The measurement of pH in saline and hypersaline media at sub-zero temperatures:
Characterization of Tris buffers by Stathys Papadimitriou, Socratis Loucaides, Victoire Rérolle,
Eric P. Achterberg, Andrew G. Dickson, Matthew Mowlem, Hilary Kennedy
Supplementary Information
This section includes the e.m.f. measurements in solutions of HCl in synthetic seawater (S = 35)
and in synthetic seawater-derived brines (S = 45 – 100) in cells (B) and (C), respectively. These
measurements, along with salinity, temperature, and pertinent solution composition information, are
*
given in Table S1 below; they were used to determine the apparent standard potential ( Eo ) of cells
(B) and (C) in the presence of sulphate in the synthetic solutions of this study as described in the
section The apparent standard potential of the Harned cell with synthetic seawater (S = 35) and
synthetic brine (S > 35) of the main article. This is followed by information about the standard error
from the Regression output of individual fitted coefficients of equations (1) to (3) (Table S2),
described in the section The standard potential of the Harned cell to the freezing point of synthetic
seawater and brines, and equations (4) to (8) (Table S3), described in the section The pH of Tris
buffers to the freezing point of synthetic seawater and brines.
This section also includes plots of the residuals in E*o as a function of temperature between the
experimental values and fitted values (a) from equation (1) for seawater (S = 35) and temperatures
from 55 to –1.7 °C, and (b) from equation (2) for seawater and brines at their freezing point (Fig.
S1). Finally, the residuals in pHTris as a function of temperature are shown in Figure S2 between the
experimental values and fitted values (a) from equation (4) for the equimolal Tris buffer (molality
ratio, RTris = mTris/ m Tris H  = 1) in seawater (S = 35) at temperatures from 45 to –1.7 °C, (b) from
equation (5) for the equimolal Tris buffer in seawater and brines at their freezing point, and (c) from
equation (6) for the non-equimolal Tris buffer (RTris = 0.5) for seawater and brines at their freezing
point.
1
Table S1. The e.m.f. (E, in V) of the Harned cell with HCl solutions in synthetic seawater (S = 35)
and synthetic seawater-derived brines (S > 35). The reported E values were corrected to a hydrogen
fugacity of 101.325 kPa and were adjusted to the Eo of Bates and Bower (1954) ( EoBB ), with EoBB
computed from the relevant temperature function in Dickson (1990b) (e.g., EoBB = 0.22240 V at 25
°C and 0.23659 V at 0 °C). The adjustment to EoBB was done using the average difference ( EoBB , in
V) of EoBB from the Eo values ( Eomeasured ) derived from e.m.f. measurements of dilute HCl solutions in
de-ionized water at 0, 5, and 25 °C during the course of the investigation as described in the section
The standard potential of pure HCl solutions. Therefore, the E values reported below derive from
the measured e.m.f. (Emeasured) as E = Emeasured – EoBB . The ionic strength (I) and the concentrations
of total sulphate ( mSO 24  ), HCl (mHCl), and total chloride ( mCl  ) in the synthetic salt solutions are in
mol kg H12O .
