THE HYDROGEN-ION CONCENTRATION OF
NATURAL WATERS, i. THE RELATION OF
pH TO THE PRESSURE OF CARBON DIOXIDE
BY J. T. SAUNDERS
(From the Zoological Laboratory, Cambridge.)
(Received 16th March 1926.)
THE evidence that the variations which occur in the hydrogen-ion concentration
of a natural water have any direct effect on the inhabitants living under natural
conditions is scanty and not very convincing. On the other hand, there is good
evidence to show that many animals are tolerant of the changes in hydrogen-ion
concentration of their native habitat. These variations can hardly be related to
distribution, epidemics of conjugation and the like, for these are known to occur
at very different values of the hydrogen-ion concentration. Occasionally it can be
shown that the variations are sufficiently extreme to cause the total extinction of
certain species, but this will only be in very small pools. It is true, of course, that
profound changes can be produced in biological reactions in the laboratory by
altering the hydrogen-ion concentration of the medium in which the reaction is
taking place, but these changes are nearly always greatly in excess of the natural
changes occurring in the normal environment. It appears to me that the real
importance of the measurement of the hydrogen-ion concentration of a natural
water is that it can be used as an accurate measure of the carbon dioxide produced
by the animals and of the photosynthetic activity of the plants. But to use the
measure of the hydrogen-ion for this purpose we must know something of the
underlying principles involved in the measurement and must not merely be content
with matching the colour produced by the addition of an indicator with the colour
of a buffer solution prepared by a rule of thumb method.
The object of this paper is to show that the hydrogen-ion concentration of a
natural water depends on (1) the concentration of the dissolved alkaline and
alkaline earth carbonates and bicarbonates, (2) the concentration of the dissolved
carbon dioxide, (3) the temperature, and (4) the concentration of dissolved salts
(neutral salts) other than alkaline and alkaline earth carbonates and bicarbonates
which may be present in the solution. If we know the values of (i), (2), (3) and (4)
these can be substituted in a very simple equation which will give us the
the hydrogen-ion concentration.
Neglecting for the present the effect of temperature and of neutral salts and
assuming that a natural water behaves in every respect as a mixture of a weak
The Hydrogen-ion Concentration of Natural Waters
47
acid (carbonic acid) with the salt of a strong base, then by applying the law of mass
a n we can show that
where
H" = hydrogen-ion,
ka = dissociation constant of the acid,
HA = undissociated acid,
A = dissociated acid,
and the brackets [ ] denote the concentration, thus [H'] denotes the concentration of the hydrogen-ion.
Now, since the dissociation constant of carbonic acid is very small the undissociated residue, HA, will be very nearly equal to the total concentration of
the acid. Further, it is characteristic of the alkaline and alkaline earth salts that
they are highly dissociated in solution, so that by far the greatest portion of the acid
ions, A, are supplied by the dissociation of this salt. If the salt is present in very
small concentrations, as is the case in natural waters, it will be almost entirely
dissociated so that the concentration of the salt may be substituted for [A] in
equation (i), which then becomes
. i . i .
[salt]
In natural waters the salt in equation (2) will be the carbonates and bicarbonates
of alkaline and alkaline earth metals, the concentration of which may be conveniently written, following Hasselbalch, [Bik], and the acid will be carbonic acid
which will be written [CO2]. If the dissociation of the salt is not total, as we have
assumed it to be, then the concentration of the salt must be multiplied by the
• • *•
*
u- u • t.
*•
salt ionised
,. ,
,, _
lonisation constant which is the ratio
-.
= r—r and is denoted by 8.
total concentration 01 salt
Introducing S into equation (2) this becomes
/-H^logS-log^ + l o g ^
(4).
If for the expression log S — log ka we write pKx, then we have
(5),
which is the well-known equation of Hasselbalch.
The values of ka and S at different concentrations of carbonates and bicarbonates have not been accurately measured, but the value of ^ ^ can easily be found
e^™:imentally by saturating solutions of bicarbonate of known concentration with
caroon dioxide at a known temperature and pressure *and then measuring thepH.
The equivalent concentration of carbon dioxide was calculated by Hasselbalch
48
J. T. SAUNDERS
from measurements of the pressure of carbon dioxide in a mixture of this gas with
hydrogen, with which mixture the bicarbonate solution was saturated. Pure ^ ^ ) r
at i8°C. and 917 mm. pressure was calculated by Hasselbalch to react as an
acid of o-oi normal concentration. For this purpose Hasselbalch used Bohr's
tables of solubility of carbon dioxide. I have also used these tables, but for the
solubility of carbon dioxide in sea-water I have used Krogh's results. Hasselbalch
next assumes, following Henderson, (1) that only bicarbonates are present in the
solution, which is true providing that thepH of the solution does not exceed 8-50,
and (2) that the carbon dioxide dissolves in the dilute solution of bicarbonates in
same proportions as in distilled water or in a water free from bicarbonates.
Both Parsons and Michaelis have pointed out that Hasselbalch has departed
from the usual method of expressing the concentration of the dissolved carbon
dioxide. Hasselbalch regarded carbonic acid as a divalent acid and has expressed
the concentration in terms of normality, whereas the usual custom in physical
chemistry is to use molar concentrations in such equations. If, then, we use molar
concentration instead of normality,
pKt (Hasselbalch) = pKx (Parsons and Michaelis) + -3010.
Warburg has pointed out that the constant pKx needs further modification
and that equation (5) has only mathematical significance whereas in order to render
the equation true both mathematically and actually it is necessary to introduce the
conception of activity as formulated by G. N. Lewis. If the hydrogen-ion concentration of a solution is determined by measuring the potential difference between
a hydrogen-platinum electrode and the solution we make use of Nernst's equation
in the form
F— F
~ °'S77 + 0-0002 {t— 18)
*• ''
where E is the measured potential, Eo is a constant depending on the electrode used
for comparison, and t is the temperature in degrees centigrade of the solution. For
the o-i N calomel electrode Sorensen, on the basis of conductivity experiments,
obtained for Eo the value of 03777 volts. Bjerrum and Gjaldhaek from calculations
based on the activity coefficient obtained for EQ the value 0-3348. So that if we use
Bjerrum's Eo then
pH (Bjerrum) will be equal to/>H (Sorensen) + 0-048
(7)
within the limits of the experimental error of the measurements recorded later in
this paper. The meaning of this last statement is that the concentration of the
hydrogen-ion is not equal to the activity of the hydrogen-ion but that
1*117 an~ CH (Sorensen)
(8).
If we also take into consideration the apparent activity coefficient of carbonic
acid, Fa (CO2), which will be the reciprocal of the absorption coefficient, and write
the equation using molecular concentrations we then have
v v tnr\ \ v o l u m e % dissolved CO2
an = K ^ . (CO2) y o l u m e % c o m b . n e d C O
,
(9);
The Hydrogen-ion Concentration of Natural Waters
49
ushig the same method of expressing the concentration of combined and dissolved
C^Pon dioxide the Hasselbalch equation may be written
, .
,T volume % dissolved CO»
C H =K 11—r
^
rp
j-~7T X 2
v (iO),
volume % combined CO2
'
which may be written in logarithmic form as
/>H (Sorensen) = pK± (Hasselbalch) + log vol. % comb. CO2 log vol. % diss. CO2 — -3010
(11).
