Open Journal of Physical Chemistry, 2011, 1, 77-84
doi:10.4236/ojpc.2011.13011 Published Online November 2011 (http://www.SciRP.org/journal/ojpc)
77
Calculation of the pH of Buffer Solution of
2-[N-Morpholino]ethanesulfonic Acid (MES)
from 5˚C to 55˚C
Lakshmi N. Roy, Rabindra N. Roy*, Joshua T. Wollen, Jessica M. Stegner, Meagan A. Harmon,
Michael S. Martin, Blake M. Bodendorfer, Isaac B. Henson
Hoffman Department of Chemistry, Drury University, Springfield, USA
Received June 22, 2011; revised August 7, 2011; accepted September 15, 2011
Abstract
This paper reports the results for the pH of three buffer solutions free of chloride ion. The remaining six
buffer solutions have saline media of the ionic strength I = 0.16 mol·kg–1, matching closely to that of the
physiological sample. Conventional paH values for the three buffer solutions without the chloride ion and six
buffer solutions with the chloride ion at I = 0.16 mol·kg–1 from 5˚C to 55˚C have been calculated. The opera-
tional pH values for five buffer solutions at 5˚C and 55˚C have been determined based on the difference in
the values of the liquid junction potentials between the blood phosphate standard and the experimental buffer
solutions. Five of these buffers are recommended as standards for the physiological pH range 7.5 to 8.5.
Keywords: Buffers, MES, BICINE, Liquid Junction, Ionic Strength, Emf, pH
1. Introduction
The buffer substances recommended by Good et al. [1-3]
have proven very useful for the measurement of the pH
of blood and the control of pH in a region close to that of
physiological solution. In biomedical, biological, and
clinical laboratories, knowledge of the pH of blood and
physiological fluids is of great importance. Previously,
we have reported the pK2 values of 2-[N-morpholino]
ethanesulfonic acid (MES) [1] at temperatures from 5˚C
to 55˚C, including 37˚C. This zwitterionic buffer system
has been recommended by Good and coworkers [2,3] for
use as a physiological buffer. The structure of MES is as
follows:
Standardization for calibrating electrodes of the pH
meter assembly at a point close to the pH of blood (that
is, 7.407) can be obtained within the framework of the
former National Bureau of Standards (NBS) by using a
ON
S
O
O
OH
Figure 1. 2-[N-morpholino]ethanesulfonic acid (MES).
physiological phosphate pH buffer as a primary standard
[4]. The phosphate buffer has been widely used as a phy-
siological pH standard, but it is not an ideal primary pH
standard buffer for physiological use at an ionic strength
of I = 0.16 mol·kg–1. The disadvantages are as follows: 1)
phosphates act as inhibitors to enzymatic processes; 2)
phosphate precipitates occur with some polyvalent
cations, such as Mg2+ and Ca2+, present in the blood; and
3) the temperature coefficient of the phosphate buffer is
–0.0028 pH unit/K as compared to that of whole blood
(–0.015 pH unit/K) and plasma (0.01 pH unit/K) [5].
Good and his associates [2,3] provided 25 primarily
new biological buffers which are mostly compatible with
common physiological media. They outlined suitable
criteria for the evaluation of these materials. Roy et al. [6]
have published the pK2 and pH values of the biological
buffer [bis(2-hydroxyethyl)amino]acetic acid (BICINE),
and the values of pH for the zwitterionic buffer N-[tris
(hydroxymethyl)methyl-3-amino]propanesulfonic acid (T-
APS) [7]. Both of these buffers have been recommended
as pH standards in the range of physiological application.
Feng and coworkers [8] have published the values of pK2
and pH of the zwitterionic buffer N-(2-hydroxyethyl)
piperazine-N-2-ethanesulfonic acid (HEPES). The HEP-
ES buffer has been certified by the National Institute of

