Field Measurement of 

Alkalinity and pH

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1535-H
Field Measurement of 

Alkalinity and pH

By IVAN BARNES

GEOCHEMISTRY OF WATER

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1535-H

Method for determinations of pH in the 

field and of end points for alkalinity 

titrations

L S. Geological Surtey

; APR 3 0 1964

LiU

Nashville, Tennessee

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.G. 20402
CONTENTS

Page

Abstract..______________________________________________________ HI

Introduction-_____________________________________________________ 1

Materials and methods ________^______^____________________________ 1

Electrode behavior________-_____________--^________-_-______--__- 5

Bicarbonate determination...-.______________________________________ 8

References cited.__________________________________________________ 17

ILLUSTRATIONS

Page 

FIGURE 1. pH of buffer solutions as functions of temperature._________ H3

2. Histogram showing frequency distribution of pH£___________ 6

3. Plot showing random distribution of pHj vs. temperature_.._ 7

4. Linearity of pH response of electrodes from buffer comparison-. 7

5. Linear function between observed and true pH data__________ 8

6. End point of titration by two methods_____________________ 10

7. Equilibrium constants for carbonate and bicarbonate hydrolysis reactions given as functions of temperature______ 14

TABLES

Page 

TABLE 1. Suppliers of buffer solutions-____________________-___-----_ H2

2. Values of parameters for the Debye-Hiickel equation__________ 12

3. Hypothelical NaHCOa solutions__________________________ 13

4. End points for alkalinity titration______--_____----_-_------ 15

in
GEOCHEMISTRY OF WATER

FIELD MEASUREMENT OF ALKALINITY AND pH

By IVAN BARNES

ABSTRACT

The behavior of electrometric pH equipment under field conditions departs 

from the behavior predicted from Nernst's law. The response is a linear function 

of pH, and hence measured pH values may be corrected to true pH if the instrument is calibrated with two reference solutions for each measurement. Alkalinity 

titrations may also be made in terms of true pH. Standard methods, such as 

colorimetric titrations, were rejected as unreliable or too cumbersome for rapid 

field use. The true pH of the end point of the alkalinity titration as a function of 

temperature, ionic strength, and total alkalinity has been calculated. Total 

alkalinity in potable waters is the most important factor influencing the end 

point pH, which varies from 5.38 (0° C, 5 ppm (parts per million) HCOs") to 

4.32 (300 ppm HCO3",35° C), for the ranges of variables considered. With proper 

precautions, the pH may be determined to ±0.02 pH and the alkalinity to ±0.6 

ppm HCOs" for many naturally occurring bodies of fresh water.

INTRODUCTION

Accurate pH data were necessary in a detailed study of the carbonate 

chemistry of a stream (Birch Creek, Inyo National Forest, Inyo 

county, Calif.). Study of the methods and data showed that individual measurements of pH were as much as 0.5 pH unit in error. 

The large (0.5 pH) errors occurred when the sample had a pH considerably different from that of the reference (buffer) solutions. Errors 

of this magnitude cannot be tolerated when the pH meter is used to 

determine the end point of the alkalinity titration.

MATERIALS AND METHODS

The meter used throughout was a Beckman (Beckman Instrument 

Co., Fullerton, Calif.) model N pH meter. Keference electrodes 

were 5-inch fiber-wick saturated calomel electrodes having 30-inch 

leads, Beckman Instrument Co. No. 39170. Glass electrodes were 

5-inch general purpose glass electrodes having 30-inch leads, Beckman 

Instrument Co. No. 40498. Buffer solutions were obtained from the 

sources listed in table 1.

HI
H2 GEOCHEMISTRY OF WATER

TABLE 1. Suppliers of buffer solutions

pH (25° C) Supplier 

4.00±. 01 _________ _______ Beckman Instrument Co.

7.00±.02__ ______________ Do.

8.00±.02______________ Fisher Scientific Co.

The pH of each buffer is plotted against temperature in figure 1.

All electrodes were tested in the laboratory before use in the field. 

The test consisted of calibrating the instrument at pH=8.00 at 25° C 

and measuring the pH of the pH4 buffer. The pH8 buffer has a pH 

of 8.00±.02 at 25° C, and the pH4 has a pH of 4.00±.01. The 

observed pH value of the pH4 buffer (pH£) was in the range 4.00 to 4.03 

for all pairs of electrodes. The glass and the calomel electrodes were 

transported to the field in the manufacturer's original packings. 

