~ ~ 

lO 

~ 

.... 

"' l 

!:;> 

""' ""' =' 00 

! 

~ 

~ 00 

e; 

<.> 

Calcium Carbonate Saturation 

in Ground Water, From 

Routine Analyses 

·~ GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1535-D 

"¢ 

"' l 

~ 

00 

1>-4 

,.;:i 

s 

~ 

z 

~ ~ 

0 

~ 

I 

~ ~~t .... ·~ rl' su\c\ l,\i)tati ~ Cr}.otad\.l \ 

Calcium Carbonate Saturation 

in Ground Water, From 

Routine Analyses 

By WILLIAM BACK 

GEOCHEMISTRY OF WATER 

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1535-D 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1961 
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEW ART L. UDALL, Secretary 

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director 

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

Washlnl!.ton 25, D.C. • Price 45 cents (paper cover) 
CONTENTS 

Page 

Abstract---------------------------------------------------------- I>-1 

Introduction_______________________________________________________ 1 

Purpose------------------------------------------------------ 1 

Acknowledgments __ -------------------- ___ --------- ____ ------- 2 

I>ependence of equilibrium constants on temperature__________________ 2 

Calculation of the activity of the ions________________________________ 4 

Application of the method to ground-water samples____________________ 7 

Evaluation of errors _______ ---------------------------------------- 10 

Summary--------------------------------------------------------- 12 

References cited _____ ------- ______ --------------------------_______ 13 

ILLUSTRATIONS 

Page 

PLATE 1. Values for equilibrium constants obtained by various 

methods------------------------------------------In pocket 

FIGURE 1. Equilibrium constants used in the calculations of activity of 

calcium and bicarbonate ions-------------------------- I>-5 

2. Activity coefficients for calcium and bicarbonate ions_______ 6 

3. Ratio of difference between the analyzed and calculated 

values to the analyzed value for calcium-ion concentration 

plotted with the ionic strength_________________________ 7 

TABLES 

Page 

TABLE 1. Selected chemical analyses of ground water from Kentucky 

and Texas-------------------------------------------- I>-8 

2. Analyzed and calculated calcium-ion concentration, in parts 

permillion------------------------------------------- 10 

III 

GEOCHEMISTRY OF WATER 

CALCIUM CARBONATE SATURATION IN GROUND WATER, 

FROM ROUTINE ANALYSES 

By WILLIAM BACK 

ABSTRACT 

A method is developed to calculate, from standard ground-water analyses, the 

calcium-ion concentration under conditions of assumed equilibrium as an indication of the extent of departure from equilibrium attained between calcium 

carbonate and ground-water solutions. These calculations require an acceptable 

value for the equilibrium constants (K values) for calcium carbonate and the 

bicarbonate ion. The results of four methods used to obtain the K values as a 

function of temperature show close agreement within the temperature range of 

0° to 50° C. Theoretical calcium-ion concentrations are calculated for 25 chemical analyses of water samples collected from limestone terranes. The greatest 

source of error is in the reported pH values from laboratory measurements. 

More precise field data are required before reliable geologic inferences can be 

extended to limestone areas in general. 

INTRODUCTION 

P'OltPOSE 

The purpose of this study is twofold; the first objective is to introduce a method to compute a theoretical calcium-ion concentration as 

a measure of the saturation of calcium carbonate attained in ground 

water, and the second is to demonstrate the application of this method 

to a series of ground-water analyses. A comparison of the calcium 

concentration as shown by the chemical analysis with the value obtained by calculating what the concentration would be if the ground 

water were saturated with calcium carbonate provides a basis for 

determining the extent to which ground water may be in equilibrium 

with calcium carbonate (calcite in this study). 

The basic assumption is that an excess of available solid-phase 

calcium. carbonate exists within the environment under consideration. 

This method is valid only in normal ground water and cannot be 

applied to more concentrated solutions. Table 1 contains chemical 

analyses of 25 samples of ground water from areas underlain by 

limestone in Kentucky and Texas, selected from existing publications 

(Walker, 1956; Harvey, 1956; Petitt, 1956). 

