Buffer standards for the physiological pH of the zwitterionic compound of 3-(N-morpholino)propanesulfonic acid (MOPS) from T = (278.15 to 328.15) K

Abstract

This paper reports the pH values of five NaCl-free buffer solutions and eleven buffer compositions containing NaCl at I = 0.16 mol·kg⁻¹. Conventional pa_H values are reported for sixteen buffer solutions with and without NaCl salt. The operational pH values have been calculated for five buffer solutions and are recommended as pH standards at T = (298.15 and 310.15) K after correcting the liquid junction potentials. For buffer solutions with the composition m₁ = 0.04 mol·kg⁻¹, m₂ = 0.08 mol·kg⁻¹, m₃ = 0.08 mol·kg⁻¹ at I = 0.16 mol·kg⁻¹, the pH at 310.15 K is 7.269, which is close to 7.407, the pH of blood serum. It is recommended as a pH standard for biological specimens.

1. Introduction

Biological buffers are of great importance for research in biomedicine and clinical diagnosis. A considerable interest attaches to the acid-base behavior of zwitterionic amino acids [1–2], the buffer solutions of which are useful for the control of acidity in the physiological pH range of 6 to 8. Previously, Roy et al.[3–4] have reported the pK₂ values and some limited pH values of buffer solutions of 3-(N-morpholino)-propanesulfonic acid (MOPS) at temperatures from T = (278.15 to 328.15) K. In order to provide reliable and accurate pH values, we have studied five MOPS buffer solutions without NaCl and eleven isotonic saline solutions at I = 0.16 mol·kg⁻¹ in the temperature range (278.15 to 328.15) K. The structure of MOPS is as follows:

The phosphate buffer has been universally used as a physiological pH standard [5], but it may not be ideal for some situations. For example, (i) phosphates can act as inhibitors to enzymatic processes; (ii) phosphate can precipitate with polyvalent cations present in blood ingredients; and (iii) the temperature coefficient of the pH of the phosphate buffer is −0.0028 K⁻¹ as compared to that of whole blood (−0.015 K⁻¹) [6].

Roy et al. [7] have reported the pK₂ and pH values of the biological buffer bis-[(2-hydroxyethyl)amino]acetic acid (BICINE). This buffer has been recommended as a pH standard in the range of physiological application. The HEPES buffer was studied by Feng and coworkers [8] and has been certified by the National Institute of Standards and Technology (NIST) as a primary reference pH standard. The values of pK₂ and pH for 3-(N-morpholino)-2-hydroxypropanesulfonic acid (MOPSO) [9] have been reported. The pH of these solutions closely matches that of the common clinical media. In 1973, Bates et al. [10] recommended pH standard for a buffer solution of 0.06 mol·kg⁻¹ TRICINE + 0.02 mol·kg⁻¹ sodiumTRICINEate. Goldberg et al. [12] reported the results of the thermodynamic quantities of more than 60 physiological buffers. The review article did not include any reliable results of pH for MOPS.

As shown in figure 1, we now have undertaken to investigate MOPS in order to provide accurate and reproducible pH values for the following buffer compositions: (a) MOPS (0.02 mol·kg⁻¹) + NaMOPS (0.04 mol·kg⁻¹), I = 0.04 mol·kg⁻¹; (b) MOPS (0.02 mol·kg⁻¹) + NaMOPS (0.08 mol·kg⁻¹), I = 0.08 mol·kg⁻¹; (c) MOPS (0.03 mol·kg⁻¹) + NaMOPS (0.09 mol·kg⁻¹), I = 0.09 mol·kg⁻¹; (d) MOPS (0.04 mol·kg⁻¹) + NaMOPS (0.08 mol·kg⁻¹), I = 0.08 mol·kg⁻¹; (e) MOPS (0.08 mol·kg⁻¹) + NaMOPS (0.02 mol·kg⁻¹), I = 0.02 mol·kg⁻¹; (f) MOPS (0.02 mol·kg⁻¹) + NaMOPS (0.02 mol·kg⁻¹) + NaCl (0.14 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (g) MOPS (0.02 mol·kg⁻¹) + NaMOPS (0.04 mol·kg⁻¹) + NaCl (0.12 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (h) MOPS (0.04 mol·kg⁻¹) + NaMOPS (0.02 mol·kg⁻¹) + NaCl (0.14 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (i) MOPS (0.04 mol·kg⁻¹) + NaMOPS (0.08 mol·kg⁻¹) + NaCl (0.08 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (j) MOPS (0.04 mol·kg⁻¹) + NaMOPS (0.04 mol·kg⁻¹) + NaCl (0.12 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (k) MOPS (0.05 mol·kg⁻¹) + NaMOPS (0.05 mol·kg⁻¹) + NaCl (0.11 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (l) MOPS (0.06 mol·kg⁻¹) + NaMOPS (0.06 mol·kg⁻¹) + NaCl (0.10 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (m) MOPS (0.08 mol·kg⁻¹) + NaMOPS (0.08 mol·kg⁻¹) + NaCl (0.08 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (n) MOPS (0.06 mol·kg⁻¹) + NaMOPS (0.03 mol·kg⁻¹) + NaCl (0.13 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (o) MOPS (0.08 mol·kg⁻¹) + NaMOPS (0.02 mol·kg⁻¹) + NaCl (0.14 mol·kg⁻¹), I = 0.16 mol·kg⁻¹; (p) MOPS (0.09 mol·kg⁻¹) + NaMOPS (0.09 mol·kg⁻¹) + NaCl (0.07 mol·kg⁻¹), I = 0.16 mol·kg⁻¹.