L. N. ROY ET AL.
78
Standards and Technology (NIST) as a primary reference
standard [8]. The values of pK2 and pH for 3-(N-mor-
pholino)propanesulfonic acid (MOPS) [9] and 3-(N-
morpholino)-2-hydroxypropanesulfonic acid (MOPSO)
[10] have been reported. The pH of these solutions
closely matches that of the common clinical media. In
1973, Bates et al. [11] recommended pH standard for a
buffer solution of 0.06 m TRICINE + 0.02 m Na-
TRICINEate. Goldberg et al. [12] reported the results of
the thermodynamic quantities of about 68 physiological
buffers. The comprehensive review article indicated that
no results of pH are available in the literature for MES.
We now propose to investigate MES in order to pro-
vide very accurate and reproducible pH values in the
range of physiological application.
2. Materials and Methodology
MES was obtained from Research Organics (Cleveland,
OH). The details of the purification by further crystalli-
zation as well as the determination of the assay have
been reported in an earlier paper [1]. In the present
study, the analyses of the unpurified and purified MES
were 99.71% and 99.88% pure, respectively. All mass
measurements were made with a mass factor uncertainty
of 0.02% including the substance MES, NaCl (ACS re-
agent grade dried at 110˚C), a standard solution of NaOH
to prepare NaMES, and finally calculated amounts of
CO2-free doubly distilled water. Air buoyancy correc-
tions were applied for all masses used.
The following buffer compositions on the molality
scale are given:
(a) MES (0.04 mol·kg–1) + NaMES (0.04 mol·kg–1),
I = 0.04 mol·kg–1
(b) MES (0.04 mol·kg–1) + NaMES (0.08 mol·kg–1),
I = 0.08 mol·kg–1
(c) MES (0.08 mol·kg–1) + NaMES (0.08 mol·kg–1),
I = 0.08 mol·kg–1
(d) MES (0.04 mol·kg–1) + NaMES (0.04 mol·kg–1)
+ NaCl (0.12 mol·kg–1), I = 0.16 mol·kg–1
(e) MES (0.05 mol·kg–1) + NaMES (0.05 mol·kg–1)
+ NaCl (0.11 mol·kg–1), I = 0.16 mol·kg–1
(f) MES (0.06 mol·kg–1) + NaMES (0.06 mol·kg–1)
+ NaCl (0.10 mol·kg–1), I = 0.16 mol·kg–1
(g) MES (0.08 mol·kg–1) + NaMES (0.08 mol·kg–1)
+ NaCl (0.08 mol·kg–1), I = 0.16 mol·kg–1
(h) MES (0.04 mol·kg–1) + NaMES (0.08 mol·kg–1)
+ NaCl (0.08 mol·kg–1), I = 0.16 mol·kg–1
(i) MES (0.03 mol·kg–1) + NaMES (0.06 mol·kg–1)
+ NaCl (0.10 mol·kg–1), I = 0.16 mol·kg–1
The preparation of the hydrogen electrodes and the sil-
ver-silver chloride electrodes of the thermal electrolytic
type [13], the design of the all-glass cells, the purifica-
tion of the hydrogen gas, preparation of the solutions,
control of temperature, and use of digital voltmeter have
been reported previously [1,9]. A correction for the re-
sidual liquid-junction potential is required if accurate pH
values are to be achieved. Thus the cells studied were the
following:
Pt(s), H2(g, 1 atm)│MES (m1) + NaMES (m2)
+ NaCl (m3)│AgCl(s), Ag(s) (A)
where m1, m2 and m3 indicate molalities of the respective
species, and the pressure of hydrogen in SI units is 1 atm
= 101.325 kPa. The flowing junction cell (B), was used
for the evaluation of the liquid junction potential at the
contact between the buffer solution and the heavier satu-
rated KCl solution of the calomel electrode shown with a
double vertical line.
Pt(s), H2(g, 1 atm)│MES(m1) + NaMES(m2)
+ NaCl(m3)││KCl(satd)│Hg2Cl2(s), Hg(l) (B)
where the abbreviations (s), (l) and (g) denote solid, liq-
uid, and gaseous state, respectively.
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 recommended for pH measurements in
physiological solutions.
Pt(s), H2 (g, 1 atm)│phosphate buffer││
KCl(satd)│Hg2Cl2(s), Hg(l) (C)
The values of the liquid junction potential, Ej, for the
physiological phosphate solutions and other experimental
buffer solutions of MES from cell (B) were obtained [8,
9] using the following equation [9]:
–
p
H
jSCE
EEE k

(1)
where E is the emf value in volt dependent on the buffer
compositions, SCE = –0.2415 V, k = 0.059156 V, and
pH = 7.415 (physiological phosphate buffer solution) at
25˚C; = –0.2335, k = 0.061538 V, and pH =
7.395 at 37˚C. We have attempted to calculate values of
the liquid junction potential for five buffer solutions out
of nine buffer solutions. The difference in Ej between the
phosphate standard and each experimental buffer solu-
tion is an important factor when different standards are
selected to obtain the values of the operational pH for an
unknown medium. This error can be estimated by the
operational definition of pH, indicated as pH(x):
E