Warburg's equation (9) above in logarithmic form is
pa (Bjerrum) = pKx + log vol. % comb. CO2 — log vol. % diss.
CO2-log^a(CO2)
Now
pKi- logFa(CO2) = pK1' (Warburg)
(12).
(13),
and as at 180 C. the absorption coefficient of carbon dioxide is 0-927, log Fa (CO2)
will be 0-033.
From the equations (10), (11), (12) above we can easily see the relationship
between the various brands of pKx.
At 180 C.
pKx (Hasselbalch) = />KX (Parsons and Michaelis) + -3010
(14)
(15).
= pKx' (Warburg) + -219
The general relationship between Kx (Hasselbalch) and K/ (Warburg) is given
by the equation
, 1793^! (Hasselbalch)
.
K
(l6)
= - — ;
It must of course be pointed out, as Warburg has already done, that these
relationships will not be satisfied unless we use Sorensen's Eo in calculating the pKt
of Hasselbalch or Parsons and Michaelis, while Bjerrum's Eo must be used in calculating the pKy of Warburg.
The complete equation for the relation between the pH of a solution of alkaline
carbonates saturated with carbon dioxide at varying pressures is given by Warburg as
K ' tFa (CO)
aaaa -- Kj
(CU)
volume
% dissolved CO2
where K^' is a constant which bears the same relations to k%, the second dissociation
constant of carbonic acid as K/ does to ky, the first dissociation constant, so that
at considerable dilutions we may put
= A 8 = i x 10- 10
Then
K ' - h.Fa ( H C Q a')
m?
^2-^2
(18).
Fa(CO3')
As the value of K?' is small its effect on the equation below pH 8-50 is negligible
and it will only begin to exceed the experimental error when the pH exceeds 8-90.
BJEBMVi
50
J. T.
SAUNDERS
For the experimental determination of pKt Hasselbalch used solutions of
sodium bicarbonate saturated with carbon dioxide and hydrogen at known press^A.
Warburg, in addition to using sodium bicarbonate, used potassium bicarbonate
as well, and his experiments covered a wider range of pressure and concentration
than Hasselbalch's. As is well known, Hasselbalch found that the value of />Kj
was constant over a wide range of pressures of carbon dioxide provided that the
concentration of the sodium bicarbonate remained constant. Other workers have
confirmed this and Warburg further showed that the value of pK1 was dependent
on the concentration of the neutral salts, such as sodium chloride, present in
addition to the bicarbonate. The pH of the solutions in equilibrium with carbon
dioxide at a known pressure was measured by means of the hydrogen electrode.
Warburg has criticised the technique employed by Hasselbalch and has shown
that the wire electrode making minimal contact with the solutions gives readings
which are not quite constant and are 008 to o-iopH below the correct value. As
will be seen later in this paper, I, too, fell into this same error.
The question now arises as to whether natural waters can be treated as simple
solutions of bicarbonates and carbonates. Are the equations given above applicable
in their entirety to natural waters or are there other substances present which will
prevent their direct application? The bicarbonates present in natural waters are
chiefly those of calcium and magnesium. Neither of these salts is very soluble and
the solubility is, as Schloesing showed as long ago as 1872, dependent on the
pressure of carbon dioxide with which the solution is in equilibrium. As a result
of this in a normal hard water, which contains calcium bicarbonate to the extent
of 0-002 normal, the water will be supersaturated with this salt when the pressure
of carbon dioxide falls to 3/10,000 of an atmosphere, which is the normal pressure
of carbon dioxide in fresh air. The calcium carbonate is not, however, thrown down
as a precipitate immediately the pressure of carbon dioxide falls below the limit
required to maintain it in solution. The solution will remain supersaturated for
a long time and will behave to all intents and purposes as a solution of sodium
bicarbonate of the same strength. While there can hardly be a stronger base present
in a natural water than those commonly found, viz. calcium, magnesium, sodium
and potassium, there might quite well occur many stronger acids than carbon
dioxide. Analysis shows the presence of small quantities of phosphoric, silicic,
boric and humic acids in some, but not in all, waters; but of these only phosphoric
acid has a dissociation constant greater than that of carbonic acid and none of them
occur in quantities sufficient to affect the carbonic acid-bicarbonate equilibrium.
There is, therefore, every possibility that natural waters will behave in the same way
as solutions of sodium bicarbonate do when the pressure of the carbon dioxide is
relatively great, but we must expect a difference when this pressure falls below the
limits necessary to maintain the carbonates of calcium and magnesium in solution.
The Hydrogen-ion Concentration of Natural Waters
51
EXPERIMENTAL APPLICATION OF THE HENDERSON-HASSELBALCH
EQUATION TO NATURAL WATERS.
In order to test the validity of the application of the Henderson-Hasselbalch
equation to natural waters, we must be able to measure accurately (1) the value of
[Bik], (2) the pressure of carbon dioxide in order to ascertain the value of [CO2],
(3) the pH at any given concentration of Bik or CO2. Particulars of the methods
of measuring these quantities will now be given.
Measurement of the concentration of bicarbonates. The concentration of the
bicarbonates present in natural waters does not commonly exceed 0-05 normal
and may be as low as 0-00005 normal. The easiest and the most accurate method
of measuring this concentration is to titrate the water with o-oi normal sulphuric
acid using methyl orange as an indicator. The end point of the reaction is the
colour given when methyl orange is added to pure distilled water saturated with
carbon dioxide. This is a method which has been shown by Kiister to give very
accurate results, the error being no more than 0-05 per cent, with proper precautions.
The actual titration is performed by taking 5 c.c. of the water to be tested and
placing it in a test tube. In another test tube of similar bore is placed 5 c.c. of
distilled water saturated with carbon dioxide. To the water in each of these test
tubes is added a drop of methyl orange. The distilled water, when compared with
the water to be tested, should show a faint reddish tinge. Centinormal sulphuric
acid is now added to the water to be tested until the colour matches that shown
by the distilled water saturated with carbon dioxide. It will be necessary, when
making the final comparison, to increase the volume of the distilled water by an
amount equal to that of the acid added, so that the depth of colour in both tubes
is the same. The small quantity of water used does not diminish the accuracy of
the titration, rather it increases it, for, if the two test tubes are held against a white
background, the end point is very clearly defined. When the water contains only
a very small concentration of bicarbonates, such as occurs in waters from districts
where the soil is very poor in lime, it will be necessary to use 25 c.c. for the titration.
If a boiling tube is used instead of a test tube the end point can be controlled in
the same way as before. In practice if the concentration of bicarbonates in the
solution is less than o-ooi normal 25 c.c. of the water should be used. The distilled
water saturated with carbon dioxide plays a very important part in the titration
by providing us with a constant colour for the end point of the reaction. Ordinary
laboratory distilled water prepared by a continuous still is generally useless and it
will be found that the colour of methyl orange does not change when this water
is saturated with carbon dioxide. Good distilled water should show a distinct
change of colour, after adding methyl orange and saturating it with alveolar air by
breathing into the water. But the most important point of all is for the observer,
to accustom his eyes to seeing the colour change and so obtaining an accurate
£tch of the two test tubes at the end point of the reaction. Accurate and conent results with this method cannot be expected immediately the experiment is
attempted. The following table shows the accuracy of the method. Pure dry sodium
carbonate prepared in the usual way by heating sodium bicarbonate (I used Kahl-
52
J. T. SAUNDERS
baum's for analysis) was weighed and dissolved in distilled water to give a solution
o-i normal. From this solution all the other solutions were prepared by dil
The o o i normal sulphuric acid used for the titration was standardised again
NaOH, which had been carefully standardised by titrating weighed amounts of
recrystallised potassium phthalate dissolved in water. Both pipettes and burettes
were checked as to accuracy by weighing the quantity of water delivered. After
calibration the volume delivered by these could be measured with an error of no
more than o-oi c.c.
