The Determination

of the Hydrogen Ion Concentration of Inland Lake Watersl).

BY

Stephen Freeman, V. W. Meloche and Chancey Juday. University of Wisconsin. With 3 figures in the text

Introduction.

Observations on the hydrogen ion concentration of the waters of the inland lakes of Wisconsin have been made for a considerable number of years by the Wisconsin Geological and Natural History Survey. Previous to the summer of 1932, the regular pH readings were taken only by colorimetric methods. In the course of these studies, it was observed in many cases that somewhat different results were given by two overlapping indicators when used on the same sample of water; this was true particularly of the samples of soft water lakes, that is, those whose waters held only small amounts of dissolved material in solution. It was noted also that pH values determined colorirnetrically often digered from those obtained electrometrically and from those calculated on the basis of the carbon dioxide titrations.

In the light of our present knowledge, the anomalous results ob- tained on these soft waters do not seem unusual. F a w c e t t and A c r e e (1929), A c r e e and F a w c e t t (1930), and K o l t h o f f (1931), in their studies of the colorimetric determination of hydrogen ion concentration of weakly buffered solutions, have shown that the results will be in error unless the indicator is specially adjusted for each individual case. The pH readings of these lake waters were made in a summer field labora- tory, or sometimes on the shores of the lakes from which the samples were taken, so that it was not convenient to use adjusted indicators for each of the samples examined, especially since the various waters had such a wide range, varying from pH 4.4 to pH 9.4. It was thought

l ) This investigation was made possible by a grant from the University Research Allotment of the University of Wisconsin.

The Det,ermination of the Hydrogen Ion Concentration 347

clesirable, therefore, to carry out some experiments with an electro- metric method adapted for field determinations.

A more precisemeasurement of the pH made i t necessary to use a, cell in which the sample was exposed to the air as little as possible; that is, the pH would change if the water absorbed or lost carbon cli- oxide by such an exposure during the measurement. This also raised the question whether a sample could be taken from the deep water a t a low temperature, raised to the surface, and the pH determined without introducing an appreciable error. In orclinary solutions, the change in temperature has only a relatively small effect upon the pH providing the value is in the acid range. The weakly buffered lake waters, however, contained varying amounts of carbon dioxide and there was no assurance that the equilibrium of this gas remained un- disturbed \Then the temperature and pressure were changed by brin- ging the sample to the surface.

After considerable experimentation, a quinhycirone-calomel cell was designed which made it possible to take the pHreadings in situ, that is, a t different depths without bringing the samples to the surface. The purpose of the present paper is to describe and illustrate this cell and to compare some of the results obtained by means of this instrument with (1) those yielded by the Youden quinhyclrone-calomel cell on samples brought to the surface for the readings and (2) those calculated from the carbon dioxide titrations.

The Deep Water Quinhydrone Half-Cell. The various parts of the quinhydrone half-cell are shown in Fig. 1.

The low-er part of the cell consists of a hard rubber cylinder which contains a piston chamber, an electrode compartment ( B ) with a platinum disk in it, and a qninhydrone compartment ( A ) . The elec- trode is connected with one strand of the copper wire in the rubber covered cable by means of a platinum mire; the other end of this copper wire is attached to the reading instrument in the boat. The joint between these two wires must be covered very carefully so that water will not penetrate the covering even when the cell is lowered to consi- derable depths. The hard rubber tube which covers the joint prevents seepage by pressure on the rubber gaskets. Note also that the length of the platinum wire removes the soldered joint so far from the cell (B , Fig. 1) that the water does not penetrate the beeswax- rosin filled channel.

348 Stephen Freeman, V. W. Meloche and Chancey Juday

The piston of the cell is operated by means of a 450 gm. lead weight. The lead weight is attached to the end of a calibrated sounding line, which shows the depth of the cell a t the time the reading is taken, and

Fig. 1. Diagram of the deep water quinhydrone half-cell.

Fig. 2. Diagram of the sa- turated potassium chloride-

calomel half -cell.