SCE
E
 
x
s
EE E
pH xpH sk
 
 j
(2)
where Ex is the emf value of the unknown buffer MES +
NaMESate; Es is the emf of the reference solution (NIST
physiological phosphate buffer) of known pH and δEj =

L. N. ROY ET AL.
79
the cell potential (E) listed in Tables 1 and 2, the mo-
lality of the chloride ion, and E˚, the standard potential of
the silver-silver chloride electrode are listed at the bot-
tom of Table 1. The expression for the acidity function
[11,13] is given by:
Ej(s) – Ej(x). If δEj = 0, then Equation (2) takes the form:
pH (x) = pH(s) +
x
s
EE
k
 (3)
3. Results
10
() log
HCl
EE
pa k




mCl (4)
The cell potential data for cell (A) containing three
buffer solutions without the presence of the chloride ion,
and six buffer solutions in which NaCl has been added to
make I = 0.16 mol·kg–1, have been corrected to a hydro-
gen pressure of 101.325 kPa. The values of the cell po-
tential at 25˚C are the average of two or three readings
(at the beginning, in the middle, and sometimes at the
end of the temperature run). Duplicate cells usually gave
readings on the average within (0.02 ± 0.01) mV in the
temperature range 5˚C to 55˚C. All these results are
listed in Tables 1 and 2, respectively.
where k is the Nernst slope.
Values of the acidity function p(aHγCl) were derived at
each temperature for each buffer solution and were plot-
ted as a function of mCl-, straight lines of small slopes
were obtained. The values of the intercepts, p(aHγCl)˚, for
three buffer solutions without the presence of NaCl listed
above from (a) to (c), were calculated using Equation (5)
and are given in Table 3. The acidity function, p(aHγCl)
for six buffers (d)-(i) listed above are entered in Table 4
from 5˚C to 55˚C. The uncertainty (mean deviation) in-
troduced in this type of graphical extrapolation is usually
less than 0.002 from the lines drawn. Conventional paH
values for the three solutions without the presence of the
chloride ion were calculated by the following expression:
Conventional paH values have been evaluated by the
method of Bates et al. [11,14-16] for three buffer solu-
tions without NaCl and six buffer solutions in the pres-
ence of NaCl. The complete buffer compositions (a)-(i)
are listed in the introduction section. paH = p(aHγCl)˚ + 10
log Cl


(5)
In order to calculate paH values for three buffer solu-
tions without NaCl, calculations of the values of the
acidity function p(aHγCl)˚ in the absence of Cl–, and
p(aHγCl) for the six buffer solutions in the presence of Cl–
were made in the temperature range 5˚C to 55˚C, from
where the single-ion activity coefficient, Cl


, cannot be
measured experimentally. A non-thermodynamic conven-
tion [4,9] for the estimation of Cl


