertainties were estimated by combining the various sources of error: (i) assumption for the calculation of the ${log}_{10}{\gamma }_{Cl}^{\circ }$; (ii) extrapolation to p(a_Hγ_Cl)° at m_Cl⁻ = 0 (within ± 0.001 pH unit); (iii) liquid junction potential measurement; and (iv) error in the experimental emf measurement (± 0.02 mV). The overall uncertainty is about ± 0.009 pH unit. The operational pH values at T = (298.15 K and 310.15) K (table 6) for four buffer solutions are recommended as pH standards for the measurement of the pH of physiological solutions.

TABLE 6.

Emf of Cell B and pH values with δE_j correction at (298.15 and 310.15) K for TRICINE buffer

m1	m2	m3	I	Ex/V		δEjb/mV		Withoutc δEj corr	Withd δEj corr	Extendede D-H eqn.	Withoutc δEj corr	Withd δEj corr	Extendede D-H eqn.
				298.15 K	310.15 K	298.15 K	310.15 K	298.15 K			310.15 K
0.09	0.03	0.00	0.03	0.69003	0.68740	0.3	0.4	7.538	7.543	7.544	7.329	7.334	7.335
0.08	0.02	0.14	0.16	0.68180	0.67861	2.1	2.3	7.399	7.434	7.435	7.188	7.223	7.224
0.09	0.03	0.13	0.16	0.68926	0.68591	2.1	2.2	7.526	7.561	7.562	7.305	7.340	7.341
0.06	0.02	0.14	0.16	0.68902	0.68599	2.1	2.2	7.522	7.556	7.557	7.307	7.342	7.342
Emf of Cell Ca				Es/V		fEj/mV
0.008695 m KH2PO4 + 0.03043 m Na2HPO4				0.68275	0.69147	2.6	2.9

^aPublished data [4, 6, 8] for physiological phosphate buffer solutions; units of m, mol·kg⁻¹

^bThe residual liquid junction potential, δE_j = E_j(s) − E_j(x), which can be calculated from equation (1) and the values of tables 4 – 6. The pH of the primary standard phosphate buffer is 7.415 and 7.395 at T = (298.15 and 310.15) K, respectively.

^cValues obtained from equation (3) and E_x and E_s data from this table

^dObtained from equation (2) using values of E_x, E_s, and δE_j from this table, and k = 0.059156 V and 0.061538 V at 298.15 K and 310.15 K, respectively

^eObtained from extended Debye-Hückel (DH) equation of the Bates-Guggenheim convention, data listed in tables 4–5

^fE_j is the liquid junction potential in mV.

FIGURE 1.

N-[2-hydroxy-1,1-bis(hydroxymethyl)ethyl]glycine (TRICINE)

Highlights.

• This work reports pH values of TRICINE buffer

• Liquid junction potential correct is applied

• These values will be used by clinical and biomedical scientists

• The pH values lie within 6.8 to 7.5