FIGURE 1.

3-(N-morpholino)-propanesulfonic acid (MOPS)

2. Experimental

MOPS was purchased from Research Organics (Cleveland, OH). The details of the purification by further crystallization as well as the determination of the assay have been reported in an earlier paper [3]. From the titration of purified MOPS with a standard solution of NaOH, the average mass fraction purity was 0.9995 ± 0.001. All mass measurements were made using MOPS, NaCl (ACS reagent grade dried at T = 383.15 K), a standard solution of NaOH to prepare NaMOPS, and finally calculated amounts of CO₂-free doubly distilled water. Apparent mass was converted to mass with buoyancy corrections which, on the average, for all buffer solutions were calculated to be 1.00106 based on the average density of 1.00139 g·cm⁻³. The mass undertainty is estimated to be 0.02 percent.

The preparation of the hydrogen electrodes and the silver-silver chloride electrodes of the thermal electrolytic type [12], the design of the all-glass cells, the purification of the hydrogen gas, preparation of the solutions, control of temperature, and use of digital voltmeter have been reported previously [3–4]. The following cell of the type (A), having no liquid junction, was used:

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

where m₁, m₂ and m₃ indicate molalities of the respective species, and 101.325 kPa is the pressure of hydrogen. A correction for the residual liquid-junction potential is needed in order to obtain accurate pH values. The flowing junction cell (B), was used for the evaluation of the liquid junction potential shown with a double vertical line:

$$\text{Pt}(\text{s})\mid {\text{H}}_2(\text{g}),p=101.325\text{kPa}\mid \text{MOPS}(m_1)+\text{NaMOPS}(m_2),\text{NaCl}(m_3)\mid \mid \text{KCl}(\text{satd})\mid {\text{Hg}}_2{\text{Cl}}_2(\text{s})\mid \text{Hg}(1)$$ (B)

For cell (C), the phosphate salts were NIST standard reference materials with the composition KH₂PO₄ (0.008695 mol·kg⁻¹) + Na₂HPO₄ (0.03043 mol·kg⁻¹) and its solutions are widely used for pH measurements in physiological solutions.

$$\text{Pt}(\text{s})\mid {\text{H}}_2(\text{g}),p=101.325\text{kPa}\mid \text{phosphate}\text{buffer}\mid \mid \text{KCl}(\text{satd})\mid {\text{Hg}}_2{\text{Cl}}_2(\text{s})\mid \text{Hg}(1)$$ (C)

The values of the residual liquid junction potential, δE_j = E_j(s) − E_j(x), for the physiological phosphate solutions and other experimental buffer solutions of MOPS from cell (B) were obtained [4,8] using the following equation:

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

and the similar equation is applicable for E_j(x) where pH(s) is replaced by pH(calc) and E_s by E_j(x). The value of the standard electrode potential of the saturated calomel electrode, where $E_{\mathit{SCE}}^{\circ }=-0.2415\text{V}$, k = 0.059156 V, and pH(s) = 7.415 (physiological phosphate buffer solution) at T = 298.15 K; $E_{\mathit{SCE}}^{\circ }=-0.2335$, k = 0.061538 V, and pH(s) = 7.395 at T = 310.15 K. We have attempted to calculate values of the δE_j for five buffer solutions out of sixteen buffer solutions. The operational definition of pH, indicated as pH(x),

$$\text{pH}(\text{x})=\text{pH}(\text{s})+(E_{\text{x}}-E_{\text{s}}+\delta E_{\text{j}})/k$$ (2)

where the subscript (x) refers to the pH of MOPS + NaMOPSate buffer solution; (s) is the reference solution (NIST physiological phosphate buffer) of known pH. The equation (2) takes the following form when δE_j = 0:

$$\text{pH}(\text{x})=\text{pH}(\text{s})+(E_{\text{x}}-E_{\text{s}})/k$$ (3)