D-1 
D-2 GEOCHEMISTRY OF WATER 

ACXNOWLEDGM:ENTS 

This paper was originally written as a term report for a geology 

course at Harvard University given by Professor R. M. Garrels in 

1957. The guidance of Professor Garrels in developing the approach 

and techniques used in this study and the criticisms and helpful 

suggestions of C. L. McGuinness, W. H. Durum, J.D. Hem, and 

J. H. Feth are gratefully acknowledged. 

DEPENDENCE OF EQUILIBRIUM CONSTANTS ON 

TEMPERATURE 

A comparison of values for the equilibrium constants (K values) for 

H2C03, HC03 and CaC03 for temperatures from 0° to l00°C determined by several different methods is shown in plate 1. The ionization constants for H2C03 were measured by Shedlovsky and Macinnes 

(1935) for 0° to 38°C and Harned and Davis (1943) for 0° to 50°C. 

The ionization constants for HCO;- were measured by Macinnes and 

Belcher (1933, 1935) for 25° and 38°C and by Harned and Scholes 

(1941) for 0° to 50°C. Larson and Buswell (1942) extrapolated the 

data of Shedlovsky and Macinnes and of Harned and Scholes to 

extend the temperature range to 80°C. Langelier (1946) further 

extrapolated the data to include temperatures to 100°C. The 

source of data he used is not stated, but evidently it is Harned's work. 

Measurements for the equilibrium constant of CaC03 in the form of 

either calcite or aragonite have not been made for 0° to 100°C; 

therefore several methods have been used to obtain these necessary 

values. Langelier (1936, p. 1512) computed the solubility products 

of CaC03 for temperatures from 0° to 90°C from the data of Frear 

and Johnston (1929, p. 2083). The temperature correction is given 

by Frear and Johnston as log r=(830/T)-2.78, where r is the ratio of 

solubility of CaC03 at t°C to that at 25°C. (In Langelier's table 4, 

p. 1512, there are two misprints; for temperatures 25°C and 70°C 

read 8.32 and 8.67, respectively). Langelier (in Hoover, 1938, p. 

1806) later modified the temperature correction to pKcaco3=8.32-

[2 (830/T)-2.78]. The values obtained from this equation are given 

in his discussion of Larson and Buswell's paper (1942, p. 1680). 

However, Larson and Buswell (p. 1671) state that neither at these 

expressions is correct because r is the ratio of the solubility and not 

the ratio of the solubility product at t°C to that at 25°C. The 

criticism relates to Langelier's more simplified treatment, which 

neglects the hydrolysis effects in the temperature corrections. 

The method used by Garrels and Preyer (1952) to calculate the 

equilibrium constants is based on the thermodynamic relationships 
CALC~ CARBONATE SATURATION IN GROUND ~ATER J)-3 

of free energy and the heat of formation of the calcium and carbonate 

species ions, as expressed in the following equations: . 

-llF1° =nE1° F 

E 0+fl1lt0 -TdE,o 1 nF- dT 

(1) 

(2) 

where llF1° is the free energy of formation of the ion; E1° is the standard electrode potential for the formation of the calcium or carbonate 

ion; llll1° is the heat of formation of the ion; n is the number of 

electrons transferred in the ionization; F is the Faraday, expressed in 

calories per mole; and Tis the absolute temperature. By this method 

E1° is calculated from equation 1, the free-energy value at 25°C being 

obtained from Latimer (1952) and from the number of electrons 

involved in the chemical reaction. This value of E1° is substituted 

into equation 2 along with the experimental value for the heat of 

· · · d b · h al f dE,o IOmzation measure at one temperature to o tam t e v · ue o dT 

expressed in volts per degree. If it is assumed that the term d:ro 

is constant within the temperature range of interest of 25° to 65°C, 

the value of E1° can be computed from equation 2 for temperatures 

other than the reference temperature for the heat of ionization. 

These values can then be substituted into equation 1 to calculate the 

free-energy values over the temperature range from 25° to 65°C. 