S
t (°C)
35 24.996
0.004
–0.001
–0.619
–1.165
–1.712
24.998
–0.001
–0.624
–1.206
–1.707
25.008
–0.014
–0.008
–0.620
–1.169
–1.717
25.001
–0.004
–0.616
–1.234
–1.711
24.992
–0.003
25.010
–0.006
I
mSO 24 
mHCl
mCl 
EoBB
0.7225 0.02927 0.039996 0.56923
–0.000012
0.7226 0.02927 0.030005 0.56923
–0.000012
0.7225 0.02927 0.020001 0.56919
–0.000012
0.7225 0.02927 0.020000 0.56919
–0.000012
0.7224 0.02927 0.009869 0.56910
–0.000012
0.7225 0.02927 0.009992 0.56922
–0.000012
2
E
0.34149
0.34284
0.34293
0.34284
0.34284
0.34284
0.34933
0.34984
0.34982
0.34981
0.34980
0.36020
0.35945
0.35946
0.35942
0.35939
0.35937
0.36020
0.35958
0.35954
0.35950
0.35946
0.37881
0.37636
0.37848
0.37601
0.34151
0.34292
0.34298
0.34293
0.34296
0.34297
0.34931
0.34976
0.34974
0.34972
0.34970
0.36017
0.35948
0.35951
0.35945
0.35942
0.35940
0.36020
0.35959
0.35956
0.35953
0.35951
0.37881
0.37630
0.37850
0.37600
0.34152
0.34285
0.34297
0.34286
0.34289
0.34292
0.34932
0.34983
0.34982
0.34981
0.34980
0.36016
0.35950
0.35955
0.35945
0.35943
0.35941
Table S1 (Continued)
S
t (°C)
35 25.008
–0.014
–0.008
–0.620
–1.169
–1.717
45 24.997
24.996
–0.005
–2.502
25.000
–0.003
–2.499
24.997
24.996
–0.005
–2.502
25.000
–0.003
–2.510
24.998
–0.006
–2.499
24.997
24.996
–0.005
–2.502
25.000
–0.003
–2.510
24.994
–0.005
–2.494
50 25.001
–0.001
–2.821
24.996
–0.002
–2.795
25.001
–0.009
–2.822
25.001
–0.009
–2.822
I
mSO 24 
mHCl
mCl 
EoBB
0.7226 0.02927 0.005003 0.56924
–0.00052
0.9387 0.03803 0.040003 0.73955
0.00000
0.9387 0.03803 0.029999 0.73951
0.00000
0.9387 0.03803 0.025007 0.73952
0.00000
0.9387 0.03803 0.020087 0.73951
0.00000
0.9378 0.03801 0.020080 0.73868
0.00000
0.9392 0.03803 0.015002 0.73985
0.00000
0.9386 0.03803 0.010009 0.73948
0.00000
0.9379 0.03801 0.010004 0.73875
0.00000
1.0484 0.04248 0.050000 0.82598
0.00002
1.0485 0.04248 0.040005 0.82599
0.00000
1.0484 0.04248 0.030009 0.82599
0.00000
1.0487 0.04248 0.019997 0.82615
0.00000
3
E
0.39678
0.39259
0.39262
0.39247
0.39237
0.39228
0.33511
0.33511
0.33658
0.33663
0.34296
0.34354
0.34351
0.34787
0.34785
0.34794
0.34787
0.35372
0.35316
0.35303
0.35377
0.35323
0.35310
0.36148
0.36147
0.36012
0.35992
0.37221
0.36984
0.36955
0.37228
0.36991
0.36961
0.32620
0.32838
0.32852
0.33227
0.33372
0.33379
0.34016
0.34078
0.34076
0.35101
0.35048
0.35035
0.39671 0.39672
0.39257
0.39259
0.39242
0.39236
0.39226
0.33513
0.33515
0.33660
0.33665
0.34296
0.34354
0.34352
0.34780
0.35374
0.35316
0.35304
0.35378
0.35320
0.35307
0.36145
0.37222
0.36984
0.36955
0.37225
0.36990
0.36962
0.32617
0.32834
0.32846
0.33227
0.33375
0.33381
0.34015
0.34075
0.34074
0.35096
0.35043
0.35031
0.37218
0.36979
0.36950
0.32619
0.32834
0.32849
Table S1 (Continued)
S
t (°C)
50 25.001
–0.009
–2.822
60 24.997
–0.004
–3.383
24.997
–0.006
–3.422
24.996
–0.007
–3.423
24.996
–0.007
–3.423
24.996
–0.007
–3.423
70 24.997
–0.004
–3.995
24.998
–0.002
–3.999
24.996
–0.002
–4.010
24.996
–0.002
–4.010
24.996
–0.002
–4.010
85 25.002
–0.002