Table I.
c.c. of
solution
taken for
titration
c.c. of
•oi N H2SO4
required to
neutralise
S
5
5
50-02
2502
500
502
5-02
2-50
252
123
1-25
0-50
052
2-50
252
1-23
125
•25
•27
•27
S
5
5
25
25
25
Normality as
Normality as
determined by determined by
titration (1)
weighing (2)
Log normality (1)
Log normality (2)
•10004
•5004
•1000
•0500
l-oo
170
l-oo
i-70
•01004
•0100
2-OO
2 00
•00502
•0050
37O
37O
•00248
•0025
339
3 4O
•00102
•0010
301
3-OO
•0010
•0010
3-00
300
•000497
•0005
4-70
470
•000105
•0001
4-02
400
Measurement of the pressure of carbon dioxide. If the water be shaken with,
or have bubbled through it, a mixture of carbon dioxide and air at atmospheric
pressure, the proportion of carbon dioxide in the mixture and hence the pressure
can easily be ascertained by withdrawing samples of the mixture and analysing
them in a Haldane apparatus.
Measurement of the pH. Hasselbalch and Warburg used the hydrogen electrode
and saturated the bicarbonate solutions with mixtures of hydrogen and carbon
dioxide. If we are going to test natural waters under natural conditions they must
be saturated with air and carbon dioxide, which will, of course, preclude the use
of the hydrogen electrode. Under these circumstances the colorimetric method
using the indicators recommended by Clark and Lubs appears to be the best available. The choice of these indicators depends on (1) their excellent virage, permitting
considerable accuracy in comparison, (2) the fact that only very small quantities
of the indicator require to be added to the solutions to be tested. The indicators
recommended by Michaelis, while admittedly very convenient, do not allow ^
same accuracy of comparison to be attained. With the indicators of Clark and Lubs
I find that the pH as measured colorimetrically will not differ from the value
The Hydrogen-ion Concentration of Natural Waters
53
measured electrometrically by more than 0-02. Accurate estimation of the/>H by
^wimetric methods depends in the first place on the accurate matching of the
tint of the indicator which has been added to a solution of unknown pH with the
tint of the same indicator added to buffer mixtures of known pH. This matching
is a matter of practice. At first it will not be possible to distinguish a difference
in tint unless the />H of the two mixtures differs by not less than 0-05, very soon,
however, the differences in tint caused by a difference of only 002pH become
easily distinguishable (see Saunders, 1923).
It is well known that colorimetric method is subject to certain "errors" which
must be taken into account if results comparable with the electrometric method
are to be attained. If j for example, we add an indicator to a buffer solution and
match the tint produced against that produced in another buffer solution the pH
of which has been measured by the hydrogen electrode, then we may say (but it
will not always be correct) that thepH of
both solutions is the same. If, now, we 70
proceed to measure (assuming this to be
possible) the pH of the first buffer mixture by means of the hydrogen electrode 60
we may perhaps find that the pH is not m
the same as the pH of the buffer which <°
it matched colorimetrically. There is, in n 5 0
fact, an "error" in the colorimetric $
measurement. This "error" or differ- 3
ence between the measurements obtained 01£40
by the colorimetric method and the a<u
hydrogen electrode may be due to c
several causes or a combination of £ 3 0
these causes. If we know the causes of
these "errors" it will be possible to
make the proper allowance for them and J20
X Brom-Thymol Blue
so to bring the results obtained coloriA Phenol Red
metrically into accord with those obtained
10
electrometrically.
O Cresol Red
v
One of these "errors," the "error"
due to the presence of proteins in the
solution need not concern us here in
dealing0 with natural waters. Natural
•
+0-1
0-0
Thymol Bluefelk)
I
I
-0-1
-0-2
pH displacement
-0-3
.
.
waters do not contain protein in solution
in Sufficient Concentration to affect the
. ,.
„
• r •
c j j
indicator. Even an infusion of dead
leaves or hay Such as is commonly used
c^^>
,.
r r>
•
.. •
f » C culture of Paramecium contains
no more than I*O grammes per litre of
Fig. 1. pH displacement by temperature of the
indicators brom-thymol blue, phenol red, cresol
red, and thymol blue (alkaline range). In order
to obtain the real pH of a solution at a temperature
a b o v e o r b e l o w l6 » c
w h e n c o m p a r e d with a
buffer mixture of known pH at 16° C. the values
of the abscissae marked with a + sign must be
a d d e d ) a n d those marked with a - sign subtracted,
from the pH of the buffer mixture, which the
protein as measured by the refracto-
s o l u t i o n m a t c h e s in tint
-
54
J- T. SAUNDERS
meter, an amount which will be very small when expressed in molecular concentration.
^B
Another " error " is that due to temperature. By this we mean that an indicator
may show different tints when added to two buffer mixtures of similar composition
andpH, but differing in temperature. We can, of course, very easily avoid this error
by doing all our experiments at the same temperature. It restricts us, however,
to a temperature at or near i8° C. for not only do most indicators change their tint,
but the buffer mixture used for comparison is itself liable to considerable variation
in pH with changes of temperature. This displacement of the indicator exponent
has been measured by Kolthoff for certain indicators between 18° C. and 700 C.
I have measured it for the indicators I have used by making use of Walbum's
records of the changes in thepH of certain buffer mixtures when these are heated.
Walbum found that all the mixtures of Sorensen's phosphates suffered no appreciable change in pH as measured by the hydrogen electrode at temperatures between
io° C. and 700 C. Mixtures of Sorensen's phosphates were prepared of suitable
pH so as to coincide with that portion of the range of the indicator, where the virage
was strongest, and each of these portions was divided into two after the addition
of indicator. One portion was heated and the other was maintained at a temperature
of io° C. The tint of the indicator in the heated portion was then matched against
a mixture at 10° C , thepH of which was known. In this way I was able to determine the heat "error" of brom-thymol blue, phenol red and cresol red. For determining the heat "error" of thymol blue I used Sorensen's borate-HCl mixtures,
as the pH of these had been measured at different temperatures by Walbum. The
details of these comparisons are given in Table II below. The results are plotted
in Fig. 1.
It appears, therefore, that brom-thymol blue is very little affected by changes
of temperature, while phenol red, cresol red and thymol blue are most affected but
behave in practically the same manner. Kolthoff gives the displacement of the pH
between 180 C. and 70° C. as being 0-4 for thymol blue and 0-3 for phenol red.
The last " error," which it is necessary to take into account, is the salt " error."
If the composition of the buffer mixture used for the comparison differs very much
in the concentration of salts from that of the mixture whose pH is to be ascertained,
the pH of the buffer mixture which the unknown matches is not the pH of the
unknown. If, however, we know the concentration of the salts in both the buffer
mixture of known pH and in the mixture of unknown pH, then, from a colorimetric
comparison, we can easily ascertain the pH of the unknown. I have already published an account of the method of estimating the salt error in the case of cresol red,
but, as I have reason to believe that the method is applicable to all the sulphonphthalein indicators, I have thought it worth while to republish (in a more convenient
form) the curve given in my previous paper and briefly to summarise the method.