The equilibrium constant can be computed from the temperaturecorrected free energy by 

A third series of values for equilibrium constants were computed 

for this paper by a method based on the equation 

Values for llF0 in kilocalories and 8° in calories per degree are listed 

by Latimer, 1952. For example, the calculation follows for the 

reaction 

From Latimer (p. 30 and p. 128), for 25°C, 

llF a= [0.0-126.22]-[ -140.31] = + 14.09 
D-4 GEOCHEMISTRY OF WATER 

The similar entropy relationship is as follows: 

.tlSB=[0.0-12.7]-[22.7]=-35.4 cal=-0.0354 kcal 

By integration 

~FB=-T~SR+constant of integration 

+ 14.09=-(298)(-.0354)+0 

0=+3.54 

For various temperatures, such as 0°0=273°K 

~F.R=-[(273)(-.0354)]+3.54 

~F.R=+13.20 

and 

~FB=-RTln K+13.20=-(1.98)(2.30)(273) log Kacoa 

+13.20=-1.242log Kacoa 

log Kacoa=-10.63 

Kacoa=1o-lo.63 

The values obtained from the equilibrium constants of Oa003, 

H200a, and H003 by the various methods agree closely for the 

temperatures from 0° to 50°0. Above 50°0 the agreement is poorer. 

A comparison of these values provides an estimate of the amount of 

discrepancy that can be expected in calculations based on various 

assumptions about the effect of temperature on the equilibrium 

constants. 

Harned's values for constants of H003, H200a, and H20 and 

Larson and Buswell's values for Oa003 were used for calculations in 

this paper and are replotted at an expanded scale on figure 1. 

CALCULATION OF THE ACTIVITY OF THE IONS 

In the reaction 

OaC03=0a++ +CO; 

ac,.++ · aco; 

acaco3 

(3) 

Where the a terms represent activities and ac .. co3 IS unity. By 

definition 

(4) 
u 

0 

w 

a:: 

::0 

f-

<t 

a:: 

w 

0.. 

::i' 

w 

fCALCIUM CARBONATE SATURATION IN GROUND WATER D-5 

50 

4~ 

40 

35 

30 

20 

20 

15 

10 

0 

3 2 

1\ 

\ 

\ L orson and Buswell/ 

1942, page 1673 

~ 1 

I 1 

I 

\ 1/ 

\ 

\ 

\ J Horned and Hamm 

1933, page 2149 

r , ! 

\ 1 

\ r Horne 

1941 

and Scholes 

page 1706 

\ I 

~ j t 

I \ r I 

l \ j ~ \ Horned and Davis, 

1943, page 2030 \ 1 \ ~ \ ~ 6 .0 .2 .4 .6 .B 7.0 .2 .4 .6 8.0 .2 .4 .6 .B 10.0 .2 .4 .6 .B 

VA L UE S FOR EQ UIL IBRIUM CONSTANTS =-LOG K 

FIGURE I.- Equilibrium constants used in the calculations of activity of calcium and bicarbonate ions. 

where m is molality and "Y is the activity coefficient. Values for "Yea++ 

are read from the graph in figure 2. Temperature corrections for the 

activity coefficients were not made for this paper. Klotz (1950, p. 

331- 332) tabulated the activity coefficients computed by Kielland 

(1937) from the first approximation of the Debye- Huckel equation. 

To read the value of the activity coefficient for the calcium and 

bicarbonate ions from figure 2, the ionic strength, J.L, of the solution is 

computed from the following equation: 

(5) 

581730 0-61--2 
D-6 

0 

0 

I() 

(\J 

en 

Iz 

w 

u 

~ 

lJ.. 

w 

0 

0 

>-

I-

> 

i= 

0 

<t 

1.0 

).... 

0.9 

.......... 

0 .8 

0 .7 

0 .6 

0 .5 

0.4 

0 .3 

.001 

GEOCHEMISTRY OF WATER 

- r-- ~ ;>- HC0 3

-

i-1-

------"a. ............ 

~ 

.............. ~ r-... 

1'--" 'r--...., 

" "'~ ~~Co++ 

~ 

~ 

""-r-. 

i"--, 

'~"- ...., 

.002 .003 .004 .006 .01 .02 .03 .0 4 .05 .06 0. 1 

IONIC STRENGTH 

FIGURE 2.-.Activlty coefficients for calcium and bicarbonate ions. 

where m is the molality of the ion, i, which has a charge z in the solution. In most ground waters mco; is too small to be determined 

by the usual analysis. However, aco; can be computed from the 

HCO; concentration and the pH. 