3. Methods and Results

The cell potential data for cell (A) containing five buffer solutions without the presence of the chloride ion and eleven buffer solutions with the addition of NaCl to make I = 0.16 mol·kg⁻¹, have been corrected to a hydrogen pressure of 101.325 kPa. The values of the cell potential at T = 298.15 K are the average of two readings. The standard deviation, on the average, was 0.02 mV for the experimental temperature range. All these results are listed in tables 1 and 2, respectively.

TABLE 1.

Electromotive force E of Cell A (V): Pt(s); H₂(g, p = 101.325 kPa) | MOPS (m₁), NaMOPS (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
0.02	0.04	0.005	0.78930	0.79272	0.79604	0.79908	0.80184	0.80455	0.80701	0.80805	0.80940	0.81155	0.81341	0.81545
0.02	0.04	0.010	0.77215	0.77526	0.77820	0.78091	0.78345	0.78583	0.78805	0.78889	0.79006	0.79191	0.79360	0.79520
0.02	0.04	0.015	0.76200	0.76495	0.76769	0.77020	0.77262	0.77480	0.77689	0.77761	0.77870	0.78036	0.78192	0.78330
0.02	0.04	0.020	0.75451	0.75734	0.75988	0.76225	0.76459	0.76662	0.76865	0.76924	0.77025	0.77179	0.77335	0.77447
0.02	0.08	0.005	0.80530	0.80898	0.81257	0.81587	0.81880	0.82182	0.82458	0.82569	0.82713	0.82969	0.83189	0.83421
0.02	0.08	0.010	0.78935	0.79279	0.79602	0.79904	0.80176	0.80454	0.80701	0.80798	0.80932	0.81145	0.81342	0.81533
0.02	0.08	0.015	0.78013	0.78341	0.78645	0.78931	0.79196	0.79446	0.79692	0.79783	0.79909	0.80108	0.80296	0.80467
0.02	0.08	0.020	0.77387	0.77705	0.77997	0.78270	0.78526	0.78766	0.78994	0.79078	0.79199	0.79371	0.79555	0.79704
0.03	0.09	0.005	0.80076	0.80435	0.80771	0.81092	0.81379	0.81662	0.81937	0.82044	0.82182	0.82427	0.82645	0.82852
0.03	0.09	0.010	0.78439	0.78772	0.79080	0.79371	0.79628	0.79881	0.80119	0.80214	0.80338	0.80545	0.80734	0.80908
0.03	0.09	0.015	0.77473	0.77787	0.78080	0.78352	0.78596	0.78830	0.79044	0.79132	0.79249	0.79437	0.79611	0.79766
0.03	0.09	0.020	0.76812	0.77115	0.77397	0.77656	0.77890	0.78106	0.78304	0.78393	0.78499	0.78661	0.78823	0.78964
0.04	0.08	0.005	0.79131	0.79479	0.79820	0.80112	0.80404	0.80672	0.80923	0.81012	0.81143	0.81338	0.81540	0.81719
0.04	0.08	0.010	0.77465	0.77788	0.78088	0.78358	0.78604	0.78838	0.79087	0.79136	0.79252	0.79426	0.79594	0.79742
0.04	0.08	0.015	0.76484	0.76788	0.77062	0.77323	0.77535	0.77746	0.77992	0.78021	0.78126	0.78288	0.78440	0.78572
0.04	0.08	0.020	0.75780	0.76085	0.76345	0.76595	0.76780	0.76975	0.77220	0.77228	0.77330	0.77485	0.77623	0.77745
0.08	0.02	0.005	0.73957	0.74232	0.74450	0.74684	0.74880	0.75065	0.75226	0.75289	0.75369	0.75477	0.75583	0.75655
0.08	0.02	0.010	0.72287	0.72528	0.72718	0.72914	0.73087	0.73239	0.73369	0.73417	0.73478	0.73563	0.73636	0.73673
0.08	0.02	0.015	0.71280	0.71499	0.71674	0.71846	0.72006	0.72135	0.72247	0.72283	0.72334	0.72407	0.72460	0.72477
0.08	0.02	0.020	0.70572	0.70778	0.70941	0.71097	0.71246	0.71361	0.71459	0.71485	0.71530	0.71595	0.71634	0.71635
E° (V) of Ag-AgCl:			0.23416	0.23147	0.22863	0.22562	0.22244	0.21913	0.21572	0.21429	0.21214	0.20840	0.20455	0.20064

TABLE 2.