/ B

Fiatinurn Dirk

Fig. 2

it is also fastened to the piston rod of the cell by means of a small line about 20 cm. long. Thus by raising or lowering the sounding line about 30 cm. while the cable is stationary, the weight is transferred to the piston or to the sounding line as desired.

In lowering the cell, the weight is borne. by the sounding line. When

the cell has been lowered to the desired depth, the cable is held at this depth and the sounding line is lowered about 30 cm. further, thus transferring the weight to the piston; the weight pulls the piston down and a sample of water is drawn into the cell at A (Fig. 1). In this chamber ( A ) , the water passes through a small sack of quinhydrone, is saturated, and then passes into the electrode compartment ( B ) . The pH reading is then taken and the used sample is removed by

Fig. 1.

The Determination of the Hydrogen Ion Concentnation 349

raising the sounding line until it supports the lead weight; this per- mits the spring on the piston rod to force the piston up and thus push the water out of the cell.

The Saturated Potassium Chloride-Calomel Half-Cell. The potassium chloride-calomel half-cell was constructed from a

glass tube 12 cm. by 2 cm., with a platinum foil sealed through the closed end and the open end fitted with a groundglass stopper. (See Fig. 2.) Byelec- trolyzing the foil on the inside of the cell in mercurous nitrate solution, the foil was so completely wet with mercury that very little free mercury was required in the cell. Pure calomel was ground into saturated potassium chloride solution and about five grams of the paste were placed in the cell. The remaining space was filled with a saturated solution of potassium chloride and the ground glass stopper was inserted, care being used to exclude the air. A piece of tape was placed over the protru- ding end of the glass stopper to hold it securely in position. The platinum connec- tion of the calomel cell was soldered to the strand of copper wire drawn from the rubber covered cable about 30 cm. above the quinhydrone cell connection. The slit in the cable from which the wire was taken for the calomel cell, was filled with be- eswas-rosin cement and then covered with rubber tape as shown in Fig. 3. I n order to strengthen the soldered joint a t the

Fig. 3. The two half-cells and calomel cell, it was also covered with a their when ELssem- liberal coat of beeswax-rosin cement. bled for D~ reaclings

- * .+

(See Fig. 2.) This was then covered with okonite rubber tape.

In order to protect the calomel cell, it was fastened by a strip of tape to the quinhydrone cell in such a manner that the glass stopper was as close as possible to the intake ( A ) of the qiunhydrone cell.

at various depths.

350 Stephen Freeman, V. W. Meloche and Chancey Juday

Placing the two electrodes close together decreases the water gap between them and thus increases the sensitivity of the apparatus. Fig. 3 shows how the two cells are attached to each other and their connections with the cable.

The Cable. The two half-cells are connected to 60 m. of rubber coated ‘<18-2”

Tirex, cable which has two independent, insulated copper wires, one for the quinhydrone and the other for the calomel half-cell. Tests which were conducted in the laboratory, using buffer solutions of knownpH, showed that the potential drop along the cable was negli- gible as far as our measurements were concerned.

Measuring Apparatus. The measuring apparatus includes a standard Leeds and Northrup

potentiometer, a four dial resistance box, and a Leeds and Northrup galvanometer, No. 2420 C, whose sensitivity is 0.026 ma/mm. division. In determining the voltage of the deep water cell, a 2 micro farad con- denser was connected across the poles of the cell. It should be noted that, while we used a separate standardized portable set for the elec- trometric determination of pH on the samples brought to the surface, it is possible to use the same potentiometer that is used for the deep water cell by merely changing the connections. The potentiometer was mounted on a board so that it could be handled conveniently in a boat. The excess cable for the deep water cell was stored on a reel. I n our fist attempts to make measurements in a boat, a support free froin vibration was provided for the galvanometer, but this proved to be unnecessary; the heavily laden boat had little motion when the oc- cupants were quiet.