From the reaction 

HCO;~CO; + H+ 

and the law of mass action 

(6) 

and by transposition and application of equation 1 

(7) 
CALCIUM CARBONATE SATURATION IN GROUND WATER D-7 

In equation 7, a value for mnco3 is obtained directly from the analyses, 

table 1. 'Yncoa- is read from the graph in figure 2, and KHco3 is read 

from figure 1 at the temperature of the ground water. aH+ is obtained 

from the pH; that is, a pH of 7. 9 means that aH + is 1 o-7

· 9• Therefore, 

by transposition of equation 3, 

++-Kcaco3 aca - a co; 

The activity of the calcium ion under equilibrium conditions can be 

calculated by reading the value for the equilibrium constants at the 

temperature of the ground water from figure 1. The molality is 

obtained by use of equation 4 and converted to concentration in parts 

per million. 

APPLICATION OF THE METHOD TO GROUND-WATER 

SAMPLES 

The theoretical activity of the calcium ion under assumed equilibrium conditions was calculated for 25 ground-water analyses. The 

calculated calcium-ion concentration, in parts per million, is shown in 

table 2 with the values obtained by chemical analysis. The results 

expressed by the ratio 

Analyzed Ca++ (ppm)- calculated Ca++ (ppm) 

Analyzed Ca++ (ppm) 

are plotted on figure 3 against the ionic strength of the ground water. 

+ 

+ 0 

u 

0 

w 

>- + 

"' + ..J c :::> u u 

..J 0 

"' w u N 

I ,.. ..J 

+ 

+ "' z c "' u 

0 

w 

N 

,.. 

..J 

"' z 

"' 

1.0 0 

22 11 23 - r-- .75 

.50 

~ ,; , n r- 2 8 lD 

~ 12 ?el 18 

17 24 

.25 

3 w 19 

0 

-.25 15 

-.50 . 16 

- .75 

-1.00 4 

5 

- 1.25o .001 .002 .003 .004 .005 .006 .007 .008 .009 .010 .0 11 .0 12 .01 3 .014 .0 15 .0 16 

IO NIC STRENGTH 

FIGURE 3.-Ratio of difference between the analyzed and calculated values to the analyzed value for calcium-ion concentration plotted with the ionic strength. 
D-8 GEOCHEMISTRY OF WATER 

TABLE I.-Selected chemical analyses of 

[Analyses sample Nos. 1-8 (Walker, 1956), 9-13 (Harvey, 1956), 14-25 (Petitt, 1956). Parts per million 

Depth TemBam- of Date of pera- Silica Total Cal- Mag- pie Location wells Stratigraphic unit collec- ture (S!Oo) Iron clum neslum 

No. (feet) tlon ("F) (Fe) (Ca) (Mg) 

------------ 1 8720-3646-61 90 Mississippian lime- 6- 7-50 62 8.2 0.19 69 11 stone. 1. 72 .46 