Electromotive force E of Cell A (V): Pt(s); H₂(g, p = 101.325 kPa) | MOPS (m₁), NaMOPS (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
0.02	0.02	0.14	0.69493	0.69692	0.69843	0.69979	0.70125	0.70225	0.70325	0.70350	0.70390	0.70427	0.70448	0.70455
0.02	0.04	0.12	0.71356	0.71568	0.71787	0.71938	0.72120	0.72273	0.72402	0.72442	0.72512	0.72599	0.72665	0.72730
0.04	0.02	0.14	0.67956	0.68097	0.68220	0.68324	0.68391	0.68450	0.68472	0.68513	0.68538	0.68552	0.68553	0.68541
0.04	0.08	0.08	0.72626	0.72845	0.73055	0.73230	0.73397	0.73521	0.73653	0.73696	0.73761	0.73858	0.73932	0.74005
0.04	0.04	0.12	0.70007	0.70169	0.70334	0.70474	0.70602	0.70700	0.70776	0.70807	0.70846	0.70899	0.70942	0.70960
0.05	0.05	0.11	0.70279	0.70439	0.70584	0.70728	0.70859	0.70945	0.71022	0.71052	0.71097	0.71162	0.71208	0.71241
0.06	0.06	0.10	0.70527	0.70716	0.70891	0.71011	0.71169	0.71240	0.71326	0.71358	0.71397	0.71452	0.71503	0.71525
0.08	0.08	0.08	0.71208	0.71354	0.71523	0.71660	0.71785	0.71883	0.71991	0.72018	0.72066	0.72139	0.72218	0.72278
0.06	0.03	0.13	0.68187	0.68325	0.68452	0.68549	0.68629	0.68692	0.68714	0.68760	0.69782	0.68799	0.68809	0.68801
0.08	0.02	0.14	0.64691	0.64764	0.64806	0.64855	0.64909	0.64957	0.64979	0.65008	0.65029	0.65045	0.65073	0.65132
0.09	0.03	0.13	0.67325	0.67449	0.67554	0.67645	0.67677	0.67715	0.67737	0.67747	0.67753	0.67738	0.67721	0.67684

3.1 The pH of MOPS Buffer

Conventional pa_H values have been evaluated by the method of Bates et al. [10,13–17] for five buffer solutions without NaCl and eleven buffer solutions in the presence of NaCl.

The values of the acidity function p(a_Hγ_Cl)° in the absence of Cl⁻, and p(a_Hγ_Cl) for all eleven buffer solutions in the presence of Cl⁻ were made in the temperature range T = (278.15 to 328.15) K. The expression for the acidity function p(a_Hγ_Cl) [10,12] is given by:

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

where m° = 1 mol·kg⁻¹, k = Nernst slope = RTln10/F, R = 8.3145 J·mol⁻¹ K⁻¹, T = temperature in kelvins, F = Faraday constant = 9.648534 J·V⁻¹·mol⁻¹, and ln(10) = 2.30259.

Straight lines of small slopes were obtained when the values of the acidity function p(a_Hγ_Cl) were plotted as a function of m_Cl−. The values of the intercepts, p(a_Hγ_Cl)°, listed in table 3, for five buffer solutions without the presence of NaCl were calculated using equation (5). The acidity function, p(a_Hγ_Cl) for eleven buffers with NaCl are entered in tables 4 and 5 from (278.15 to 328.15) K. The uncertainty introduced in this type of graphical extrapolation is less than 0.002. Conventional pa_H values were calculated by the following expression:

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

where the single-ion activity coefficient, ${\gamma }_{Cl}^{\circ }$, cannot be measured experimentally. A nonthermodynamic convention [4,5, 16,17] for the estimation of ${\gamma }_{Cl}^{\circ }$ has been adopted. The pH values obtained from the residual liquid junction cell are referred to as the “operational” pH, whereas the “conventional” pH calculated from equation (5) is designated as pa_H.