Procedure With The Deep Water Cell. fresh sack of quin-

hydrone is placed in the half-cell a t A , Fig. 1, and the whole cell is lowered to the desired depth, supporting the weight of the lead and the cell upon the calibrated sounding line. The cable is then made fast to the boat so that the cell remains a t the desired depth. The sounding line is lowered until the lead weight is supported by the cable; this transfers the weight to the piston rod of the cell, thus de- pressing the piston and drawing a sample of water into the electrode compartment (Fig. 1, B). In order to displace the air, it is advisable to

To make a reading with the deep water cell,

The Determination of the Hydrogen Ion Concentration 351

flush the cell a t least twice before making a reading. The flushing should be done slowly in order to avoid using too much quinhydrone in the process.

The potentiometric circuit is now balanced against the standard cell and then is balanced against the unknown cell. In determining the E. M. F. of the cell, the null point was approached from both sides and the average reading recorded. This was necessary because the water, in most cases, had comparatively small amounts of dissolved substances in solution and the sensitivity of the apparatus was cor- respondingly low.

A reversible thermometer is lowered with the cell so that the tem- perature may be recorded for each sample examined. A temperature correction is included in calculating the pH from the observed E. M. F. of the deep water cell according to the following equation of K o l t - hoff (1931, p. 103):

0.4532 - 0.00009 (t - 26) - E pH = 0.0591 + 0.0002 ( t - 25)

The capacity of the quinhydrone compartment is such that a num- ber of readings can be made with the deep water cell before it is ne- cessary to haul the apparatus to the surface and place another sack of quinhydrone in the chamber.

Other Determinations.

Two determinations of pH were made a t the surface; one was a reading with a Youden portable qninhydrone-saturated calomel cell and the other was a titration of the free and bound carbon dioxide with the subsequent calculation of. t,he pH according to the following equa- tion of K o l t h o f f (1926, p. 192):

x 3 x lo-' when the carbonic acid concen- [COJ [HCO,-] 1. [ H + ] =

tration was not less than 'Ilo of the bicarbonate concentration. When the carbonic acid concentration was less than 'Ilo of the bicarbonate concentration, the corrected equation was used.

Free CO, = b Bound COz x 2 = a [HCO;] = O.9S8a (Substitute in equation 1). [CO,] = b + a x 1.2 x lo-, (Substitute in equation 1).

352 Stephen Freeman, V. W. Meloche and Chancey Juday

The corrected values allow for the hydrolysis of the bicarbonate which tends to predominate when the bound CO, is high.

For these determinations, the water was obtained by means of a water sampler. The sample was transferred to the Youden cell (8 cc. capacity) or to the titration flask with as little contact with the air as possible. To facilitate the examination of the water in the Youden cell, a small portion of quinhydrone was placed in the empty cell, the water was transferred directly from the sampler to the cell, the elec- trodes were placed in it, and the reading was taken almost imme- diately. A short time may be allowed for the sample to come to the normal surface temperature. Since the stopper holding the electrodes closes the top of the small cell, the sample is not in contact with the air.

A convenient routine which provides a maximum number of read- ings in a short time is as follows : Lower the deep water cell and adjust it at the desired depth; lower the thermometer to the same depth and then, while these two instruments are coming to equilibrium, bring the sample to the surface for the measurement with the Youden cell and for the titration of the free and bound carbon dioxide. By the time these three determinations are completed, the thermometer and the deep water cell will be in temperature equilibrium with the water at the selected depth and their readings may be taken.

Results. The following table includes pH results obtained by using the three

1. By the deep water quinhydrone-calomel cell. 2. By a Youden portable quinhydrone-calomel cell, samples brought

3. By calculation from free and bound carbon dioxide titrations on

The pH values reported in Table I for Muskellunge, Trout and Men- dota were all obtained on the same day; those taken with the deep water cell on Lost Canoe, Silver, and Weber lakes were secured some time after the other two types of measurements were made, as indi- cated in the table.

Under field conditions, variations of 4- 0.1 pH unit may be ex- pected, so that the results presented in Taxle I seem quite acceptable.

methods already described, namely :

to the surface for the readings.

samples brought to the surface.