has been adopted for
the calculation of paH by Equation (5). The pH values ob-
Table 1. Electromotive force of cell A: Pt(s); H2(g, 1 atm)|MES(m1), NaMES(m2), NaCl(m3)|AgCl(s), Ag(s).
m1a m2a m3a 5˚C 10˚C 15˚C 20˚C25˚C30˚C 35˚C37˚C40˚C45˚C 50˚C 55˚C
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.08
0.08
0.08
0.08
0.04
0.04
0.04
0.04
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.005
0.010
0.015
0.020
0.005
0.010
0.015
0.020
0.005
0.010
0.015
0.020
0.71532
0.69926
0.68993
0.68340
0.73248
0.71658
0.70747
0.70106
0.72001
0.70308
0.69295
0.68552
0.71843
0.70209
0.69260
0.68593
0.73596
0.71974
0.71041
0.70385
0.72301
0.70584
0.69555
0.68808
0.72137
0.70443
0.69456
0.68754
0.73927
0.72271
0.71308
0.70647
0.72585
0.70833
0.69791
0.69026
0.72413
0.70698
0.69696
0.68981
0.74225
0.72543
0.71558
0.70891
0.72866
0.71090
0.70023
0.69252
0.72667
0.70929
0.69911
0.69200
0.74521
0.72804
0.71796
0.71110
0.73149
0.71343
0.70262
0.69474
0.72931
0.71186
0.70177
0.69468
0.74798
0.73065
0.72069
0.71376
0.73401
0.71562
0.70471
0.69671
0.73170
0.71395
0.70366
0.69647
0.75081
0.73313
0.72290
0.71602
0.73632
0.71770
0.70658
0.69849
0.73266
0.71477
0.70442
0.69717
0.75171
0.73396
0.72365
0.71663
0.73728
0.71856
0.70740
0.69929
0.73392
0.71592
0.70549
0.69820
0.75333
0.73535
0.72498
0.71779
0.73860
0.71968
0.70840
0.70017
0.73589
0.71764
0.70708
0.69973
0.75569
0.73746
0.72682
0.71965
0.74062
0.72140
0.70998
0.70168
0.73790
0.71925
0.70848
0.70091
0.75806
0.73952
0.72873
0.72135
0.74282
0.72327
0.71165
0.70317
0.73968
0.72075
0.70981
0.70208
0.76029
0.74140
0.73034
0.72289
0.74472
0.72487
0.71303
0.70443
Values of E˚ 0.23416 0.23147 0.22863 0.22562 0.222440.219130.215720.214290.212140.20840 0.20455 0.20064
aUnits of m, mol·kg–1.
Table 2. Emf of the cell A (in volts): Pt(s); H2(g, 1 atm)|MES(m1), NaMES(m2), NaCl(m3)|AgCl(s), Ag(s).
m1a m2a m3a 5˚C 10˚C 15˚C 20˚C25˚C 30˚C35˚C37˚C 40˚C 45˚C 50˚C 55˚C
0.04
0.05
0.06
0.08
0.04
0.03
0.04
0.05
0.06
0.08
0.08
0.06
0.12
0.11
0.10
0.08
0.08
0.10
0.64471
0.64639
0.64805
0.65259
0.66820
0.65992
0.64654
0.64820
0.64991
0.65443
0.67035
0.66183
0.64819
0.64991
0.65160
0.65626
0.67243
0.66371
0.64973
0.65142
0.65317
0.65779
0.67429
0.66541
0.65107
0.65285
0.65465
0.65941
0.67588
0.66717
0.65228
0.65412
0.65571
0.66068
0.67768
0.66864
0.65337
0.65526
0.65680
0.66189
0.67918
0.67005
0.65358
0.65546
0.65717
0.66229
0.67974
0.67064
0.65401
0.65592
0.65768
0.66283
0.68048
0.67127
0.65462
0.65659
0.65847
0.66375
0.68175
0.67242
0.65509
0.65707
0.65911
0.66443
0.68290
0.67335
0.65578
0.65780
0.65973
0.66515
0.68386
0.67418
aUnits of m, mol·kg–1.