The glass electrodes were transported dry and the calomel electrodes 

were transported with the working end covered by a rubber cap filled 

with a saturated KC1 solution. No evidence of physical damage to the 

electrodes was observed when the electrodes were unpacked for use in 

the field. All glass electrodes were soaked in water for at least two 

days before use.

The pH meter was turned on 1 hour before measurements were 

made. The meter was left on during each sampling period (24-36 

hours). The electrodes were immersed 2 to 3 inches in the stream at 

all times, except during sampling. For temperature control all 

buffers and the standard (0.01639Ar H2SO4 ) acid for alkalinity titrations were kept in plastic bottles immersed in the stream, except during 

actual use.

The following steps were found necessary for accurate pH and 

alkalinity determinations:

1. Measure water temperature with the thermometer in shade.

2. Set temperature compensator on meter to water temperature.

3. Wash electrodes in a stream of buffer whose nominal pH is near 

that of the water.

4. Immerse electrodes 1 inch in the buffer.

5. Balance and set meter at the nearest integral value of the buffer 

pH.

6. Rinse electrodes in water.

7. Collect water sample in beaker.

8. Measure the pH of the sample.

9. Pipet 50 ml of sample into dry beaker.

10. Titrate with standard acid and record pH with each increment of 

acid in the range from pH 5 to pH 4.

11. Rinse electrodes in water.

12. Wash electrodes in a stream of pH4 buffer.

13. Measure pH of pH4 buffer.
FIELD MEASUREMENT OF ALKALINITY AND pH H3 

7.20

7.10

7.00

i I I

4.00

3.90

1 I I T

5 10. 15 20 25 30 35 40 

TEMPERATURE (°C)

FIGURE 1. pH of buffer solutions as functions of temperature.

14. Replace electrodes and reagent bottles in water.

The temperature measurement (in the shade, to avoid radiant 

heating) is necessary because the pH of the buffer solutions is temperature dependent. The temperature compensator corrects the meter 

reading to the output of the electrodes which changes with tempera-
H4 GEOCHEMISTRY OF WATER

ture, but it does not correct for the changes of pH of buffers having 

changing temperature.

Rinsing the electrodes in a stream of the solution to be measured 

(steps 3, 6, 11, and 12) avoids the necessity for wiping drops of solution from the electrode tip. The glass membrane is quite sensitive 

to abrasion, and wiping the electrode with even the least abrasive 

tissue introduces needless risk of damaging the electrode. Under 

field conditions, especially when the wind is high, sand and grit may 

be unwittingly rubbed on the glass membrane if the electrodes are 

wiped. If the water is polluted, oil films and other contaminants on 

the glass electrode may require different procedures.

The electrodes are immersed in 1 inch of solution both for maximum 

accuracy of measurement and also to thermostat the electrodes.

Visual interpolation is unnecessary and increased accuracy is 

obtained if the meter is set on a scale mark. As a regular practice 

(to avoid confusion), the meter should be set on an integral pH value 

nearest the nominal pH of the buffer.

Following diurnal variations in pH requires reading the meter by 

both daylight and artificial light. Commonly accepted practices of 

instrumental measurement were used. Readings were made by daylight and by means of a flashlight and gasoline lantern at night. For 

maximum accuracy the eye, needle, scale marking, and light source 

should be in the same vertical plane; otherwise misleading shadows 

result. During daylight measurement the meter should be shaded 

for the same reason.

Measurements of pH should be made in static samples. A reproducible streaming potential corresponding to 0.10 pH unit was 

observed at a stream velocity of 1 ft per sec (0.3 m per sec). In 

systems where flow varies, streaming potentials may also be expected 

to fluctuate. In the present study the sample beaker was immersed 

in the stream for temperature control. Where it is not feasible to 

immerse samples in a reservoir of the water body being studied during 

measurements, insulated beakers or DeWar bottles are recommended. 

Temperature changes in the sample during measurement are possible 

when air temperatures are not close to water temperatures or if 

samples are exposed to bright sunlight.