The Determination of the Hydrogen Ion Concentration

T a b l e I. Results obtained by the three different methods used for the pH determinations in the summer of 1932. Lake Mendota is located at Madison, Wisconsin, while the other five lakes, which have much smaller amounts of electrolytes in solution, are situated in the High-

land Lake District of northeastern Wisconsin.

353

7.8 7.9 8.0 7.7

6.9 6.7 6.6 -

-

Lost Canoe Lake

meters

7.8 7.7 7.7 7.8 7.1 6.9 6.8 6.6 6.6

0 3 5 6 7 8 9

10 11

0 3 5 8

10 11 12 15 19

21.6 21.5 21.2 20.3 18.1

1 14.8 12.1 9.8 9.0

21.3 21.3 21.3 20.7 14.5 13.8 12.0 10.5 10.1

Aug. 27 Aug. 3

7.9 8.2 8.2

7.0 6.7 6.4 6.5 6.3

-

Silver Lake Aqg. 27

0 3 5 8

10 12 15 18 18.8

_____

21.0 21.0 21.0 20.1 10.1 8.7 7.2 6.8 6.e

7.9 7.9 7.7 7.8 7.9 7.3 6.8 6.6 6.6

Aug. 25

Calculated from CO,

7.8 7.8 7.8 7.8 7.3 7.0 6.7 6.7 6.6

- 8.0

7.5 6.7 6.5 6.4 6.5 6.4

r r 1 . 1

8.0 8.0 8.0 7.6 6.9 6.7 6.6 6.6 6.6

Aug. 13

7.6

7.9 7.7 7.9 7.1 6.9

-

- -

7.6

7.7 7.9 7.6 7.3 6.9 6.6 6.6

-

354 Stephen Freeman, V. W. Meloche and Chancey Juday

Depth in meters

0 5

10 15 20 25 30 32

T a b l e I, continued. Trout Lake Aug. 22

Temperature c . Deep water

cell

20.7 8.3 20.6 8.1 15.5 7.6 8.6 7.5 7.9 7.1 7.4 6.7 5.2 6.7 5.0 6.7

Youden cell

8.3 8.1 7.6 7.5 i. 1 6.7 6.7 6.7

Calculated from CO,

7.8 7.8 7.7 7.3 7.1 6.9 6.7 6.7

Weber Lake Aug. 25 Aug. 23

0 21.6 5 21.3

10 ' 16.8

12 1 14.8

6.5 6.1 6.2 6.2

6.9 6.1 6.1 5.9

6.9 6.3 6.2. 5.9

Lake Menclota Pc3pt. 26

0 5

10 14 15 17 19 20

17.9 17.9 17.9 17.9 15.2 13.0 -

I 12.2

- 8.1 8.1

7.5 7.5

7.4

-

-

8.2 8.2 8.2

7.5

7.4 7.3

-

-

Since the results obtained by these three methods show fair agreement, it may be concluded, even from these preliminary experiments, that a reasonably precise determination of the pH of these poorly buffered waters may be secured by bringing the samples t o the surface and making the readings in the boat with a portable quinhydrone-satu- rated calomel system. The electrometric methocl seems to be more reliable than the titration method because one encounters variable lighting conditions in the field which interfere with the uniform cleter- mination of the end points in the titration of the free and bound carbon dioxide. If the water is taken to the laboratory for the titrations, two transfers of the sample are involved, one from the water sampler to

The Determination of the Hydrogen Ion Concentration 355

the container and the other from the container to the titration bottle, so that the chance of gaining or losing carbon dioxide is increased.

No difficulty whatever was experienced in operating the deep water cell a t 32 m. in Trout Lake, which was the deepest lake available a t the time these experiments were in progress. Since the temperature of the water a t this depth was only 7.0", the deep water cell was lowered to this point and allowed t o remain there while the other tm-o types of measurements were made. I n order t o be sure that the cell had come to a temperature equilibrium, two check determinations were made; since they showed a close agreement, it was assumed that the cell had become constant.

J u d a y , F r e d , and Wilson (1924) studied the hydrogen ion con- centration of the water of Lake Mendota from 1919 to 1922, inclusive. The results which they record from the lower water during the latter part of September agree closely with those obtained by electrometric methods on this lake on September 26, 1932, but the upper water was the more alkaline in the earlier observations.