This curve is printed as Fig. 2 of this paper.
In order to allow for the salt "error" it is necessary first to ascertain the ^
mality of the metallic kations in the buffer solution used for the comparison. This
is very simple as the solution used for this purpose will always be of known composition and the normality can be calculated from the formula for its preparation.
The Hydrogen-ion Concentration of Natural Waters
55
Next it is necessary to know the normality for metallic kations of the solution whose
J^Hs to be found. In the case of fresh-waters where the carbonates and bicarbonates
form by far the largest proportion of the dissolved salts, it is sufficiently accurate
to assume that the concentration of these, which is determined by titration in the
manner indicated above, represents the concentration of all the dissolved salts. In
the case of brackish or sea-water the concentration of the metallic kations can be
derived from the density which is easily measured by the floating hydrometer by
assuming that all the density is due to NaCl. With mineral waters it may be necessary
to resort to chemical analysis, but here again a hydrometer and the assumption
that all the density is due to NaCl is usually sufficiently accurate.
Table II.
(I)
(2)
(3)
Composition of
buffer mixture heated
or cooled
Indicator
used
Temperature
in degrees
centigrade
(4)
(5)
(6)
(7)
Apparent
pH of buffer
Buffer mixture mixture
difference in
at i6°C. Change in pH
used to match which matches
in buffer due to pH of the
the mixture
heating or
two mixtures
tint the mixheated to tem- in
cooling (from
due to the
ture heated to
perature in
Walbum'stables)
heating of the
the
temperature
col. (3)
indicator
in col. (3)
16
37
7O
Sorensen's
phosphates
681
685
6-92
12-6 c.c. primary Brom+ 7 4 c.c. secon- thymol
dary (Sorensen's blue
phosphates)
16
35
67
Sorensen's
phosphates
6-50
6-52
6-59
5-70 c.c. primary Phenol
+1430 c.c. sec- red
ondary (Sorensen's phosphates)
35
45
Palitzsch's
borax-boric
acid
7-25
736
7-45
7'57
OOO
+ O-II
+ O-20
+ O32
Palitzsch's
borax-boric
acid
7-82
787
-OOS
801
813
+ O-I4
+ O-26
1 "7 c.c. primary + Cresol
183 c.c. secon- red
dary (Sorensen's
phosphates)
IS c.c. of Soren- Thymol
sen's borate + s blue
c.c.ofo-i JVHC1
14
70
10
40
60
10
16
30
50
70
Palitzsch's
borax-boric
acid
do do do do 00
Equal parts of BromSorensen's phos- thymol
blue
phates
Nil
»
O-OO
+ 004
+ O-II
OOO
+ O-O2
+ 0-09
o-oo
+ 003
OOO
-009
-0-19
-031
-OO3
OOO
+ 0-09
+ 0-19
+ 0-31
Fig. 2 shows graphically the pH at which a buffer mixture, to which NaCl is
added in varying proportions, remains constant in tint on the addition of cresol red
as an indicator. The method of using this curve is fairly obvious. For example, some
fresh-water known to be 0-004 normal for bicarbonates matches in tint Sorensen's
phosphate mixture of pH 7-80 when cresol red is added. The normality of metallic
kations in the phosphate buffer mixture is 0-125. According to the curve a mixture
of />H 797 and 0-125 normal for NaCl will match in tint a mixture of/>H8i6
^^0-004 normal. We must therefore add 0-21 to 7-80 in order to obtain the real
or electrometric pH of the fresh-water. On the other hand, if sea-water, which is
very nearly o-6 normal for NaCl, matched exactly th*e tint of Sorensen's phosphate
mixture of pH 7-80, then from the curve it is seen that a mixture of pH 7-80 and o-6
The Hydrogen-ion Concentration of Natural Waters
57
mal for NaCl will match exactly a buffer mixture of pH 7-97 and 0-125 normal,
must, therefore, subtract 0-17 from 7-80 in order to obtain the real or electro•
metric pH of the sea-water. If, therefore, the normality of the metallic kations
in the solution of unknown />H exceeds that of the buffer mixture with which it
compares in tint we must subtract the correction from thepH of the buffer mixture
in order to obtain the real pH; on the other hand, if the normality in the solution
of unknown pH is less than that of the buffer then we must add the correction to
the pH of the buffer mixture. The difference in pH between solutions of different
normal concentration matched in tint will be the same for the whole range of pH
covered by the sulphonphthalein indicators.
It has sometimes been assumed, but without justification, that it is unnecessary
to apply any correction when the concentration of the dissolved salts in the solution
of unknown pH is very small, as is the case in most fresh-waters. Actually, as we
have just seen, the amount of the correction to be applied depends on the difference
in the normality of the metallic kations in the solutions compared. There is a very
considerable difference in this concentration both in the case of fresh- and seawater, but the correction to be applied for fresh-water will be of opposite sign to
that used for sea-water and it may, moreover., be considerably larger.
The last "error" which concerns us here is that caused by the addition of the
indicator to a mixture which is very weakly buffered. In the case of natural waters,
when the concentration of the bicarbonates falls below o-ooi normal the addition
of the indicator may make an appreciable difference to the pH, so that the pH
measured is not the pH of the water but the pH of the water after the addition of
the indicator. At concentrations of bicarbonate exceeding o-ooi the pH of the
water will not be changed to any measurable extent by the addition of the indicator.
When the indicator is added in the acid form we may make an approximate allowance for the effect by the use of the equations given by Michaelis in his book (Die
Wasserstoffionenkonzentration, 1922 edition), pp. 40 and 41. The indicators of
Clark and Lubs are, however, added in the form of the sodium salt of the indicator
which is a weak acid, the effect of the addition of the indicator in this form can be
estimated as follows. The hydrogen-ion concentration in the solution before the
addition of the indicator will be represented by the equation
and, after the indicator is added, by the equation
rxj-i _ ^1 [ ac 'd] + ^2 [indicator]
•• •*
[salt']
where
kx = first dissociation constant of carbonic acid,
^2 = dissociation constant of indicator acid,
[acid] = molecular concentration of carbonic acid,
[indicator] = molecular concentration of indicator,
[salt] = molecular concentration of alkali before the indicator is added,
[salt'] = molecular concentration of alkali after the indicator is added.
58
J. T.
SAUNDERS
If the concentration of the alkali in the solution whose />H is to be foun
o-oooi M, the carbonic acid is 0-00005 M and the indicator after addition
^P
solution 0-00003 M, then, if brom-thymol blue, the dissociation constant of which
is 1 x io~ 7 , be used, we find by substituting these values in the equations (20)
and (21) above, that the pH of the solution before the addition of the indicator is
6-824, anc* after the addition it is 6-858. So, in this case, the observed pH will be
0-03 greater than that of the pH of the solution. If phenol red (dissociation constant 1-2 x. io~8) were used instead of brom-thymol blue in the case stated above
the/>H observed would be 6-934, or o-i 1 too much. Variation in the added indicator
of the ratio of the concentration of indicator acid to the.concentration of alkali will,
of course, vary the error due to the addition of the indicator. It will be possible
so to adjust this ratio that, at a given concentration of alkali and carbonic acid, the
addition of indicator will not alter the^>H of the solution to which it is added. But
if it be added to any other concentration of alkali and carbonic acid, this indicator
will alter thepH. by varying amounts.