It is essential to record acid volume and pH over the pH range from 

5 to 4. Until the true response of the electrodes is known, the significance of the observed pH is unknown. Owing to the changing response of the measuring system, the pH of the end point (say the true 

value is 4.5) may be indicated as any value from 5.0 to 4.5 by the 

meter. The measurement of the pHf will permit calculation of true 

pH of the water (pH£,) from the observed pH values of the water
FIELD MEASUREMENT OF ALKALINITY AND pH H5

When the electrode fails to give a stable reading, that is, when the 

meter indicates a fluctuating value for the pH of a sample, the glass 

electrode can frequently be tested by touching a finger to the barrel 

of the electrode. A large and immediate change in the indicated pH 

or a more pronounced fluctuation generally indicates the electrode is 

no longer serviceable and should be discarded. Presumably the 

electrode has become polarized, or has suffered other damage, but 

neither the exact nature of the trouble nor its causes are known. 

Attempts at rejuvenation of the electrode in the field, by either washing in acid or by cyclic washing with acid and base, have failed in 

every case to restore the electrode to proper behavior. Most glass 

electrodes are restored to their proper behavior after several 

weeks of dry storage.

ELECTRODE BEHAVIOR

Bates (1960) pointed out that the emf (electromotive force) response of many glass electrodes is a linear function of pH over the 

pH range from 3 to 10. The response is in many instances predictable according to Nernst's law, which is conveniently written in the 

form

emfa-emf& =2' 3°^r (PH<-PH£), (1)

where emfa and emf 6 refer to the observed potentials between the glass 

and reference electrodes in samples a and b respectively, and R is the 

gas constant (8.31439 abs j per deg mole), T is the temperature in 

degrees Kelvin, F is the Faraday (96, 484 abs coulombs), and pH^ 

and pH£ are the true pH values of solutions a and b respectively. 

The above equation reduces to

emfa-emf6=0.19845T(pH^-pHi) (2)

where the emf is in millivolts. Perfect electrodes would yield a 

particular emf for a particular true pH. The lack of pH' predictability of the emf for electrodes at a particular true pH is evidenced 

by the calibration procedures recommended by instrument manufacturers. The calibration procedures merely fix emf6 as a convenient 

function of pH£, where emf6 refers to the emf between the glass and 

reference electrodes in a buffer b, and pH£ is the true pH of buffer b. 

The uncertainty of emf 6 as a function of pH£ in no way invalidates the 

Nernst law, but it does require a calibration procedure if pH' values 

are to be read directly.

The Nernst law not only specifies a linear relation between observed potentials and pH, but it specifies the slope of the function be 

0.19845 T. The slope of the function was tested in 60 samples by 

measuring the pH of the pH4 buffer (pH|) after setting the meter at

705-991 63 2
H6 GEOCHEMISTRY OP WATER

pH=8.00 for the pH8 buffer. The frequency distribution of pHt 

values is shown in figure 2. The possibility that the variation of 

pH| will be affected by temperature is negated by the clearly random 

data of figure 3, which shows no relation between pH| and temperature. 

In one instance the pH of the pH4 and pH7 buffers was measured 

after calibration at pH=8.00 for the pH8 buffer, as shown in figure 4. 

If pHl, pH^, pH|, pH|, and pH? are known and if it is assumed that 

the pH response of the measuring system is a linear function of pH, 

pHr may be calculated. The known value of pH| of 7.03 may be 

compared with the calculated true value of 7.02. It was concluded 

that the pH response of the electrodes over the pH range from 4 to 

8 was linear.

12

10

4.0 4.1 4.2 4.3 4.4 4.5

FIGURE 2. Histogram showing frequency distribution of pHJ.

The relationships used for computing pH* from pH° are illustrated 

in figure 5. From the general form of the function

(3)

(4) 

-pHl)- 1 , (5)

and a knowledge that the slope (s) is given by

pH«-pHS_pH8-pHS

it may be shown that
FIELD MEASUREMENT OF ALKALINITY AND pH H7

4.5

4.4

4.3

4.2

4.1

4.0

10 12 14 16 18 20

TEMPERATURE (°C) 

FIGTIEE 3. Plot showing random distribution of pHj vs. temperature.