L. N. ROY ET AL.
80
Table 3. p(aHγCl)˚ of (MES + NaMES) buffer solutions from 5˚C to 55˚C, computed using Equation (5)a.
t (˚C)
0.04 m MES
+ 0.04 m NaMES
I = 0.08 m
0.04 m MES
+ 0.08 m NaMES
I = 0.08 m
0.08 m MES
+ 0.08 m NaMES
I = 0.08 m
5
10
15
20
25
30
35
37
40
45
50
55
6.411
6.360
6.315
6.267
6.218
6.173
6.131
6.115
6.089
6.047
6.010
5.971
6.718
6.669
6.622
6.573
6.529
6.481
6.440
6.422
6.400
6.359
6.323
6.286
6.511
6.456
6.403
6.355
6.311
6.265
6.220
6.203
6.178
6.136
6.100
6.062
aUnits of m, mol·kg–1.
Table 4. p(aHγCl) of (MES + NaMES) buffer solutions from 5˚C to 55˚C, computed using Equation (4)a.
t (˚C)
0.04 m MES
+ 0.04 m NaMES
+ 0.12 m NaCl
I = 0.16 m
0.05 m MES
+ 0.05 m NaMES
0.11 m NaCl
I = 0.16 m
0.06 m MES
+ 0.06 m NaMES
+ 0.10 m NaCl
I = 0.16 m
0.08 m MES
+ 0.08 m NaMES
+ 0.08 m NaCl
I = 0.16 m
0.04 m MES
+ 0.08 m NaMES
+ 0.08 m NaCl
I = 0.16 m
0.03 m MES
+ 0.06 m NaMES
+ 0.10 m NaCl
I = 0.16 m
5
10
15
20
25
30
35
37
40
45
50
55
6.518
6.467
6.418
6.371
6.325
6.280
6.237
6.218
6.191
6.148
6.106
6.070
6.511
6.459
6.410
6.362
6.317
6.273
6.230
6.210
6.184
6.141
6.099
6.063
6.499
6.448
6.398
6.351
6.306
6.258
6.214
6.197
6.171
6.130
6.089
6.051
6.485
6.432
6.383
6.333
6.290
6.244
6.200
6.183
6.157
6.116
6.076
6.037
6.768
6.715
6.666
6.617
6.568
6.527
6.483
6.467
6.441
6.402
6.364
6.325
6.715
6.660
6.610
6.561
6.518
6.473
6.431
6.416
6.389
6.351
6.312
6.273
aUnits of m, mol·kg–1.
Table 5. paH of (MES + NaMES) buffer solutions from 5˚C to 55˚C, computed using Equations (4)-(6)a.
t (˚C)
0.04 m MES
+ 0.04 m NaMES
I = 0.08 m
0.04 m MES
+ 0.08 m NaMES
I = 0.08 m
0.08 m MES
+ 0.08 m NaMES
I = 0.08 m
5
10
15
20
25
30
35
37
40
45
50
55
6.333
6.283
6.236
6.189
6.139
6.094
6.051
6.035
6.008
5.965
5.928
5.888
6.619
6.570
6.522
6.473
6.427
6.379
6.337
6.319
6.297
6.255
6.218
6.180
6.411
6.356
6.303
6.255
6.210
6.164
6.118
6.101
6.075
6.032
5.995
5.956
aUnits of m, mol·kg–1.
tained from the liquid junction cell are referred by the
“operational” pH, whereas the “conventional” pH calcu-
lated from Equation (5) is designated as paH.
The convention is reasonable but is not subject to any
proof. The Equation (6) of a “pH convention” [4], based
on an extended Debye-Hückel equation, has been widely
used. In the assignment of paH values and in the estab-
lishment of NIST pH standard [8,10,14-18], the calcula-
tion of 10 log Cl


for all of the buffer-chloride solutions
were made by using the following equation:
10
log 1
Cl
AI CI
Ba I
  



(6)
where I is the ionic strength of the buffer solution, A and

L. N. ROY ET AL. 81
2
B are the Debye-Hückel constants [6-7,13], hydrolysis of
the buffer species is negligible, C is an adjustable pa-
rameter, Ba˚ was taken to be 1.38 kg½·mol-½ at all tem-
peratures [9]. In the Bates-Guggenheim convention [4],
the value of Ba° was assigned to be 1.5 kg½·mol-½ and C
= 0 for ionic strength I ≤ 0.1 mol·kg–1. The following
equation is used for the calculation of the parameter C
[8,9]:
46
6.210(25)8.710(25)
25
CC TT

  (7)
where C25 = 0.032 mol·kg–1 at 25˚C and T is the absolute
temperature [8].
The values of paH are listed in Table 5 for three buffer
solutions of MES without NaCl. These are calculated
using Equations (4)-(7) and are expressed as a function
of temperature.
For MES (0.04 mol·kg–1) + NaMES (0.04 mol·kg–1)
paH = 6.140 – 9.1710–3(T – 25) + 2.5510–5(T – 25)2  
(8)
For MES (0.04 mol·kg–1) + NaMES (0.08 mol·kg–1)
paH = 6.426 – 9.1110–3(T – 25) + 3.0410–5(T – 25)2
 
(9)
For MES (0.08 mol·kg–1) + NaMES (0.08 mol·kg–1)
paH = 6.208 – 9.3910–3(T – 25) + 3.2910–5(T – 25)2
 
(10)
where 25˚C ≤ T ≤ 55˚C. The standard deviations of re-
gression for the paH of the three chloride-free buffer so-
lutions are 0.0014, 0.0013 and 0.0017, respectively.
For the six buffer solutions containing NaCl at an in-
dicated ionic strength, I = 0.16 mol·kg–1, the values of
paH listed in Table 6 are expressed by the equations:
For MES (0.04 mol·kg–1) + NaMES (0.04 mol·kg–1) +
NaCl (0.12 mol·kg–1)
paH = 6.198 – 9.3010–3(T – 25) + 1.8910–5(T – 25)2
 
(11)
For MES (0.05 mol·kg–1) + NaMES (0.05 mol·kg–1) +
NaCl (0.11 mol·kg–1)
paH = 6.191 – 9.28