2 872o-3660-19 60 _ •••• do ••••• _____________ 6- 7-50 60 10 .12 64 12 

1.60 .49 

3 8726-3646-24 66 ••••• do _______ •• _________ 6- 7-50 60 8.0 .27 40 24 

1.00 .99 

4 8726-3645-41 23 ••••• do •••• ________ ------ 1-25-60 54 4.6 .16 62 4.6 

1.65 .18 

5 8626-3645-65 (1) __ ••• do ••••• _____________ 6- 7-50 58 13 .86 48 4.1 

1.20 .17 

6 8726-3646-157 73 ••••• do ••••• _____ ._ •••••• 3- 7-50 58 7.2 .19 31 22 

.77 .90 

7 8726-3650-15 65 ---•• do •••••••• __ ---••••• 6- 7-50 63 7.0 .59 6.2 3.5 

.15 .14 

8 8731)-3646-6 93 __ ••• do •.••• ---•••••• ---. 6- 7-50 63 7.8 .12 62 24 

1. 56 .99 

9 8730-3746-32 180 Penns~an shale 3-3Q-50 57 5.6 .37 74 13 

and estone. 1.86 .53 

10 873o-37 5o-66 126 __ ••• do ____ •• _____ ••••••• 3-3Q-50 57 9.6 4.4 86 32 

2.16 1.32 

11 8736-3746-6 110 Quaternary alluvium ___ 12-29-49 56 12 4.5 92 31 

2.29 1.27 

12 8736-3745-77 209 Pennsylvanian shale 3-29-50 55 21 6.8 8.0 3.9 

and limestone. .20 .16 

13 8736-3745-138 60 Quaternary alluvium ___ 3-29-50 56 11 13 92 48 

2.29 1.97 

14 H-5-1 350 Cretaceous limestone ••• 11- 2-45 72 11 .08 74 9.6 

Uvalde Co. 1.86 

15 I-4-37 1,493 _ •••• do __________________ 11- 2-45 80 14 .12 88 29 

Uvalde Co. 2.20 -------- 16 I-3-133 1,600 __ .•• do •••••• ____ ---•••• _ 11- 2-45 76 14 .08 66 16 

Medina 1.66 -------- Co. 

17 261 703 • •••• do ••••••••••••• ----- 6-21-50 74 16 .00 50 17 

Bexar Co. 1.25 -------- 18 283 1,361 ••••• do ___________ •••• --- 6-14-52 81 17 .01 65 19 

Bexar Co. 1.62 -------- 19 D-12 360 ••••• do ____ --- __ •• _.----- 4- 8-64 71 10 ------- 78 16 

Bexar Co. 1.95 -------- 20 043 426 _____ do _______ •• _________ 3-17-50 72 14 .01 63 18 

Bexar Co. 1. 58 -------- 21 J-86 720 ••••• do ••.••••• _._ •••• ___ 12-13-48 75 24 .00 50 14 

Bexar Co. 1.26 -------· 22 E-38 325 ••• _.do _____ • _____ •• ----_ 1-2646 66 10 .06 58 33 Hays Co. 1.46 ""39 ____ 23 G-58 600 ---•• do __________________ 9-28-63 74 10 ------- 100 

Hays Co. 2.50 -------- 24 H-19 766 ••••• do ________ ----_----- 1Q-21H9 76 13 .02 72 43 

Hays Co. 1.80 --Tii-- 26 K-14 44 • ---.do _____________ ----- 1-19-64 70 7.2 .08 44 

Hays Co. 1.10 --------

I Spring. 
CALC~ CARBONATE SATURATION IN GROUND vrATER D-9 

ground water from Kentucky and Texas 

(upper number), molality x 10• (lower number). Analytical results in parts per million except as indicated) 

Dis- Specific 

conductSodium Potas- Blear- Sulfate Chlo- Fluo- Nitrate solved Ionic Hard- ance (Na) 

I 

slum bonate (SOl) ride ride (NO a) solids strength ness as (micro- pH 

(K) (HCOa) (Cl) (F) residue CaCOa mhos at on evap- 25°C) 