FIGTIEE 4. Linearity of pH resporWof electrodes from buffer comparison. Data collected 11:55 a.m 

(Pacific daylight time), June 5,r1961, Birch Creek, Inyo County, Calif. Temperature, 18° C.
H8 GEOCHEMISTRY OF WATER

where pH£, and pH£ are, respectively, true and observed pH values 

of the water sample. If some other buffer solution had been used 

rather than the pH8 buffer, substitution of pH£ and pHg for pH| and 

pH| would be appropriate. It is essential that pHf, be known at the 

temperature of the water sample. Buffers whose true pH is known 

over a range of temperatures are available commercially or may be 

prepared by the user. Bates (1960) gives data on primary reference 

buffers.

ft:

o.

FIGURE 5. Linear function between observed and true pH data. 

Data collected 8:56 p.m. (Pacific daylight time), June 5,1961, 

Birch Creek, Inyo County, Calif., temperature, 12.5° C.

BICARBONATE DETERMINATION

The bicarbonate titration may be expressed by

HCO3-+H+=H2CO3 . (6)

The titration may be to either a potentiometric or colorimetric end 

point. Colorimetric end points are convenient for field use but are 

of questionable accuracy due to wide variation in illumination and to 

fatigue of the investigator. Observations of potentiometric titrations should not be affected by light conditions as long as graduations 

on the meter are visible, and because they are less subjective than the 

observation of a colorimetric end point, the potentiometric end points 

are less affected by the fatigue of the operator, unless rapid repetitive 

measurements are required.

It has been shown in the preceding discussion that the observed 

(pH°) and the true (pH') pH values do not necessarily agree, and that 

the difference is a random one. Were the differences between pH° 

and pH' either constant or systematically distributed, a single calibra-
FIELD MEASUREMENT OF ALKALINITY AND pH H9

tion or set of calibrations would suffice to define the end point in 

terms of pH°. It is necessary either to obtain the end point in terms 

of true pH values or to determine a titration curve for the end point 

of each alkalinity titration. Experience has shown that it is not 

economical to determine titration curves hourly. The briefer the 

time for the determination of each variable, the more time is available for other observations. The end point of the titration was 

determined in terms of true pH values as shown below. The relationships derived permit calculation of the true bicarbonate content 

of waters in the office and permit full utilization of field time for 

observations.

End points of potentiometric titrations usually are determined 

either by picking the maximum slope from a plot of emf vs. titrant

volume or by plotting A ,. ' - against total titrant and choosing J * & A titrant &

the maximum in this curve as the end point (fig. 6). The discrepancy 

between the two methods in the end-point determination is due to 

large increments of acid and represents 6.8 ppm (parts per million) 

HCOs- The results given in figure 6 are typical for field titrations 

where the true pH is not directly measured and emphasize the need 

for several pH-titrant volume data for each titration. The discrepancy could be decreased by assuming .^ - to be constant over A titrant

each A pH, but the slope is obviously not constant and the reliability 

of such a "correction" is questionable. The inconstancy of the 

measuring system precludes a prior knowledge of the end point and 

does not permit a predetermined schedule of increments of titrant to 

educe A titrant near the end point. Regardless of which method is 

used to determine the end point of the titration, the criterion for the 

end point is that the rate of change of pH with increment of acid be a 

minimum.

The true pH for the bicarbonate end point can be readily calculated 

for any set of conditions which may be of interest. The following 

calculations make allowance for the effect of total concentration of 

carbonate species (H2CO3 , HCOjT, CO2 (aq) and COs 2), ionic strength 

(salt effect), and temperature.

Two sets of end points were calculated, on the basis of two different 

assumptions. The first assumption (case 1) was that there was no 

loss of CO2 from the sample. Case 1 would correspond to a rapid 

titration with minimal stirring and a restricted access of the atmosphere to the surface of the solution. The second set of calculations 

(case 2) was made on the assumption that the sample was always in 

equilibrium with the partial pressure of COg (Pco2 ) of the normal 

earth's atmosphere (PCo2 =10~3>6 atm) at the temperature of the solu-
mo GEOCHEMISTRY OF WATER

6.00

5.50 -

5.00 -

4.50 -

4.00

-3

5 -2

10.0 11.0 12.0 13.0 14.0 

TITRANT VOLUME/IN MILLILITERS

FIGURE 6. End point of titration by two methods. Data collected 2:45 p.m. (Pacific daylight time), May 26,1961, Birch 

Creek, Inyo County, Calif.

tion. Such an equilibrium could be maintained by slow titration and 

rapid stirring and by bubbling air through the sample. 