Here it might be as well to point out the futility of attempting to measure the
pH of distilled water by the use of indicators. When an indicator is added to pure
distilled water it is diluted and the pH which is thus measured is the pH of the
diluted indicator and may be quite different from that of the distilled water to
which it has been added. The use of brom-thymol blue adjusted by the addition
of NaOH to a certain colour before it is added to the distilled water has been
recommended. This recommendation is based upon the fact that the measurements
given by this indicator after adjustment compare with the hydrogen electrode
measurements. What in effect has been done is to adjust the indicator so that when
it is diluted on being added to distilled water the pH of the indicator so diluted is
approximately that of the distilled water as measured by the hydrogen electrode.
But if such an indicator gives a correct reading for pure distilled water it will cease
to do so if the distilled water contains a very small quantity of carbon dioxide in
solution. A small quantity of carbon dioxide will cause a relatively great increase
in the hydrogen-ion concentration in the distilled water, but this effect will be
almost completely masked on the addition of the indicator. For example, let us
suppose that brom-thymol blue in the form of the sodium salt is added to distilled
water which contains carbonic acid to the extent of o-ooooi molecular. The hydrogen-ion concentration of such a solution will be v i x io~ 5 x 3 x io" 7 ori-73X io~6
(or pH 5 76). The indicator in the form in which it is added is a buffer mixture
formed by the base and the weak acid indicator, further it is adjusted before
addition to a green colour so that the pH of the indicator as added must be about
6-8o with the alkali and indicator present in equal concentration. When it is added
to the distilled water the indicator is diluted to a concentration of 000003 molecular. The dissociation constant of brom-thymol blue is I-I x io~ 7 , then, substituting in equation (21) we have
..„., _ 3 x io~7 x -ooooi + 1 x io~7 x -00003
*•
whence
*
pH = 6-70.
-00003
The Hydrogen-ion Concentration of Natural Waters
59
Thus the effect of the indicator, when added to distilled water containing a
^
quantity of dissolved CO2, is to cause an error of i-o in estimating the pH,
an error so large as to make the indicator method useless.
Having thus outlined the methods applicable to natural waters for measuring
pH, [Bik] and [CO3] in equation (5), the validity of the application of the equation
itself to these waters can now be tested experimentally. For this purpose a very
simple apparatus may be used (Fig. 3). A CO2-air mixture is prepared by breathing
into a large carboy. This mixture taken from the carboy is drawn through the test
tubes by an aspirator until equilibrium is reached. The amount of the CO2 in the
mixture bubbling through the test tubes is measured by withdrawing samples by
*
I
V
asbiitral/
n)
Fig. 3. Diagram showing the construction of the apparatus used for bringing the solutions into
equilibrium with a CO2-air mixture and for measuring the pH of the solutions.
the three-way tap and analysing these in a Haldane apparatus. The pressure of the
CO2 is obtained by readings of the barometer and of a mercury manometer attached
to the aspirator (hot shown in the diagram). The attainment of equilibrium is
shown by the indicator added to the water in the test tubes maintaining a constant
colour with continued bubbling. Natural waters often take a long time to reach
equilibrium whereas with solutions of sodium bicarbonate it reached very rapidly,
he pH at equilibrium exceeds 8-5 equilibrium is reached very slowly and the
at which the final equilibrium is reached greatly increases as the pH exceeds
this value. The effect of salt is also to render the attainment of the final equilibrium
a much slower process. The necessity for this prolonged bubbling when the pH
60
J. T. SAUNDERS
exceeds 8-5 is a well-known fact. Sorensen, who bubbled hydrogen through sodi
bicarbonate found that equilibrium was not reached even after 24 hours,
^
came to the conclusion that it was impossible to record electrometrically the pH
of a solution of bicarbonates during the transition from bicarbonates to carbonates.
If, however, instead of pure hydrogen, we use a mixture of air and carbon dioxide
and if the pressure of carbon dioxide is so small that the pH at equilibrium is 9-0,
then I find that stable equilibrium is reached despite the fact that the mixture now
contains both carbonates and bicarbonates. It takes a very long time to reach this
equilibrium. If we have two solutions of sodium bicarbonate, the one o-oi normal
and the other 0-005 normal, and bubble through both solutions at the same rate
fresh air at atmospheric pressure containing three parts per ten thousand of carbon
dioxide final equilibrium is reached in the weaker solution in 30 minutes, whereas
it takes six hours before the final equilibrium is reached in the stronger solution.
In effect then the formation of carbonates from bicarbonates when the pressure
of carbon dioxide in equilibrium with the solution is reduced is an extremely slow
process. It is doubtful if the reaction is ever complete if the carbon dioxide pressure
be reduced to zero. Generally speaking, equilibrium is reached fairly rapidly
whatever the pressure of carbon dioxide, provided that the pH of the final equilibrium does not exceed 8-50. Above 8-50 the rate at which equilibrium is reached
falls off rapidly, and this rate is further slowed down by the presence of neutral salts.
In sea-water it is reached very slowly and Warburg has noticed that the presence
of sugar added to a solution of sodium bicarbonate increases very considerably the
time taken to reach equilibrium.
The results of the methods outlined above are summarised in Table III. The
HCOg' normality in column (2) is determined by titration. The Na' normality
is given in column (3) and immediately below it, in brackets, is the cube root of
this normality. The Na' normality will be the same actually as the HCO 3 ' normality in the sodium and calcium bicarbonate solutions. In the natural freshwaters I have assumed that it is also the same except where the contrary is stated in
column (3). In Cambridge tap-water the sum of the normalities of the NaCl, KC1,
CaSO4 and MgSO4 present in solution only amounts to 00006, so that the tapwater is actually 0-0050 normal for all metallic kations, a difference which will be
without influence in estimating the salt error of the indicator. But in the softer
waters, such as those from Plymouth and Manchester, published analyses show that
the error involved in making the assumption that the Na' normality is the same as
the HCOg', may be as much as 1000 per cent. This appears to be a very large error,
but, as can be seen from Fig. 2, it will not cause an error at this dilution of more
than 0-05 pH in estimating the salt error of the indicator. Such an error in estimating the pH is about the same as the experimental error in these very dilute
solutions. Below the double line in the table where the Na' normality is shown
in column (3) as exceeding the HCO 3 ' normality, it was determined in the case of
sea-water from the density and in the other cases by the addition of
^B
quantities of pure, dry NaCl.
The pressure of CO2 in column (4) is derived from the proportion of CO2
The Hydrogen-ion Concentration of Natural Waters
61
the mixture passing over the test tubes, which consists of air, water vapour
CO 2 , the proportion being determined by the Haldane apparatus. The proportion of CO2 multiplied by the total pressure of the mixture gives the pressure
of CO2. The total pressure of the mixture is derived from readings of the barometric pressure. As the mixture is drawn through the test tubes by the aspirator
purhp, the pressure in each tube will be less than that of the preceding one. When
the mixture is drawn through six tubes in series the decrease in pressure as
indicated by the manometer attached to the aspirator pump is 30-5 mm. In calculating the pressure, allowance may be made for this drop but it is of small importance. If six tubes are used in series, the pressure in the first will be, say,
760 - 5 mm., and the pressure in the last test tube 730 mm. The correction for the
lowering of pressure in the last tube of six in series to be applied in equation (5)
will be log f§§ , which is — -015, a difference of pH which is barely detectable by
colorimetric methods. Without creating any serious error, and with a great gain in
convenience, we can reckon the total pressure in all the tubes of the series to be
(•-!»')•
where B is the barometric pressure and n is the number of the tubes in the series.