TABLE 3.

p(a_Hγ_Cl)° of (MOPS+ NaMOPS) buffer solutions from (278.15 to 328.15) K, computed using equation (5)

T/K	0.02 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS	0.02 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS	0.03 mol·kg−1 MOPS + 0.09 mol·kg−1 NaMOPS	0.04 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS	0.08 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS
	I = 0.04 mol·kg−1	I = 0.08 mol·kg−1	I = 0.09 mol·kg−1	I = 0.08 m mol·kg−1	I = 0.02 mol·kg−1
278.15	7.768	8.038	7.962	7.797	6.863
283.15	7.698	7.968	7.892	7.727	6.798
288.15	7.633	7.902	7.824	7.663	6.728
293.15	7.568	7.837	7.758	7.594	6.667
298.15	7.502	7.769	7.691	7.534	6.603
303.15	7.441	7.709	7.629	7.472	6.542
308.15	7.378	7.646	7.569	7.408	6.481
310.15	7.357	7.624	7.546	7.386	6.459
313.15	7.321	7.586	7.508	7.349	6.422
318.15	7.263	7.531	7.453	7.286	6.361
323.15	7.203	7.472	7.396	7.229	6.303
328.15	7.151	7.412	7.341	7.171	6.244

TABLE 4.

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

T/K	0.02 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS + 0.14 mol·kg−1 NaCl	0.02 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS + 0.12 mol·kg−1 NaCl	0.04 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS + 0.14 mol·kg−1 NaCl	0.04 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS + 0.08 mol·kg−1 NaCl	0.04 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS + 0.12 mol·kg−1 NaCl
	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1
278.18	7.495	7.766	7.217	7.820	7.521
283.15	7.431	7.698	7.147	7.749	7.449
288.15	7.363	7.636	7.079	7.682	7.382
293.15	7.298	7.568	7.014	7.614	7.316
298.15	7.240	7.510	6.947	7.550	7.254
303.15	7.178	7.452	6.883	7.483	7.190
308.15	7.120	7.393	6.817	7.421	7.127
310.15	7.096	7.369	6.797	7.396	7.103
313.15	7.061	7.335	6.763	7.360	7.067
318.15	7.001	7.279	6.704	7.302	7.009
323.15	6.943	7.222	6.648	7.243	6.953
328.15	6.886	7.168	6.592	7.188	6.896

TABLE 5.

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

T/K	0.05 mol·kg−1 MOPS + 0.05 mol·kg−1 NaMOPS + 0.11 mol·kg−1 NaCl	0.06 mol·kg−1 MOPS + 0.06 mol·kg−1 NaMOPS + 0.10 mol·kg−1 NaCl	0.08 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS + 0.08 mol·kg−1 NaCl	0.06 mol·kg−1 MOPS + 0.03 mol·kg−1 NaMOPS + 0.13 mol·kg−1 NaCl	0.08 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS + 0.14 mol·kg−1 NaCl	0.09 mol·kg−1 MOPS + 0.03 mol·kg−1 NaMOPS + 0.13 mol·kg−1 NaCl
	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I= 0.16 mol·kg−1	I = 0.16 mol·kg−1	I= 0.16 mol·kg−1
278.15	7.533	7.536	7.563	7.226	6.625	7.070
283.15	7.459	7.467	7.484	7.155	6.554	6.999
288.15	7.388	7.401	7.414	7.088	6.482	6.930
293.15	7.322	7.330	7.344	7.020	6.417	6.865
298.15	7.259	7.270	7.278	6.955	6.358	6.794
303.15	7.193	7.201	7.211	6.891	6.302	6.729
308.15	7.129	7.137	7.149	6.824	6.246	6.665
310.15	7.105	7.113	7.124	6.805	6.228	6.641
313.15	7.070	7.077	7.087	6.770	6.198	6.604
318.15	7.013	7.018	7.030	6.711	6.149	6.543
323.15	6.957	6.962	6.976	6.655	6.105	6.486
328.15	6.902	6.904	6.923	6.599	6.068	6.428

The ‘pH convention’, based on an extended Debye-Hückel equation, has been widely used [5,9]. For the establishment of NIST pH standard [8–9, 13–17], the calculation of ${log}_{10}{\gamma }_{Cl}^{\circ }$ for all of the buffer-chloride solutions were made by using the following equation:

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

where I is the ionic strength of the buffer solution, C is an adjustable parameter, A and B are the Debye-Hückel constants, a° is the ion size parameter, and Ba° = 1.38 kg^½·mol^−½ for all experimental temperatures. The following equation is used for the calculation of the parameter C [4,8]:

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

The values of pa_H are listed in table 6 for five buffer solutions of MOPS without NaCl and are expressed as a function of temperature.