For the assumption that no CO2 is lost,

where 

Differentiating

From the reaction

From the reaction

is a constant.

0 =

H++HC03-=H2C03 ,

H++CO-«=HCO-,

(7)

(8)

(9)

(10)

(11)
FIELD MEASUREMENT OF ALKALINITY AND pH Hll

z dmco- 2 . (12)

From the reaction

H++OH-=H2O, (13)

(draH+)3= dra0H-- (14) 

If the increments of mH+ are added,

+) 2 + (dra +)/+ (dmn+) a , (15)

where

r is the total H+ added

(dmH+)/ is the increase in free H+. 

From the functional definition,

(16)

and

aH+ =10-pH . (17)

From the equilibrium constants,

(18)

and

WHCOrTHCOjT m°°; K^^ 10DHNow

wHco;"7Hcor 

^=g1 10-pHmHco-37Hco3- + g^ 10pH +mHco3-, (20)

and it follows that

The activity coefficient for H2CO3 may be estimated from the data 

cited by Harned and Owen (1958) on their page 736 and the equation cited on their page 532. The salting coefficient was estimated 

to be 0.06 at 25° C. The maximum ionic strength considered in this 

paper is 0.01. Substituting in the equation,

log 7H2C03 =&mM (22)

where km is the salting coefficient, and

7H8co3=1.001. (23)
H12 GEOCHEMISTRY OF WATER

The assumption

WH2C03 =«H2C03 (24)

is seen to be correct to within 0.1 percent at 25° C. The assumption 

will be made throughout the following calculations.

Activity coefficients of ionic species were calculated from the DebyeHuckel limiting law in the form

1/2

where

7i is the activity coefficient of species i,

z is the charge on the iih species,

A and B are functions of temperature,

a,i is the effective ionic diameter in angstroms.

Values of A and B used in the computation were taken from Klotzj 

1950, p. 330, as shown in table 2.

TABLE 2. Values of parameters for the Debye-Huckel equation

Temperature (°C)

0... _ . __ ... _ . _____ . __ ..... ___ .. __ .. .......

5-... ___ ..................... _ .... _____ ... _____ . ...

10 ._ 

15...... __ ......... _ ................ ______ ...........

20. ___ . . ............... ___ .... 

25...... .......... . _. ...... ..

30 ........... ._ . 

35.. ____ .... ______ . _ ......... _ . ___ .............

A

0.4883

.4921

.4960

.5000

.5042

.5085

.5130

.5175

B

0. 3241

.3249

.3258

.3266

.3273

.3281

.3290

.3297

The values of at were 4.0 for HCO3 . and 4.5 for CO3 2 Values for the 

equilibrium constant

from the work of Harned and Davis (1943) and

from Harned and Scholes (1941) are given in fig. 7. 

For the hydrolysis of water,

H2O=H++OH-

(27)

(28)

(29)
FIELD MEASUREMENT OF ALKALINITY AND H13

Values of Kw were those of the International Critical Tables as reported in Dorsey, 1940, p. 378. From 29, above,

From equation 17,

. (30)

(mH+),=10-pH (TH+)- 1 . (31) 

A description of the hypothetical solutions is given in table 3.

TABLE 3. Hypothetical NaHCO3 solutions

Total carbonic species as HCO3 (ppm)

5 

10-.. _ 

60 

100 

160 

200.- _ . 

250-- _ 

300- _ _ ... 

m

8. 2yiO-«

1 *uvin-4

8. 20X10-*

1. 64X10-*

2. 46X10-*

3. 28X10-'

4 11X10"*

Lowest 

possible 

ionic 

strength 0«)

8.2X10-'

1. 64X10-*

8. 20X10-*

1. 64X10-*

2. 46X10-*

3. 28X10-*

4. 11X10-*

4. 92X10-*

The calculated end points in table 4 are for titrations undertaken at 

0°, 5°, 10°, 15°, 20°, 25°, 30° and 35° C. A similar set of calculations was made for an ionic strength of 0.01 (0.01m for 1:1 salts) 

to determine the effect of different concentrations of neutral salts on 

the end point.