When the present investigation was first undertaken, a quinhydrone- calomel system was designed in which the calomel half-cell was moun- ted in the boat with the potentiometric equipment. The half-cell was connected to the surface of the water by means of a salt bridge ; only the quinhydrone half-cell was lowered to the depths a t which measure- ments were to be made. Consequently there was a high resistance water gap between the two half-cells and the sensitivity of the system was so low that it was necessary to use one stage of amplification in order to make voltage determinations possible. This system was aban- doned as soon as the present calomel half-cell was developed. When the calomel half-cell is lowered into the water with the quinhydrone half-cell according to present technique (Fig. 3), only a small water gap exists between the two half-cells and the sensitivity of the system is greatly increased.

Although the deep water cell was thoroughly tested in the labora- tory, certain difficulties were encountered when the apparatus was used in the field. Particularly on humid days, a film of moisture collec- ted on exposed switches causing leaks and giving discordant results. It, has been mentioned that connecting the conclenser across the two wires from the cell increases the sensitivity of the system; unfortu- nately this also increases the effects of the leaks. The difficulty may be eliminated, however, by enclosing the switches in a moisture proof box.

356 Stephen Freeman, V. W. Meloche and Chancey Juclay

Another type of leak is that caused by the pressure of the water at the various depths on the joints between the cable and the two half- cells. The special hard rubber joint on the quinhydrone half-cell eli- minated this source of trouble from that cell. In the case of the calomel cell, the beeswax-rosin cement used to cover the platinum-copper junction offered only temporary protection. This cement is used to cover the platinum-copper connection of the present calomel cell in order to make the joint more rigid. This joint, as well as the point at which the rubber insulated copper wire enters the cable, is well co- vered with okonite rubber tape as an additional protection against water leaks.

When the water sample is drawn into the quinhydrone half-cell, the water must be saturated with quinhydrone ; this material is placed in small cotton sacks in order to prevent the loss of the crystals when the cell is flushed.

In selecting the saturated calomel-quinhydrone combination for the deep water cell, the effect of temperature change is eliminated to a large extent, since the temperature coefficient for this system is quite small. The following data illustrate this point.

Table 11. Temperature effect on quinhydrone-calomel system.

Depth 8 m. 10 m. Temperature 14.8" 9.8" Observed E. M. F. + 0.047 + 0.060 pH at 25" 6.9 6.7 pH corrected 6.9 6.6

The term "soft water" has been used to indicate the relative hard- ness of the waters examined in this investigation. The following typi- cal analyses are presented in Table I11 in order to give a clearer idea of the problems involved.

The preliminary pH results given in Table I were obtained in August and September, 1932, the first time the new deep water cell was used in the field. Certain irregularities are apparent, but some of these will doubt- less be eliminated when the apparatus is made permanently leak proof. Irregularities in the alkaline range above pH 8.5 will not be eliminated. The limitations of the quinhydrone cell in the alkaline range are well known and the system described is not recommended, therefore, for use in lake waters where the hydrogen ion concentration is above pH 8.5.

The Determination of the Hydrogen Ion Concentration 35'7

Table 111. Some analyses of the waters of the lakes on which elec- trometric pH readings were made. The minus sign in the free carbon dioxide column for the surface of Lake Mendota shows that the water

was alkaline to phenolphthalein.

Specific con-

ductance x 1 0 - 8

Carbon dioxide mgll Depth in meters

Tempera- ture ' C.