oration 

at 180° C 

------------------------ 2.8 'JZl 25 5.8 .2 3.4 240 0.0069 217 393 7.8 

.12 3. 72 .26 .16 .05 

7.6 228 15 13 .5 4.3 231 .0067 209 388 7.9 

.33 3. 74 .16 .37 .07 

4.2 204 29 3.5 2.0 .1 211 .0064 198 352 7.9 

.18 3.34 .30 .10 0 

.2 190 9.3 2.8 .2 4.6 189 .0053 173 320 7.3 

.01 3.11 .10 .08 .07 

20 190 8.2 3.5 .3 12 200 .0050 137 317 7.5 

.87 3.11 .08 .10 .19 

75 282 68 5.6 4.5 11 357 .0089 168 607 8.0 

3.26 4.62 .71 .16 .18 94 214 48 5.5 .6 .5 274 .0055 30 431 7. 7 

4.09 3. 51 .50 .15 .01 

7.5 302 11 5.5 .7 1.4 267 .0080 253 477 7.8 

.33 4.95 .11 .15 .02 

24 326 2.6 6.8 .3 13 308 .0082 238 527 7.9 

1.04 5.34 .03 .19 .21 

15 398 45 4.4 .2 0 388 .0115 346 639 7.6 

.65 6.52 .47 .12 0 0 

11 414 27 8.5 .1 2.1 390 .0114 357 680 8.0 

.48 6. 78 .28 .24 .03 

9.4 46 11 3.6 .1 2. 5 86 .0016 36 110 7.6 

.41 . 75 .11 .10 .04 

49 639 .8 2.1 .4 5.9 524 .0149 427 897 7.5 

2.13 10.47 .01 .06 .09 

24 7 277 19 24 .4 4.1 319 .0082 224 570 7.0 

--------- -------- 4.64 -------- -------- -------- 17 9. 5 254 142 20 .6 3. 470 .0126 338 722 7.1 

--------- -------- 4.16 -------- -------- -------- 4.8 3.4 244 16 18 .2 3.8 263 .0074 230 438 7.0 

--------- -------- 4.00 -------- -------- --------

5.2 .8 190 32 13 .3 3.5 246 .0065 195 490 7.8 

--------- -------- 3.17 -------- -------- -------- 10 1.6 238 35 18 .3 5.0 296 .0080 240 498 7.6 

--------- -------- 3.90 -------- -------- -------- 6.1 .9 298 13 13 -------- 5 .. 6 313 .0083 260 531 7.4 

--------- -------- 4.89 -------- -------- -------- 10 3.6 233 34 20 .6 3.8 287 .0078 231 484 7. 7 

--------- -------- 3.82 -------- -------- -------- 13 .4 176 35 19 .4 2.5 244 .0064 182 425 7.9 

--------- -------- 2.89 -------- -------- -------- 3.0 3.0 280 38 12 1.8 .o 301 .0090 280 540 8.2 

--------- -------- 4.59 -------- -------- 7.8 1.4 330 122 15 -------- 14 491 .0139 410 654 8.0 

--------- -------- 5.41 -------- -------- -------- 17 5.2 283 129 22 3.6 .o 490 .0129 356 725 7.6 

--------- -------- 4.64 -------- -------- 4.9 1.0 151 2.0 3.8 -------- 2.5 147 .0038 116 261 8.2 

--------- -------- 2.48 -------- -------- --------
D-10 GEOCHEMISTRY OF WATER 

If we assume no errors of measurement or calculation, those samples 

that plot above the zero line are supersaturated with calcium carbonate 

and those that plot below the zero line are undersaturated. Samples 

4, 7, and 12 are not plotted because of the low value of the ratio. 

TABLE 2.-Analyzed and calculated calcium-ion concentration, in parts per million 

Sample No. 

1--------------------------------- 2 ________________________________ _ 

3--------------------------------- 4 ________________________________ _ 5 ________________________________ _ 

6 ________________________________ _ 

1--------------------------------- s ________________________________ _ 

9--------------------------------- 10 _______________________________ _ 

11-------------------------------- 12 _______________________________ _ 13 _______________________________ _ 

14.------------------------------- 15 _______________________________ _ 16 _______________________________ _ 17 _______________________________ _ 

18-------------------------------- 19 _______________________________ _ 20 _______________________________ _ 21 _______________________________ _ 

22 .. ------------------------------ 23 _______________________________ _ 

24 _______________________________ _ 

25--------------------------------

Analyzed 

69 

64 

40 

62 

48 

31 

6.2 

62 

74 

86 

92 

8 

92 

74 

88 

66 

50 

65 

78 

63 

50 

58 

100 

72 

44 

Calculated 

40 33 

36 

179 

98 

24 

49 

29 25 

45 

11 

297 

38 

150 

121 

155 

31 

36 

71 

36 

27 

11 14 

47 

16 

EVALUATION OF ERRORS 

Anal-calc 

Anal 

+O. 42 

+O. 48 

+.10 

-1.9 

-1.0 

+. 23 

-6.9 

+.53 

+. 66 

+.48 

+. 88 

-36. 

+.59 

-1.0 

-. 37 

-.57 

+.38 

+. 44 

+.09 

+.43 

+. 46 

+. 81 

+. 86 

+. 34 

+. 64 

Before it can be concluded that any single sample is undersaturated 

or supersaturated, the possible errors must be evaluated. The 

greatest source of error is the pH measurement. The pH valuesreported in the table of analyses were determined in the laboratory. 