10–3(T – 25) + 1.9310–5(T – 25)2
(12)
For MES (0.06 mol·kg–1) + NaMES (0.06 mol·kg–1) +
NaCl (0.10 mol·kg–1)
paH = 6.178 – 9.33

10–3(T – 25) + 2.3910–5(T – 25)2
(13)
For MES (0.08 mol·kg–1) + NaMES (0.08 mol·kg–1) +
NaCl (0.08 mol·kg–1)
paH = 6.162 – 9.28

10–3(T – 25) + 2.4610–5(T – 25)2
(14)
For MES (0.04 mol·kg–1) + NaMES (0.08 mol·kg–1) +
NaCl (0.08 mol·kg–1)
paH = 6.444 – 9.24

10–3(T – 25) + 3.0610–5(T – 25)2
(15)
For MES (0.03 mol·kg–1) + NaMES (0.06 mol·kg–1) +
NaCl (0.10 mol·kg–1)
paH = 6.391 – 9.17

10–3(T – 25) + 3.0410–5(T – 25)2
(16)
where T is the temperature in ˚C. The standard deviations
for regression of the “observed” results from Equations
(11) to (16) are 0.0014, 0.0015, 0.0009, 0.0009, 0.0012
and 0.0015, respectively.
4. Discussion
The MES is a zwitterionic buffer material. It is like a
neutral molecule and hence makes no contribution to the
ionic strength. The values of K2 of MES lie between 10–6
and 10–8 and hence are useful in the preparation of buffer
solutions for pH control in the physiological interest.
Similar recommendations were made for two other
buffer systems, HEPES [19] and HEPPS [20], which are
useful for pH measurements in the clinical laboratory.
The cell potential data of the cells (B) and (C) at 25˚C
and 37˚C are given in Table 7. By means of the flowing
Table 6. paH of (MES + NaMES) buffer solutions from 5˚C to 55˚C, computed using Equations (4)-(6)a.
t (˚C) 0.04 m MES
+ 0.04 m NaMES
+ 0.12 m NaCl
I = 0.16 m
0.05 m MES
+ 0.05 m NaMES
+ 0.11 m NaCl
I = 0.16 m
0.06 m MES
+ 0.06 m NaMES
+ 0.10 m NaCl
I = 0.16 m
0.08 m MES
+ 0.08 m NaMES
+ 0.08 m NaCl
I = 0.16 m
0.04 m MES
+ 0.08 m NaMES
+ 0.08 m NaCl
I = 0.16 m
0.03 m MES
+ 0.06 m NaMES
+ 0.10 m NaCl
I = 0.16 m
5
10
15
20
25
30
35
37
40
45
50
55
6.393
6.342
6.292
6.246
6.198
6.153
6.109
6.090
6.062
6.019
5.976
5.938
6.385
6.333
6.284
6.237
6.191
6.146
6.103
6.083
6.055
6.012
5.969
5.931
6.374
6.323
6.272
6.226
6.180
6.131
6.086
6.069
6.042
6.000
5.959
5.920
6.359
6.306
6.257
6.208
6.163
6.117
6.073
6.055
6.028
5.987
5.945
5.906
6.642
6.590
6.540
6.492
6.442
6.400
6.356
6.339
6.312
6.272
6.233
6.193
6.589
6.535
6.484
6.436
6.391
6.346
6.303
6.286
6.261
6.221
6.181
6.142
aUnits of m, mol·kg-1.

L. N. ROY ET AL.
82
Table 7. Emf of cell B for MES buffer.
m1 m2 m3 E/V
25˚C 37˚C
0.04 0.08 0.00 0.62387 0.62472
0.03 0.06 0.10 0.62004 0.62088
0.04 0.04 0.12 0.60851 0.60883
0.04 0.08 0.08 0.62306 0.62415
0.08 0.08 0.08 0.60655 0.60679
Emf of Cell Ca
Cell C E/V
25˚C 37˚C
0.008695 m KH2PO4 + 0.03043 m Na2HPO4 0.68275 0.69147
aPublished data [7,19] for physiological phosphate buffer solutions; units of m, mol·kg-1.
junction cell, the values of Ej listed in Ta ble 8 were esti-
mated by using Equation (1). As evident from the pH
data at 25˚C and 37˚C from Table 9, there is a wide va-
riation in pH (as high as ±0.04 pH units). There is no
known experimental method for accurately determining
the single-ion activity coefficient, 10
log Cl