I have never used more than eight tubes in series, as a rule the number was four.
The values of pKx' in column (9) are obtained by substituting the values given in
columns (2), (4) and (8) in equation (5), the normality of the CO2 being obtained
from the pressure by multiplying the pressure by
(see p. 48). From these
values of pKt (Hasselbalch), pKx' (Warburg) is obtained by equation (16). In
calculating the averages in column (10), I have omitted the values enclosed in
square brackets, [ ], as these particular values were sufficiently divergent from
the mean to indicate the possibility of a serious error in the experiment to which
they relate.
I have already shown (Saunders, 1923) that by the application of these methods
the value of pK1 (Hasselbalch), using a mixture of CO2 and air to saturate the sodium
bicarbonate solution and measuring the pH by indicators, is the same as that found
by the electrometric method within the limits of experimental error. But my value
of pKx agreed with the value given by Hasselbalch, whereas Warburg has pointed out
that, owing to an error in his technique, Hasselbalch's values of pKt are 008-0-10 too
low. How, then, does the same error occur in the colorimetric technique? The
answer is that it does not occur. When I was measuring the value of pK.1 by colorimetric methods, my results were consistently 0-08 higher than the figures given by
Hasselbalch. I was much puzzled by this, especially as I had taken the greatest
care in the preparation of my buffer mixtures. I therefore checked the pH of my
mixtures with a hydrogen electrode and I found that the electrode measure- '
gave a pH valuexfor the buffer mixtures which was 0-08 pH less than the
stated value. This appeared to me to explain the discrepancy. I accepted the hydrogen electrode measurements as being correct and corrected the buffer mixtures
Pal. borax
,>
Cambridge tap-water diluted
with distilled water
Calcite dissolved in distilled
water
Sodium bicarbonate
Pal. borax
Pal. borax
,I
C.R.
C.R.
9)
Pal. borax
Pal. borax
C.R.
C.R.
1)
I
1)
*
Pal. borax
C.R.
Sor. phos.
P.R.
Indicator
6.79
Buffer
~ H obuffer
f
mixture
Corrected
mixture
p H of
used for matching
solution
comtint of
parison
solution
-S O ~phos.
.
6.79
Mancheater tap-water
Pressure
of C 0 2 in
mm. Hg
Sor. phos.
(y&
Na'
HCO,'
normal~ty normality
and
Plymouth tap-water
Sodium bicarbonate
Source and nature of water
or solution
Table 111.
pK,'
6.50
--
Average
value of
PK,'
The Hydrogen-ion Concentration of Natural Waters
sb
M r f - M O O O X " C O OsOO
i-< ^J-COroO O s t ^ N in\O CO CO Os N
vO *© t^OO OO
<M c* M
M
O
J vi\O O O O
) M
i-t O
O OsOO
Osi r^GO O N ^ - (
OO CO
M *-*
*-* i-t
00 00 CO 00 00 00
O Os Os O TJ- T|- Tf OsOO Os COOO '
2
o
o .
os - -o«
u
• ft
O
oo
N M M TJMOO O M
M M N N N M f > f > c > T j - T h -^-00
8^
OH
m
6
MOOCOONinOOONO^
M r~ o •+ Tj-oo « » o
n
•H N CO CO CO ^" ^" tOGO
-us
OH'
8?
8£
4-> b o
J
S
u
f
ea
v
c
2
•<)• T j - O VO M N O
-Cambridge tap-water diluted
a0023
, with NaCl solution
Sodium bicarbonate
(.z I 6)
'010
,0078
('199)
and (dc)
Na'
nomdiF
Pond water from Newnham,
near Cambridge
1
.oo5
('171)
HCO;
nomallty
Sodium bicarbonate
Source and nature of water
or solution
Pressure
of CO, in
mm. Hg
(4)
>
29
3,
Pal. borax
Pal. borax
,,
9,
Pal. borax
Pal. borax
Pal. borax
C.R.
,,
Pal. borax
,*
Pal. borax
C.R.
1,
C.R.
C.R.
Pal. borax
C.R. & P.R.
9,
9
,,
& P.R.
C.R.
C.R.
B.-T.B.
C.R.
C.R.
Indicator
Buffer
mixture
used for
comparison
Table I11 (continued).
7'77
~Hofbuffei
mixture Corrected
p H of
matching
solution
tint of
solution
pK,'
PK;
Average
value of
Pal. borax
Pal. borax
--
Pal. borax
228
.228
228
.joo
'300
Sample of sea-water from 5
miles S.S.W. of Bolt Tail,
Plymouth. Collected Jan.
4th, 1922 and exp. done Jan.
24th, 1922
Sea-water from outsideBreakwater, Plymouth. Collected
and exp. done on April I ~ t h ,
1922
Sea-water from Lowestoft,
Oct. 16th, 1922
I
1
Pal. borax
99
9
99
Pal. borax
9,
,,
>I
Pal. borax
C.R.
,,
C.R.
C.R.
Pal. borax
C.R.
C.R.
C.R.
Sodium bicarbonate and NaCl
1
I
1
Pal. borax
.228
'228
Diluted Cambridge tap-water
and " Shore's sea salt"
Solution of calcite and NaCl
bicarbonate and NaC1
66
J. T. SAUNDERS
accordingly. But I have now no doubt, after reading Warburg's criticism^
Hasselbalch's technique, that the hydrogen electrode which I used was at
and that the buffer mixtures were of the stated values. The electrode used to check
the pH of my buffer mixtures was a platinum wire, the hydrogen was bubbled
through the buffer mixture in an open dish, and minimal contact was made with
the liquid, all of which are conditions which would favour the electrode being
depolarised by traces of oxygen. If, then, thepH of my buffer mixtures, prepared
exactly according to the directions given from chemicals which I was careful to
purify myself by several recrystallisations, are accepted as correct, then^K^ (Hasselbalch) is o-o8 too low and my measurements made by colorimetric methods agree
very closely with those made by Warburg.
•8
TO
V2
1-4
V6
V8
6-50
6-50
6-30
6-40
6-10
6-30
6^20
o
4-
* >
5*90
-
A,
•
^
V
5-70
6-10
5-50
6-00
5-30
5-90
5-10
1-0
1-2
Fig. 4. Relation of pK^ to the concentration of Na. The cube roots of the normal concentration of
Na- (and other metallic kations where and when present) are plotted as abscissae and the corresponding values oi pKi as ordinates. The marks x are the values taken from Table III of this
paper, and the marks O, A, + are values taken from Warburg's paper. To all these marks the bottom
and left hand scales apply. The points marked W, to which the upper and right hand scales apply,
are values derived from Wilke's results. The points marked W are not absolute values but are all
relative to the point marked •.
The results of the experiments recorded in Table III are expressed graphically in Fig. 4. Following Warburg I have plotted the values of pKx' as ordinates
o 1—
and as .abscissae « where c is the concentration of Na' expressed as normal. The
values found by Warburg are plotted to the same scale and indicated by the marks
used by him.