TABLE 6.

pa_H of (MOPS + NaMOPS) buffer solutions from (278.15 to 328.15) K, computed using equations (4) – (7)

T/K	0.02 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS	0.02 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS	0.03 mol·kg−1 MOPS + 0.09 mol·kg−1 NaMOPS	0.04 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS	0.08 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS
	I = 0.04 mol·kg−1	I = 0.08 mol·kg−1	I = 0.09 mol·kg−1	I = 0.08 mol·kg−1	I = 0.02 mol·kg−1
278.15	7.690	7.938	7.858	7.697	6.804
283.15	7.621	7.868	7.788	7.627	6.739
288.15	7.556	7.802	7.719	7.563	6.669
293.15	7.491	7.737	7.654	7.494	6.608
298.15	7.424	7.667	7.586	7.433	6.543
303.15	7.362	7.607	7.523	7.371	6.482
308.15	7.298	7.544	7.463	7.306	6.420
310.15	7.277	7.521	7.439	7.283	6.398
313.15	7.240	7.483	7.401	7.245	6.361
318.15	7.182	7.427	7.345	7.182	6.299
323.15	7.121	7.367	7.287	7.124	6.241
328.15	7.068	7.314	7.231	7.066	6.181

$$\text{For}\text{MOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.04\text{mol}·{\text{kg}}^{-1}):{\text{p}a}_{\text{H}}=7.424-1.27·{10}^{-2}\{(T/T^{\circ }-298.15)\}+2.69·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2$$ (8)

$$\text{For}\text{MOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.08\text{mol}·{\text{kg}}^{-1}):{\text{p}a}_{\text{H}}=7.669-1.28·{10}^{-2}\{(T/T^{\circ }-298.15)\}+3.12·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2$$ (9)

$$\text{For}\text{MOPS}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.09\text{mol}·{\text{kg}}^{-1}):{\text{p}a}_{\text{H}}=7.587-1.29·{10}^{-2}\{(T/T^{\circ }-298.15)\}+3.33·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2$$ (10)

$$\text{For}\text{MOPS}(0.04\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.08\text{mol}·{\text{kg}}^{-1}):{\text{p}a}_{\text{H}}=7.432-1.28·{10}^{-2}\{(T/T^{\circ }-298.15)\}+1.85·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2$$ (11)

$$\text{For}\text{MOPS}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.02\text{mol}·{\text{kg}}^{-1}):{\text{p}a}_{\text{H}}=6.544-1.26·{10}^{-2}\{(T/T^{\circ }-298.15)\}+1.77·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2$$ (12)

where 278.15 K ≤ T ≤ 328.15 K. The standard deviations of regression for the pa_H of the five chloride-free buffer solutions are 0.0014, 0.0015, 0.0012, 0.0015, and 0.0017, respectively.

For eleven buffer solutions containing NaCl at an indicated ionic strength I = 0.16 mol·kg⁻¹, the values of pa_H listed in tables 7 and 8 are given by the equations:

$$\begin{array}{r}\text{For}\text{MOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.14\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.114-1.24·{10}^{-2}\{(T/T^{\circ }-298.15)\}+1.64·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (13)

$$\begin{array}{r}\text{For}\text{MOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.04\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.12\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.384-1.23·{10}^{-2}\{(T/T^{\circ }-298.15)\}+2.28·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (14)

$$\begin{array}{r}\text{For}\text{MOPS}(0.04\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.14\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=6.820-1.30·{10}^{-2}\{(T/T^{\circ }-298.15)\}+3.21·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (15)

$$\begin{array}{r}\text{For}\text{MOPS}(0.04\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.08\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.422-1.31·{10}^{-2}\{(T/T^{\circ }-298.15)\}+2.87·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (16)

$$\begin{array}{r}\text{For}\text{MOPS}(0.04\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.04\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.12\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.126-1.29·{10}^{-2}\{(T/T^{\circ }-298.15)\}+2.82·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (17)

$$\begin{array}{r}\text{For}\text{MOPS}(0.05\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.05\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.11\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.130-1.31·{10}^{-2}\{(T/T^{\circ }-298.15)\}+3.65·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (18)

$$\begin{array}{r}\text{For}\text{MOPS}(0.06\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.06\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.10\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.139-1.31·{10}^{-2}\{(T/T^{\circ }-298.15)\}+2.75·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (19)

$$\begin{array}{r}\text{For}\text{MOPS}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.08\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=7.276-1.33·{10}^{-2}\{(T/T^{\circ }-298.15)\}+4.93·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (20)