Ca mg/l

Lake

Free Bound

Lost Cano 0

5 7 8 9

10 11

21.8" 21.8 15.7 12.4 10.6 9.2 8.6

1.1 1.1 4.1 8.1

15.1 19.6 32.1

11.0 11.0 11.5 11.5 12.5 14.0 18.6

44 44

50 62

3.2

Muskel- lunge 0

5 8 9

10 12 15 19

21.3 21.3 20.7

14.5 12.0 10.5 10.1

0.6 0.6 1.6 4.1 7.6

16.1 19.6 21.4

10.0 10.0 10.0 10.0 10.0 10.0 12.0 13.5

42

42 5 1 53

2.9

Silver

T r o u t

0 5 8

10 12 15 18

21.6 20.5 20.3 11.2 8.3 7.0 6.5

2.1 1.6 0.0 2.6 5.1

14.6 27.1

16.0 16.0 16.0 16.0 16.0 16.5 20.5

60

64

7.4

0 5 8

10 12 15 20 25 30 33

20.7 20.6 20.1 15.5 10.6

8.6 7.9 7.4 7.2 7.0

1.8 1.8 1.8 2.3 5.6 7.1 9.1

11.6 14.6 16.6

19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.5 20.0 20.5

74

76

9.6

358 Stephen Freeman, V. W. Meloche and Chancey Juday

Lake

T a b 1 e 111, continued.

Specific Ca Carbon dioxide mg/l con-

Free I Bound x

Depth in Tempera- meters ture a C ductance mg/l

21.8 21.8 21.4 18.7 15.6

3 5 8

10 12

1.6 1.6 1.6 2.1 4.1

M enclota 1 2: 20.4 - 8.8 12.8 ! 14.5

2.0 2.0 2.0 2.0 2.0

66.5 cc c 41.1

9 i

Acknowledgement. The authors wish to express their appreciation for the contributions

made to this investigation by Dr. P a u l Cross and the late Professor George I. Kemmerer . The design of the present quinhydrone half- cell was first suggested by Dr. K e m m e r e r during his early studies of this problem.

Summary.

1. A deep water saturated calomel-quinhydrone cell is described by means of which the pH of lake water is determined in si tu; that is, instead of bringing the sample to the surface and transferring it to a cell in the boat or taking it to the laboratory, the deep water cell is lowered to the desired depth and the voltage is read directly on instru- ments in the boat which are connected with the cell by a cable.

2. Values obtained by the deep water cell are compared with those secured by bringing samples from various depths t o the surface with a water sampler and taking readings in the boat by

a) A portable saturated calomel-quinhydrone system, b) Titration of free and bound carbon dioxide and calculating these

results to pH by the equation given by Kol thof f . 3. The results of the present investigation indicate that the p H of

lake waters may be determined conveniently and with reasonable accuracy by a deep water cell in situ, or by bringing the sample to the surface and making the reading in the boat with a portable saturated

The Determination of the Hydrogen Ion Concentration 3359

calomel-quinhydrone system. I n the latter case, care must be used to avoid undue exposure of the sample to the air.

4. The electrometric method is more convenient than the titration of free and bound carbon dioxide for the determination of pH since variable lighting conditions in the field make the recognition of a uniform end point difficult.

5. The colorimetric determinat,ion of hydrogen ion concentration in poorly buffered lake waters is not very satisfactory unless the indi- cators are adjusted to each individual system. This quest,ion will be t.reated more fully in another report.

Literature.

Acree, S. F., and Edna H. Fawcett, The problem of clilution in colorimetric H-ion measwements. 11. Use of isohyclric inbcators and superpure water for accurate measurement of hyclrogen ion concentrations and salt errors. Ind. and Eng. Chem., Anal. Ecl. 2 (1) (1930) 78-88.

Fawcett, Edna H., and S. F. Acree, The problem of dilution in colorimetric H-ion measurements. I. Isohyclric indicator methods for accurate determina- tion of pH in very dilute solutions. J. Bacter, 17 (1929) 163-204.

Juday, C., E. B. Fred and Frank C. Wilson, The hydrogen ion concentration of certain Wisconsin lake waters. Trans. amer. micros. SOC. 43 (1924) 177 to 190.

Kolthoff, I. M., and N. Howell Furman, IncLicators. Their use in quantitative analysis and in the colorimetric determination of hydrogen ion concentration. New York 1926, 269pp.

Kolthoff, I. M., The colorimetric and potentiometric determination of pH. New York 1931, 167 pp.

In t . Revue d. ges. Hydrob. u. Hydrogr. 09.