For case 2, changes in WHCO- can occur through the reaction

HC03- +H+=H2O-f CO2 (32) 

 (droHco3-)i=(dmH+)i (33) 

and from the reaction

CO3-2+H+=HCO3- (34)

(dmH +)2= (dmco- 2) = (^wHCo3-)2 . (35)

Changes in concentration of total bicarbonate may be computed from

(dmHCO-) T= (dmHco3-)i+(dmHco£-)2. (36)

The total increment of H+ is

dmQn-. (37)
H14 GEOCHEMISTRY OF WATER

6.30 6.40 6.50 6.60 6.70 6.80

10.00 10.10 10.20 1030 10.40 10.50 10.60 10.70

0.00320

FIOUEE 7. Equilibrium constants for carbonate and bicarbonate hydrolysis reactions given as functions ol 

temperature. Data for K\ curve from Earned and Da vis (1943, p. 2030); data for K% curve from Hamed 

and Scholes (1941, p. 1708).
FIELD MEASUREMENT OF ALKALINITY AND 

TABLE 4. End points for alkalinity titration

H15

Total carbonic 

species as

HCOg (ppm)

Case 1: 

5 

10 -

50 

100 

160 

200- 

250 

5 .

10 

50 

160 

200 

260 

300- - 

Case 2-. 

Ionic strength

A*

8.2X10-' . 

1.64X10-4 

8.20XKH 

1.64X10-3 ..

2.46X10-3 -- ... 

3.28X10-3......

4.11X10-3 

4.92X10-' ...

.01 

.01 

.01- 

.01 

.01 

.01 .

.01--- 

.01 - 

Lowest possible value 

(see table 3). 

.01 

End points at temperatures (°C) indicated 

35

5.27 

5.10 

4.72 

4.56 

4.47 

4.40 

4.35 

4.31 

5.28 

5.10 

4.71 

4.55 

4.47 

4.41 

4.35 

4.32 

5.68 

5.68

5.68

30

5.28 

5.10 

4.72 

4.57 

4.48 

4.42 

4.36 

4.33 

5.28 

5.10 

4.72 

4.57 

4.47 

4.41 

4.36 

4.32 

5.66 

5.66

5.66

25

5.29 

5.11 

4.73 

4.58 

4.49 

4.42 

4.37 

4.33 

5.30 

5.12 

4.73 

4.57 

4.48 

4.43 

4.37 

4.33 

5.65 

5.65

5.64

20

5.30 

5.13 

4.75 

4.59 

4.50 

4.44 

4.39 

4.34 

5.30 

5.13 

4.75 

4.59 

4.50 

4.43 

4.39 

4.34 

5.63 

5.63

5.63

15

5.32 

5.15 

4.77 

4.62 

4.52 

4.46 

4.41 

4.36 

5.32 

5.15 

4.77 

4.61 

4.52 

4.46 

4.41 

4.36 

5.62 

5.62

5.62

10

5.34

5.16 

4.78 

4.63 

4.54 

4.48 

4.43 

4.39 

5.34 

5.16 

4.79 

4.63 

4.54 

4.48 

4.42 

4.39 

»5.61 

15.61

5.60

5

5.36 

5.19 

4.81 

4.65 

4.56 

4.50 

4.45 

4.41 

5.36 

5.19 

4.81 

4.66 

4.56 

4.50 

4.45 

4.41 

5.59 

5.59

5.59

0

5.38 

5.22 

4.84 

4.69 

4.60 

4.53 

4.49 

4.44 

5.39 

5.22 

4.84 

4.69 

4.59 

4.53 

4.48 

4.44 

2 5. 58 

'5.58

5.58

1 For HCOj>150 ppm, 5.60.

2 For HCO^=50 ppm, 5.59.

Substituting bicarbonate changes,

and the carbonate change,

Substituting dmco -* for 

carbonate changes,

Combining the last two equations,

Let

Values for (mHco3~)r may be computed from

£10PH

, (38)

-). (39) 

in the equation for total bi-

(dmco- 2) . (40)

(41)

(42)

(43)
H16 GEOCHEMISTRY OF WATER

and values for mCQ- 2 from

102PH5 

=

TC0

/AA\ (44)

Titration curves were again computed for pH increments of 0.01 pH. 

In both sets of titration curves the criterion for the end point was 

that

be a minimum. The results of the computation are given in table 4.