It will be seen that my determinations of the values of />KX' at both higher ^
lower concentrations of Na' than those used by Warburg for his experiments all
fall on the same straight line. I have also calculated the value of pK±' from the
67
The Hydrogen-ion Concentration of Natural Waters
oiiservations of Wilke. These appear to show that the relationship ceases to be a
light line one at concentrations greater than i-o molecular.
The value of pKx' in Table III is the value at i8° C. The value of pKj1
changes with temperature. Julius Thomsen, by thermodynamic methods, calculated that the heat of reaction, that is the change in the constant pK-i per degree
centigrade, should be 0-0065. According to Hasselbalch's and Warburg's experiments the change is 0-0055. My experiments give results which are almost identical
with those of Hasselbalch and Warburg. In order to measure the thermal increment I prepared two solutions, one of calcium bicarbonate by dissolving calcite
in distilled water saturated with CO2 and another of sodium bicarbonate. The
solutions were adjusted so as to be of the same equivalent concentration, viz.
0-0017. Using the apparatus shown in Fig. 3 fresh air from outside the building
was drawn through the solutions, four test tubes being run in series. Thefirsttwo
Table IV.
(1)
Solution
(2)
(3)
Na*
HCO 3 '
normality normality
(4)
re
(S)
(6)
pHoi
buffer
mixtures />Hof
used for solutions
comparison
(7)
(8)
Difference in pH
(and also in pK.^)
after correcting for
solubility of CO2 and
any difference in
HCO 3 ' normality
found
calculated
•52
•si
Sodium bicarb.
Do. +NaCl
•00096
•00096
•00096
I-2O
•099
i-o6o
809
8-25
8-32
806
Sodium bicarb.
Do. +NaCl
•00112
•00106
•00112
I-2O
•104
1-060
816
8-27
801
•5°
•51
Calcium bicarb.
Do. +NaCl
•00072
•00072
•00072
•30
•670
•090
7-91
797
8-15
786
•33
•31
Calcium bicarb.
Do. +NaCl
•00180
•00174
•0018
•60
•123
8-31
840
8-Si
821
•36
•38
•775
8-37
were maintained as controls at a temperature of 18° C , while the temperature of
the last two was varied by immersing them in a large bath of water. Both the
calcium and the sodium bicarbonate solutions behaved exactly alike. The indicator
was cresol red and the buffer mixture used for the comparison was Palitzsch's
borax-boric acid. The pH of the buffer mixture, which the control tubes matched
exactly in tint, was 8-30. From equation (5) we see that when the temperature of
the solution is varied the solubility coefficient of CO2 will vary and the effect of
temperature on the pH will be measured by the difference between the logarithms
of the coefficient of solubility at the different temperatures, provided that the
:ssure of CO2 and the concentration of HCO3' remains the same and provided
that pKi does not vary. It will be seen from Table IV that when the colorimetric method is used the difference in the pH between the two solutions at
different temperatures appears to correspond almost exactly with the difference
5-2
68
J. T. SAUNDERS
in the logarithms of the coefficient of solubility of CO2 at these temperatures, and
that^K/ remains constant. But this appearance is illusory only, for it is produd^
by the indicator exponent itself changing in a similar manner. If we introduce tne
correction due to the displacement of the indicator exponent by heat (see Fig. i),
then we have pKx' changing in a manner exactly similar to the indicator. We have
already measured this change, which is a displacement of 0-385 pK between o-o and
70° C. or 0-0055 pH per degree centigrade. The effect of this change in the value
is to reduce to some extent the effect which changes of
pi i with temperature
p
ilibi
temperature would otherwise have on a solution of bicarbonates in equilibrium
with CO2. The change in pH due to changes in temperature in a solution of
bicarbonates of a given concentration in equilibrium with a given pressure of CO2
is shown graphically in Fig. 5. Approximately an alteration of the temperature
by i° causes an alteration in^>H of o-oi.
1
50
1
/
//
1
30
/
/J
20
10
///
/
//
//
/
/
/
• - *
•
•1
'
•
/
•2
pn
Fig. 5. The broken line shows the change in pH which would occur in a solution of bicarbonates,
if we were to assume that p K / remained constant, when the concentration of the bicarbonates and
the pressure of carbon dioxide remain constant but the temperature changes. The continuous line
shows the actual change, the difference between the two lines is the change in the value of pK^
with temperature. The pH at i8°C. is taken as zero, values to right of this line indicate an increase
in the pH, those to the left a decrease.
The following conclusions may be drawn from the results given in Table III
and Fig. 4: (1) that solutions of calcite behave in the same way as solutions of pure
sodium bicarbonate; (2) that natural waters which usually contain a mixture of the
bicarbonates of calcium and magnesium in varying proportions also behave in
the same way as solutions of pure sodium bicarbonate; (3) that the value of />KX'
is determined by the equivalent concentration of the kations present, not only those
derived from the ionisation of the bicarbonate itself but also those derived from
the ionisation of any neutral salts that may be present in the solution; (4) that, for
any given concentration of sodium ions, the value of pKx' is the same no
whether the bicarbonate be that of sodium, calcium, magnesium, or a mix
of these; (5) that the value of pKt' changes with temperature.
It must be pointed out as a remarkable fact that, as recorded in Table III,
The Hydrogen-ion Concentration of Natural Waters
69
equation (5) holds in the case of the Cambridge tap-water even when the pressure
o^B0 2 falls as low as the average pressure of this gas in the atmosphere and the />H
in consequence reaches nearly 9-00. Now equation (5) applies only when bicarbonates alone are present in the solution, and we must therefore conclude that in
the tap-water this is the case even though the pH has reached this high value. We
have already seen (p. 60) that the formation of carbonates from bicarbonates is an
extremely slow process. Further, we find that equilibrium in the case of the
Cambridge tap-water saturated with fresh air is reached only after from 2 to 3
hours' continuous bubbling of air through the test tubes. At the end of this time
the pH. indicated by equation (5) is reached. If the bubbling be continued the
solution remains at this pH for an hour or two longer and then the pH commences
to fall. If the water be titrated immediately thepH has reached the maximum value
the equivalent concentration of HCO3' will be found to be unchanged, but when the
pH falls, the equivalent concentration of HCO3' also falls. This fall in the equivalent
concentration is due, of course, to the fact that the carbonates of Ca and Mg are
only very slightly soluble and are precipitated from the solution soon after they are
formed. Bicarbonates are therefore converted into carbonates but only very slowly
when the pressure of CO2 is reduced. This formation of carbonates from bicarbonates appears, as might be expected, to be proportional to the concentration. If
the concentration is relatively large (0-0078 normal) we see from Table III that
neither the pH calculated from equation (5) nor (17) is reached when we bubble
fresh air through this water and this is obviously due to the carbonates forming
and precipitating too quickly. On the other hand, if the equivalent concentration
of Ca and Mg bicarbonates is reduced the formation of carbonates from bicarbonates, when the solution is exposed to the atmosphere, may be so slow that
practically no formation of carbonates is found to occur. A solution of CaHCO3
of an equivalent concentration of 0-0020 normal will remain for an almost indefinite
time in equilibrium with the pressure of CO2 in the atmosphere without the
carbonates forming in sufficient quantities to be precipitated. This fact is of
importance because it determines the maximum value of the HCO3' concentration
in the surface waters of large lakes and probably to some extent also in the sea.