$$\begin{array}{r}\text{For}\text{MOPS}(0.06\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.13\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=6.828-1.30·{10}^{-2}\{(T/T^{\circ }-298.15)\}+3.38·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (21)

$$\begin{array}{r}\text{For}\text{MOPS}(0.08\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.02\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.14\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=6.234-1.20·{10}^{-2}\{(T/T^{\circ }-298.15)\}+6.98·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (22)

$$\begin{array}{r}\text{For}\text{MOPS}(0.09\text{mol}·{\text{kg}}^{-1})+\text{NaMOPS}(0.03\text{mol}·{\text{kg}}^{-1})+\text{NaCl}(0.13\text{mol}·{\text{kg}}^{-1}):\\ {\text{p}a}_{\text{H}}=6.795-1.32·{10}^{-2}\{(T/T^{\circ }-298.15)\}+3.16·{10}^{-5}{\{(T/T^{\circ }-298.15)\}}^2\end{array}$$ (23)

where T is the temperature in K. The standard deviations for regression of the “observed” results from equations (13) to (23) are 0.0016, 0.0015, 0.0020, 0.0013, 0.0012, 0.0015, 0.0020, 0.0013, 0.0018, 0.0015, and 0.0014, respectively.

TABLE 7.

pa_H of (MOPS + NaMOPS) buffer solutions from (278.15 to 328.15) K computed using equations (4) – (6)

T/K	0.02 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS + 0.14 mol·kg−1 NaCl	0.02 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS + 0.12 mol·kg−1 NaCl	0.04 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS + 0.14 mol·kg−1 NaCl	0.04 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS + 0.08 mol·kg−1 NaCl	0.04 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS + 0.12 mol·kg−1 NaCl
	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1
278.15	7.370	7.640	7.091	7.694	7.396
283.15	7.305	7.572	7.021	7.624	7.323
288.15	7.238	7.511	6.954	7.556	7.257
293.15	7.173	7.443	6.889	7.489	7.191
298.15	7.114	7.384	6.820	7.424	7.127
303.15	7.051	7.325	6.756	7.356	7.063
308.15	6.992	7.265	6.689	7.293	6.999
310.15	6.968	7.241	6.669	7.269	6.975
313.15	6.932	7.207	6.634	7.232	6.939
318.15	6.872	7.149	6.575	7.173	6.880
323.15	6.831	7.092	6.517	7.113	6.823
328.15	6.754	7.037	6.460	7.056	6.765

TABLE 8.

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

T/K	0.05 mol·kg−1 MOPS + 0.05 mol·kg−1 NaMOPS + 0.11 mol·kg−1 NaCl	0.06 mol·kg−1 MOPS + 0.06 mol·kg−1 NaMOPS + 0.10 mol·kg−1 NaCl	0.08 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS + 0.08 mol·kg−1 NaCl	0.06 mol·kg−1 MOPS + 0.03 mol·kg−1 NaMOPS + 0.13 mol·kg−1 NaCl	0.08 mol·kg−1 MOPS + 0.02 mol·kg−1 NaMOPS + 0.14 mol·kg−1 NaCl	0.09 mol·kg−1 MOPS + 0.03 mol·kg−1 NaMOPS + 0.13 mol·kg−1 NaCl
	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I = 0.16 mol·kg−1	I= 0.16 mol·kg−1	I = 0.16 mol·kg−1	I= 0.16 mol·kg−1
278.15	7.407	7.411	7.563	7.101	6.499	7.070
283.15	7.334	7.342	7.484	7.030	6.428	7.000
288.15	7.263	7.275	7.414	6.962	6.357	6.931
293.15	7.197	7.205	7.344	6.895	6.292	6.865
298.15	7.133	7.144	7.278	6.828	6.232	6.794
303.15	7.066	7.074	7.211	6.764	6.175	6.729
308.15	7.001	7.010	7.149	6.697	6.118	6.665
310.15	6.977	6.986	7.124	6.677	6.100	6.641
313.15	6.941	6.948	7.087	6.069	6.641	6.604
318.15	6.884	6.888	7.030	6.582	6.019	6.543
323.15	6.827	6.831	6.976	6.525	5.975	6.486
328.15	6.770	6.772	6.923	6.468	5.937	6.428