These laboratory determinations may not be representative of the pH 

of the water in the aquifer because of instrument error and of changes 

in the carbon dioxide content and the temperature. The samples 

were collected by standard sampling techniques. However, even if 

the greatest care is used in collecting samples, changes occur within 

the water that cannot be compensated for in the laboratory. For 

greatest accuracy, the pH and HCO:l content should be measured in 

the field, although the effect of errors in the bicarbonate determination 

is far less than the errors in pH determination. No samples were 
CALCIUM CARBONATE SATURATION IN GROUND WATER D-11 

collected during the present study, and the chemical analyses used 

were obtained from published ground-water reports. 

Although the water samples analyzed in the laboratory may not 

truly represent conditions within the aquifer, it seems reasonable to 

assume that whatever chemical changes have occurred within the 

samples may be in the same direction and of the same magnitude for 

most samples collected under similar conditions from the same 

geologic and hydrologic system. That is, from the published data 

we may not be able to conclude that any one sample is exactly in 

equilibrium with calcium carbonate, but it may be possible to compare 

the relative degree of saturation of a group of samples. Even this 

comparison, which can be refined by study of more carefully collected 

field data, will provide a basis for a better understanding of the hydrology of limestone terranes. 

The significance of an error in the pH determination is shown by 

considering, for example, analysis 3, which shows a reported pH of 

7.9 and a concentration ratio of +0.10. If the pH were in error as 

much as 0.2 unit, the concentration ratio might be as high as +0.45 

(pH 8.1) or as low as -0.42 (pH 7.7). 

Factors other than the pH that effect the computed values for 

equilibrium constants are those of temperature and concentration of 

the ions in the water. From figure 2 it is seen that an increase in 

temperature will increase the value for the equilibrium constant for 

HCOa, and increase the computed value for a003• Accordingly, 

with the other components remaining fixed in the following equations: 

and 

muco3 · 'Yuco:l · Kuco3 aco; = _ ____..:::___.:..::,:: __ ---"' 

au• 

an error that results in a temperature measurement higher than the 

true temperature will increase Kuco3 and the computed value of a 

ca++ to make the water appear to be more saturated with calcium 

carbonate. For example, sample 3 has a recorded temperature of 

60°F, and the calculated calcium concentration is 36 ppm. If we 

assume an error of plus or minus 5°F, at 65°F the theoretical calcium 

concentration would be 31 ppm and at 55°F the value would be 42 

ppm. The corresponding concentration-ratio values are +0.22 

(65°F) and -0.05 (55°F). 

The possible error introduced by the laboratory analysis and 

computation of the ionic strength has virtually no effect on the value 
D-12 GEOCHEMISTRY OF WATER 

of the activity coefficients and therefore involves no significant change 

in the calculated values. The error due to standard analytical procedures arises primarily through the determination of calcium and 

bicarbonate. The potentially most serious error in using the reported 

calcium value for a comparison, is that any strontium present shows 

up as calcium. Fortunately, many strontium determinations have 

indicated that generally it is present in only small amounts. More 

work is currently being done on the strontium content of water. 

A far more serious analytical misrepresentation is the reported 

value for bicarbonate. This value is alkalinity expressed as bicarbonate, and therefore represents all constituents that contribute to 

the alkalinity of the water. These may include carbonate as well as 

bicarbonate, in addition to borates, phosphates, and silicates, which 

are generally present in minor amounts. Again by using sample 3 

as an example, if we assume that 10 percent of the reported value for 

bicarbonate is due to the presence of other weak acids, the true 

bicar)onate value would be 184 ppm. In most waters the contribution to alkalinity by the weak acids would be far less than the 10 

percent assumed. 

However, if loss of carbon dioxide occurred, the reported value for 

bicarbonate would be too low. This effect also could easily amount 

to 10 percent, so that the true value on sample 3 would be 224 ppm. 