The data in table 4 show that the end point varies no more than 

0.04 pH unit over a 5° C temperature interval. A deviation of 2.5° C 

from the assumed temperature should introduce no more than a 0.02 

pH unit error in the end point. The salt error or effect of ionic strength 

is no greater than 0.01 pH unit over the range considered, to as much as 

580 ppm (as NaCl) . Hence any ionic strength in that range (8.2 X 10~5 

to 0.01) may be assumed without introducing more than 0.01 pH 

unit error, or a total error (temperature and ionic strength) of 0.03 

pH unit for the end point. Although temperature and ionic strength 

have relatively minor effects, both the amount of bicarbonate present 

and the extent to which carbon dioxide may be lost from the system 

during titration influence the pH at the end point substantially. 

In case 2 titrations, the initial amount of bicarbonate present is a 

minor factor.

Several obvious methods of determining the end point for a particular solution suggest themselves. The most obvious is to plot a 

part of the titration curve as true pH vs. HCOJ, that is, plot pH 

against equivalent HCO^" for the titrant acid. Plot on the same scale 

the data from table 4 for the nearest temperature. Overlay the 

curves. Their intersection is the end point having a maximum error 

of 0.03 pH unit in the computed end-point. Errors in the measured 

pH, of course, lead to greater errors hi the end point pH. End points 

so obtained should be accurate enough for most work.

The end points thus calculated are in terms of true pH. The nonideal behavior of the electrometric system used gives rise to a problem 

in approaching the end point of the titration. If the emf-pH function 

departs appreciably from Nernst's law, the true pH cannot be obtained 

by inspection of the observed pH data without a knowledge of the 

extent of the departure. To determine what effect the uncertainty 

of true pH during titration would have on the bicarbonate determination, plots were made of pH1 against the number of milliliters of 

standard (0.01639N H2SO4) acid. For the 21 samples chosen, the
FIELD MEASUREMENT OF ALKALINITY AND pH HIT

bicarbonate concentrations ranged from 140 to 260 ppm. The average 

slope was 0.550 ml/pH, over the pH range from 4.1 to 5.1. It is of 

interest to note that straight lines could be drawn through the points 

which represented the data for each titration to within ±0.03 ml of 

acid. The maximum slope was 0.855 ml/pH and the minimum 

 0.333 ml/pH. In consequence, if enough points (preferably 3 or 

more) are available between a pH of 4.1 and 5.1, interpolation as to 

the number of milliliters of acid at the end point can be within ±0.03 

ml of acid. For the acid used,

ppmHco-=20Xml acid, (45)

hence the interpolated end point is within ±0.6 ppm HCO^" for the 

samples used. For 20 of the 21 determinations, straight lines could 

be drawn giving the number of milliliters of acid to within ±0.02 

ml acid or ±0.4 ppm HCOJ. The interpolation of acid-pH data to the 

correct end point would seem sufficiently accurate for most purposes.

The problem remains to obtain true pH data sufficiently close to 

the end point to warrant an interpolation. A suggested procedure is 

use of a color indicator to show when the end point is being approached. 

Data could then be recorded in the vicinity of color change. The pH 

data would then be converted to true pH and used to interpolate to a 

correct end point for maximum accuracy, if the suggested calibration 

procedure with two reference solutions is followed. For field use, 

indicators having sharp color changes such as methyl purple should 

be used in view of the variable light conditions.

REFERENCES CITED

Bates, R. G., 1960, Electrometric pH determination: Chimia, v. 14, p. 111-126. 

Dorsey, N. Ernest, 1940, Properties of ordinary water substance: New York,

Reinhold, 673 p. 

Harned, Herbert S., and Davis, Raymond, Jr., 1943, The ionization constant of

carbonic acid in water and the solubility of carbon dioxide in water and

aqueous salt solutions from 0° 'C to 50° C: Am. Chem. Soc. Jour., v. 65, p.

2030-2037. 

Harned, Herbert S., and Owen, Benton B., 1958, The physical chemistry of

electrolytic solutions: 3d ed., New York, Reinhold, 803 p. 

Harned, Herbert S., and Scholes, Samuel R., Jr., 1941, The ionization constant

of HCOJ from 0 to 50° C: Am. Chem. Soc. Jour., v. 63, p. 1706-1709. 

Klotz, Irving M., 1950, Chemical thermodynamics: Englewood Cliffs, N.J.,

Prentice-Hall, 369 p.

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