–5.001
25.002
–0.002
–5.001
25.002
–0.002
–5.001
I
mSO 24 
mHCl
mCl 
EoBB
1.0485
0.04248 0.014998 0.82602
0.00000
1.2716
0.05151 0.050009 1.00179
0.00000
1.2718
0.05151 0.040007 1.00192
0.00000
1.2717
0.05152 0.030012 1.00185
0.00000
1.2715
0.05152 0.020005 1.00173
0.00000
1.2716
0.05151 0.014999 1.00179
0.00000
1.4995
0.06075 0.050029 1.18133
0.00000
1.4997
0.06075 0.040033 1.18146
0.00000
1.4997
0.06075 0.030014 1.18144
0.00000
1.4995
0.06075 0.020010 1.18134
0.00000
1.4996
0.06075 0.014997 1.18138
0.00000
1.8507
0.07498 0.050000 1.45801
0.00002
1.8506
0.07498 0.039999 1.45795
0.00002
1.8507
0.07498 0.030000 1.45800
0.00002
4
E
0.35870
0.35737
0.35715
0.32092
0.32308
0.32327
0.32707
0.32853
0.32863
0.33487
0.33551
0.33552
0.34572
0.34520
0.34507
0.35341
0.35213
0.35190
0.31607
0.31832
0.31858
0.32219
0.32364
0.32379
0.33001
0.33066
0.33070
0.34093
0.34042
0.34030
0.34859
0.34732
0.34709
0.30962
0.31181
0.31217
0.31579
0.31722
0.31746
0.32365
0.32421
0.32429
0.35863
0.35731
0.35710
0.32089
0.32305
0.32324
0.32704
0.32852
0.32862
0.33487
0.33547
0.33547
0.34575
0.34522
0.34510
0.35345
0.35214
0.35192
0.31606
0.31825
0.31851
0.32220
0.33003
0.33067
0.33070
0.34092
0.34038
0.34025
0.34858
0.34729
0.34705
0.30967
0.31181
0.31218
0.31580
0.31723
0.31746
0.32355
0.32421
0.32429
Table S1. Continued.
S
85
t (°C)
24.999
–0.001
–4.940
24.999
–0.001
–4.940
24.999
–0.001
–4.940
24.999
–0.001
–5.000
100 25.000
–0.001
–5.998
25.000
–0.001
–5.998
25.000
–0.001
–5.998
25.001
–0.002
–5.999
25.001
–0.002
–5.999
25.001
–0.002
–5.999
25.000
0.001
–6.001
I
mSO 24 
mHCl
mCl 
EoBB
1.8506 0.07498 0.019999 1.45792
0.00002
1.8507 0.07498 0.015000 1.45800
0.00002
1.8507 0.07498 0.010000 1.45800
0.00002
1.8507 0.07498 0.010000 1.45800
0.00002
2.2137 0.08968 0.050000 1.74397
0.00002
2.2135 0.08967 0.039999 1.74387
0.00002
2.2136 0.08968 0.030000 1.74391
0.00002
2.2135 0.08967 0.020000 1.74387
0.00002
2.2136 0.08969 0.015000 1.74393
0.00002
2.2136 0.08968 0.010000 1.74393
0.00002
2.2136 0.08968 0.010000 1.74393
0.00002
5
E
0.33442
0.33404
0.33391
0.34235
0.34101
0.34074
0.35284
0.35081
0.35036
0.35318
0.35082
0.35037
0.30330
0.30534
0.30577
0.30953
0.31086
0.31118
0.31736
0.31784
0.31798
0.32835
0.32776
0.32763
0.33625
0.33489
0.33461
0.34704
0.34461
0.34411
0.34700
0.34456
0.34405
0.33461
0.33404
0.33393
0.34232
0.34100
0.34074
0.35289
0.35070
0.35031
0.35316
0.35081
0.35035
0.30330
0.30537
0.30581
0.30936
0.31071
0.31105
0.31734
0.31786
0.31800
0.32823
0.32780
0.32764
0.33627
0.33491
0.33462
0.34699
0.34463
0.34411
0.34698
0.34457
0.34406
0.35320
0.35086
0.35039
0.34671
0.34458
0.34406
Table S2. The t number from the Regression output of the individual fitted coefficients of equations
(1) to (3). The t number is the ratio of the coefficient value to its standard error and its absolute
value has a Student’s t distribution. Values in italics indicate less than 95% confidence level for the
significance of the coefficient.