. Partanen
and Minkkinen [19], as well as Covington and Ferra [20],
used the Pitzer theory approach for the estimation of 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 publica-
tions from this laboratory, the paH values of eight differ-
ent buffer solutions will be reported by using Pitzer for-
malism for an ionic strength I = 0.16 mol·kg–1 at 25˚C
and 37˚C. The calculation of 10
log Cl

leads to uncertain-
ty (±0.001 pH unit) in the paH values. A second source is
the error in the liquid junction potential measurement.
However, the calculated pH values and the values ob-
tained from the Ej corrections are in very good agreement
(within ±0.003). The total uncertainties were estimated
by combining the various sources of error: 1) assumption
for the calculation of the 10
log Cl


(±0.004 pH unit); 2)
extrapolation to p(aHγCl)˚ at mCl- = 0 (within ±0.001 pH
unit); 3) liquid junction potential measurement using
Table 8. Values of the liquid junction potentials for MES buffer at 25˚C and 37˚C.
System Eja/mV
25˚C 37˚C
Physiological phosphate (0.008695 m KH2PO4 + 0.03043 m NaCl) 2.6 2.9
0.04 m MES + 0.08 m NaMES + 0.00 m NaCl 2.2 2.4
0.03 m MES + 0.06 m NaMES + 0.10 m NaCl 0.5 0.6
0.04 m MES + 0.04 m NaMES + 0.12 m NaCl 0.4 0.6
0.04 m MES + 0.08 m NaMES + 0.08 m NaCl 0.5 0.6
0.08 m MES + 0.08 m NaMES + 0.08 m NaCl 0.5 0.7
aEj = E +SCE – k˚ pH from Equation (1) is the Emf from Table 7, k = Nernst slope with values 0.059156 at 25˚C, and 0.061538 at
37˚C; the pH of the primary reference standard phosphate buffer is 7.415 and 7.395 at 25˚C and 37˚C; SCE = electrode potential
of the saturated calomel electrode = –0.2415 and –0.2335 at 25˚C and 37˚C [14,15], respectively; units of m, mol·kg-1.
E
E
Table 9. Values of pH at 25˚C and 37˚C for MES buffer solutions.
Cell B 25˚C 37˚C
m1 m2 m3
Ionic
Strength, I Withouta With
b
Ej corr Ej corr Calcc
Withouta Withb
Ej corr Ej corr Calc
c
0.04 0.08 0.00 0.08 6.420 6.426 6.427 6.310 6.318 6.319
0.03 0.06 0.10 0.16 6.355 6.390 6.391 6.248 6.285 6.286
0.04 0.04 0.12 0.16 6.160 6.197 6.198 6.052 6.089 6.090
0.04 0.08 0.08 0.16 6.406 6.441 6.442 6.301 6.338 6.339
0.08 0.08 0.08 0.16 6.127 6.162 6.163 6.019 5.054 6.055
aValues obtained from Equation (3) and data of Table 7; bObtained from Equation (2) and Ej data in Table 8; cObtained from Tables 5 and 6.

83 L. N. ROY ET AL.
the flowing junction cell; 4) error in the experimental
emf measurement (±0.02 mV); and 5) standard potential
of the Ag-AgCl electrode (±0.03 mV). The overall un-
certainty is about ±0.009 pH unit.
5. Conclusions
All emf data are stable, reliable, and accurate. The MES
buffer solutions are considered as standards of assigned
paH and will be useful when buffer solutions of known
conventional paH are required. From Table 9, uncertainty
in pH values obtained with and without liquid junction is
±0.001 pH. Thus the operational pH values at 25˚C and
37˚C (Table 9) for one buffer solution with NaCl and
four buffer solutions matching the ionic strength of blood
serum are recommended as secondary pH standards for
the measurement of the pH of blood and other physio-
logical fluids.
6. Acknowledgements
The authors are grateful for the funding from the Na-
tional Institutes of Health (AREA), under the grant
2 R15 GM 066866-03 and the diversity supplemental
grant 3 R15 GM 066866-03 S1. The authors would also
like to thank David Jones and Morghan Olson for their
dedication and hard work. The content of this paper is
the sole responsibility of the authors and does not neces-
sarily represent the official views of the National Insti-
tutes of Health or the National Institutes of General
Medical Sciences.
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