In large lakes, where the water supply is derived from calcareous sources the
equivalent concentration of HCO 3 ' of the surface water rarely exceeds 0-0030
normal and is usually in the neighbourhood of 0-0020 normal. In the sea the
equivalent concentration of HCO 3 ' varies, within narrow limits, from 0-0023 in
tropical to 0-0026 normal in temperate regions.
It has often been suggested that the difficulty in raising the pH of sea-water
by bubbling through it mixtures containing CO2 at very low pressures is due to
the presence of acids other than carbonic. It is difficult to prove the presence of
these acids and analysis has never revealed them in anything like sufficient quantities
toproduce the effect required. It is much more probable that the presence of the
^ B u m chloride in the quantities in which it is present in sea-water is amply
sufficient to account for these difficulties. The addition of sugar will also extend
very considerably the time taken to reach equilibrium in a solution of sodium
bicarbonate and here there can be no question of the presence of any other acid than
70
J. T.
SAUNDERS
carbonic. If very small pressures of CO2 are used then there is the possibili^^of
some of the carbonates being thrown out of solution. The effect in this case^Bl
be that thepH at equilibrium will be lower than if all the bicarbonate had remained
in solution. It appears to me hardly necessary to drag in these extra acids, proof
of the existence of which is lacking, in order to escape from what appears to be a
difficulty, when this difficulty can be explained by simple physical means.
Shipley and McHaffie have put forward the hypothesis that in very dilute
solutions carbonates are never fully transformed into bicarbonates. This is the exact
opposite to the explanation which I have just suggested. But the experimental
work on which this hypothesis of Shipley and McHaffie is based appears to me to
be open to serious criticism. Shipley and McHaffie noticed that when solutions
of NajCOg are titrated with HC1 using the hydrogen electrode to determine the end
points of the reactions, the ratio of acid required for the first end point to that
required for the final end point is less than the expected ratio of 1/2 when the
solutions are very dilute. Down to o-ooi iV NagCOg the ratio scarcely departs from
the expected ratio by more than the experimental error. But at a concentration of
0-0005 N the ratio becomes 1/3, and, using CaCO3 instead of NagCOg, the ratio
becomes 1/3-5 a t a concentration of 0-00032 N. This departure from the expected
ratio does not become at all obvious until the dilution is very considerable, when
the experimental error may be very large and the difficulties of obtaining consistent
results are very great. Shipley and McHaffie's experiments show a fairly regular
decrease in this ratio with dilution, and this has led the authors to put forward the
suggestion (1) that at great dilutions the bicarbonate is never formed, and (2) that
the second dissociation constant of carbonic acid, k2, increases with the dilution
of the solution. They found that in the equation
[H-][C0 3 ']
**- [HCO3']
the product [H'] [C0 3 '] is a constant the value of which was determined as being
5 x io~ 13 , so that when [HCO3'J is very small k2 is large. As a result of this, when
a certain dilution is reached, k^ will be the same as kx and there will appear to be
only one end point for the titration. It appears to me that these authors have not
entirely excluded the possibility of their solutions remaining contaminated with
C0 2 . Merely bubbling hydrogen through the solutions will not remove all traces
of CO2 produced by the added acid, except, perhaps, after a very long time. These
traces of CO2 are, at the dilutions used, quite sufficient to account for the divergences from the expected ratio. These experiments are, in fact, only another
example of the difficulty, first pointed out by Sorensen, of raising the pH of a
solution of bicarbonates to the theoretical value by bubbling pure hydrogen through
the solution.
The difficulty of obtaining proper equilibrium with low pressures of CO2
in solutions of bicarbonates and also in sea-water is probably responsible f o r ^ ^
error in Henderson and Cohn's, and also in McClendon, Gault and Mulhollai^P
work. None of these workers found any constancy in the value of pK^, either in
sea-water or in simple solutions of sodium bicarbonate. McClendon's results are
only presented in graphical form, which makes them a little difficult to criticise,
The Hydrogen-ion Concentration of Natural Waters
71
moreover in the graph showing the relation of the pressure of CO2 to the/>H of sea\ ^ B r (p. 36, Carnegie Institute Publ. No. 251, 1917) he omits to mention what is
the equivalent concentration of HCO3', although he tells us elsewhere that it may
vary from 0-0023 to 0-0025 normal. The value of />K/ for sea-water (I have
assumed it to be -0025 N) as determined by readings taken from McClendon's graphs
varies from 5-78 at/>H 8-oo to 6-oi at/>H 7-00, at/>H 6-oo it again changes to 5-90.
This result, to my mind, clearly shows the graphs to be erroneous and that the
errors are due to not obtaining proper equilibrium in the solutions. Legendre
(1925) has reproduced these graphs from McClendon in his book. A few pages
earlier in this book we find the Hasselbalch equation is stated but Legendre has
failed to point out that this equation will not fit with McClendon's results.
With the exceptions just referred to, my results can be shown to be in substantial agreement with those of other workers. We can derive the dissociation
constant of carbonic acid from Fig. 4 in the following manner:
(13)
Since
/.K1' = /.K1 + logF 0 (HC0 3 ')
and since the apparent activity constant may be put as equal to the real activity
constant at very considerable dilutions and further since the activity coefficient
approaches unity as the concentration approaches zero, so that, at infinite dilution
The extrapolation of the line in Fig. 4 to infinite dilution gives the value of
as being 6-52, whence kt is 3-02 x io~7 at 180 C. This is practically identical with
Walker and Cormack's average value.
For the line drawn in Fig. 4 the equation
logP1o(HCQB') = o - S 3 ^
(23)
appears to hold. We again suppose that at considerable dilution the apparent
activity coefficient is equal to the real activity coefficient. Now the logarithm of this
real activity coefficient can be represented according to Bjerrum by the expression
— )8 v c The value of /? in this expression is, according to Debye and Hiickel
for a uniunivalent electrolyte, 0-495, which is a close approximation to the value
0-530 in the equation (23) above.
SUMMARY.
1. The Henderson-Hasselbalch equation is shown to be entirely applicable to
natural waters.
2. The value of pK±' is dependent on the normal concentration of the metallic
kations present in the solution, including those derived from any neutral salts. The
relation between pKx' and this concentration can be represented by a straight line
for concentrations up to i-o normal. The equation which expresses this relation is
pKt' = 6-52 - 0-53 sfc,
c is the normal concentration of metallic kations.
3. Methods for measuring accurately the^>H by colorimetric methods are given.
From the/>H thus measured the pressure of carbon dioxide with which the solution
is in equilibrium can be calculated with great accuracy.
72
J. T. SAUNDERS
4. By combining the results obtained the pR (corrected, if necessary
error by the curve on p. 56) of a solution of bicarbonates of normal c o n c e ^ ^
(Bik) as determined by the method described on p. 51, is related to the pressure of
CO2 in mm. Hg (/>CO2) with which the solution is in equilibrium by the equation
*H = 1070-o-53*£+log-J.^-.
5. Bicarbonates are transformed into carbonates at a very slow rate when the
pressure of carbon dioxide in the solution is reduced. The slow rate at which this
process occurs accounts for many natural waters having larger amounts of calcium
and magnesium bicarbonates held in solution than can be accounted for by the
pressure of carbon dioxide with which the solution is in equilibrium.
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