t number
parameter
constant
T
T lnT
T2
I0.5
0.5
I T
0.5
I T lnT
I0.5 T2
I
IT
I T lnT
I1.5
1.5
I T
I2
Equation (1)
Equation (2)
3.961
–2.821
2.547
–0.679
–4.366
4.411
Equation (3)
–4.361
4.389
–2.877
2.525
–0.013
–8.891
9.515
–9.924
4.024
5.498
–15.906
6
Table S3. The t number from the Regression output of the individual fitted coefficients of equations
(4) to (8). The t number is the ratio of the coefficient value to its standard error and its absolute
value has a Student’s t distribution. Values in italics indicate less than 95% confidence level for the
significance of the coefficient.
t number
parameter
constant
T–1
T
lnT
S
S2
ST
S2 T
S T–1
S2 T–1
S lnT
S2 lnT
Equation (4)
Equation (5)
Equation (6)
Equation (7)
Equation (8)
–11.929
15.155
–12.881
12.034
–0.190
0.189
–0.190
0.190
–3.709
3.711
–3.707
3.708
2.208
–1.741
2.291
–2.223
–4.432
4.808
–4.389
4.916
4.137
–4.734
4.255
–4.824
1.530
7
0.866
–1.342
–0.444
0.394
–0.443
0.369
0.444
–0.389
ΔEo* (mV)
0.20
0.16
0.12
0.08
0.04
0.00
-0.04
-0.08
-0.12
-0.16
-0.20
0.20
0.16
0.12
0.08
0.04
0.00
-0.04
-0.08
-0.12
-0.16
-0.20
(a)
-10
0
10
20
30
40
50
60
(b)
-7
-6
-5
-4
-3
-2
-1
0
t ( C)
Figure S1. Residuals in
as a function of temperature. The residuals are between the
experimental values and fitted values (a) from equation (1) for seawater (S = 35) and
temperatures from 55 to –1.7 °C, and (b) from equation (2) for seawater and brines at
their freezing point. The experimental values are from Table 2 in this study (+), from
Table 3 in Dickson (1990b) (○), and from Table 3 in Campbell et al. (1993) (□). Note
the difference in the temperature scale of the x-axis between panels (a) and (b).
8
0.005
0.003
0.001
-0.001
-0.003
(a)
-0.005
-10
0
10
20
30
40
50
0.005
ΔpHTRIS
0.003
0.001
-0.001
-0.003
(b)
-0.005
-7
-6
-5
-4
-3
-2
-1
0
-6
-5
-4
-3
-2
-1
0
0.005
0.003
0.001
-0.001
-0.003
(c)
-0.005
-7
t ( C)
Figure S2. Residuals in pHTris (in mol
on the total proton scale) as a function of
temperature. The residuals are between the experimental values and fitted values (a) from
equation (4) for the equimolal Tris buffer (molality ratio, RTris = mTris/
= 1) in
seawater (S = 35) at temperatures from 45 to –1.7 °C, (b) from equation (5) for the
equimolal Tris buffer in seawater and brines at their freezing point, and (c) from equation
(6) for the non-equimolal Tris buffer (RTris = 0.5) for seawater and brines at their freezing
point. The experimental values are from Table 3 in this study (+) and as computed from
the results for the mTris =
= 0.04 mol kg-1 buffer in Table 2 of DelValls and
Dickson (1998) (○). Note the difference in the temperature scale of the x-axis between
panel (a) and panels (b) and (c).
9