The potential difference of the cells (B) and (C) at T = (298.15 K and 310.15) K are given in table 9. By means of the flowing junction cell, the values of δE_j listed in table 10 were calculated by using equation (1). The value of the single-ion activity coefficient, ${log}_{10}{\gamma }_{Cl}^{\circ }$ cannot be measured experimentally. Covington and Ferra [19] used the Pitzer theory of specific ionic interactions 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. In separate publications from this laboratory, we will report pH values of different buffer solutions by using the Pitzer formalism for an ionic strength I = 0.16 mol·kg⁻¹ at T = (298.15 K and 310.15) K. From table 11, the calculated pH values and the values obtained from the δE_j corrections are in very good agreement (within ± 0.001). For example, a comparison of the values of pH between calculated and inclusion of the residual junction potential is 7.241 and 7.240, respectively, for m₁ = 0.02 mol·kg⁻¹ and m₂ = 0.04 mol·kg⁻¹, and m₃ = 0.012 mol·kg⁻¹ at 310.15 K. 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; and (iii) residual liquid junction potential measurement. Thus, the overall uncertainty is about ± 0.009 pH unit. The operational pH values at T = (298.15 K and 310.15) K (table 11) for five buffer solutions having the compositions (with and without the presence of NaCl) are recommended as secondary pH standards for the measurement of the pH of physiological fluids.

TABLE 9.

Emf of Cell B for MOPS buffer

m1 mol·kg−1	m2 mol·kg−1	m3 mol·kg−1	T = 298.15 K	T = 310.15 K
			E/V
0.03	0.09	0.00	0.69239	0.69350
0.02	0.04	0.12	0.67867	0.67965
0.04	0.08	0.08	0.68115	0.68154
0.06	0.06	0.10	0.66458	0.66407
0.08	0.08	0.08	0.67251	0.67256
Emf of Cell Ca
Cell C			E/V
0.008695 mol·kg−1 KH2PO4 + 0.0304 mol·kg−1 Na2HPO4			T = 298.15 K	T = 310.15 K
			0.68275	0.69147

^aPublished data [8,9] for physiological phosphate buffer solutions

TABLE 10.

Values of the liquid junction potentials for MOPS buffer at (298.15 and 310.15) K

System	δEja/mV
m/mol·kg−1	T = 298.15 K	T = 310.15 K
Physiological phosphate (0.008695 m KH2PO4 + 0.03043 m NaCl)	2.6	2.9
0.03 mol·kg−1 MOPS + 0.09 mol·kg−1 NaMOPS + 0.00 mol·kg−1 NaCl	0.5	0.7
0.02 mol·kg−1 MOPS + 0.04 mol·kg−1 NaMOPS + 0.12 mol·kg−1 NaCl	2.2	2.3
0.04 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS + 0.08 mol·kg−1 NaCl	2.1	2.2
0.06 mol·kg−1 MOPS + 0.06 mol·kg−1 NaMOPS + 0.10 mol·kg−1 NaCl	2.1	2.2
0.08 mol·kg−1 MOPS + 0.08 mol·kg−1 NaMOPS + 0.08 mol·kg−1 NaCl	2.1	2.2

^aObtained from equation (1) using Emf from table 9, k = Nernst slope with values 0.059156 at T = 298.15 K, and 0.061538 at T = 310.15 K; the pH of the primary reference phosphate buffer is 7.415 and 7.395 at (298.15 and 310.15) K, respectively; $E_{\mathit{SCE}}^{\circ }$ = electrode potential of the saturated calomel electrode = −0.2415 and −0.2335 at (298.15 and 310.15) K, respectively.

TABLE 11.

Values of pH at (298.15 and 310.15) K for MOPS buffer solutions

Cell B m/mol·kg−1			Ionic Strength, I	T = 298.15 K			T = 310.15 K
m1	m2	m3		Withouta δEj corr	Withb δEj corr	Calcc	Withouta δEj corr	Withb δEj corr	Calcc
0.03	0.09	0.00	0.09	7.578	7.586	7.586	7.428	7.439	7.439
0.02	0.04	0.12	0.16	7.346	7.383	7.384	7.203	7.240	7.241
0.04	0.08	0.08	0.16	7.388	7.423	7.424	7.235	7.269	7.269
0.06	0.06	0.10	0.16	7.109	7.143	7.144	6.950	6.985	6.986
0.08	0.08	0.08	0.16	7.242	7.277	7.278	7.088	7.123	7.124

^aValues obtained from equation (3) and data of table 9

^bObtained from equation (2) and δE_j data of table 10

^cObtained from tables 6, 7, and 8

Highlights.

1. This work reports pH values of MOPS buffer

2. Liquid junction potential correct is applied

3. These values will be used by clinical and biomedical scientists

4. The pH values lie within 6.8 to 7.5