A few calculations indicate that this range of values reflects a 

change in the ionic strength small enough to have no effect on the 

value for the activity coefficient to be used. Therefore, the change 

in the theoretical calcium-ion concentration Will result from the new 

value for molality of the bicarbonate ion. The calculated calcium 

values are 40 and 32, assuming respectively 184 and 224 ppm of 

bicarbonate. The corresponding concentration ratios are 0.0 and 

+0.20. The amount of error introduced in the analysis of calcium 

and bicarbonate content by standard methods and in the determination of equilibrium constants, activity coefficients, and temperature 

can be kept within narrow limits so far as the calculation of relative 

equilibrium is concerned. 

SUMMARY 

A change in temperature, ionic strength, or pH, according to the 

direction of change, can shift the conditions of equilibrium with 

calcium carbonate and cause the water to precipitate or to dissolve 

calcite or aragonite or both. Such changes can be brought about 

by bacterial action, by movement of the water to another environment of different temperature and pressure, or by mixing with water 

from another source which has a different temperature and ionic 

strength. 
CALCIUM CARBONATE SATURATION IN GROUND WATER D-13 

In summary, this paper suggests a method to obtain calculated 

values for the calcium ion from standard chemical analyses of water, 

in order to determine the extent of departure from calcium carbonate 

saturation. However, additional analyses of samples collected under 

more carefully controlled conditions and more accurate determinations 

of pH are necessary before reliable geologic inferences can be extended 

to limestone areas in general. 

REFERENCES CITED 

Frear, G. L., and Johnston, J., 1929, The solubility of calcium carbonate (calcite) 

in certain aqueous solutions at 25°C: Am. Chem. Soc. Jour., v. 51, no. 7, 

p. 2082-2092. 

Garrels, R. M., and Dreyer, R. M., 1952, Mechanism of limestone replacement at 

low temperatures and pressures: Geol. Soc. America Bull., v. 63, no. 4, p. 

325-380. 

Harned, H. S., and Hamer, W. J., 1933, The ionization constants of water and 

the disassociation of water in potassium chloride solutions from electromotive forces of cells with liquid junction: Am. Chem. Soc. Jour., v. 55, no. 

6, p. 2194-2206. 

Harned, H. S., and Davis, Raymond, 1943, The ionization constant of carbonic 

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

salt solutions from 0° to 50°C: Am. Chem. Soc. Jour., v. 65, no. 10, p. 

2030-2037. 

Harned, H. S., and Scholes, S. R., Jr., 1941, The ionization constant of HCOii' 

from 0° to 50°C: Am. Chem. Soc. Jour., v. 63, no. 6, p. 1706-1709. 

Harvey, E. J., 1956, Geology and ground-water resources of the Henderson area, 

Kentucky: U.S. Geol. Survey Water-Supply Paper 1356, 227 p. 

Hoover, C. P., 1938, Practical application of the Langelier method: Am. Water 

Works Assoc. Jour., v. 30, no. 11, p. 1802-1807. 

Kielland, Jacob, 1937, Individual activity coefficients of ions in aqueous solutions: Am. Chem. Soc. Jour., v. 59, no. 9, p. 1675-1678. 

Klotz, Irving, 1950, Chemical thermodynamics: New York; Prentice-Hall, 392 p. 

Langelier, W. F., 1936, The analytical control of anticorrosion water treatment: 

Am. Water Works Assoc. Jour., v. 28, no. 10, p. 1500-1521. 

---1946, Effect of temperature on the pH of natural waters: Am. Water 

Works Assoc. Jour., v. 38, no. 2, p. 179-185. 

Larson, T. E., and Buswell, A. M., 1942, Calcium carbonate saturation index and 

alkalinity interpretations: Am. Water Works Assoc. Jour., v. 34, no. 11, p. 

1667-1684. 

Latimer, W. M., 1952, Oxidation potentials: New York, Prentice Hall, 392 p. 

Macinnes, D. A., and Belcher, Donald, 1933, The thermodynamic ionization 

constants of carbonic acid: Am. Chem. Soc. Jour., v. 55, no. 7, p. 2630-2646. 

---1935, The thermodynamic ionization constants of carbonic acid at 38°C 

from electromotive f.orce measurements: Am. Chem. Soc. Jour., v. 57, no.9, 

p. 1683-1685. 

Petitt, B. M., and George, W. 0., 1956, Ground-water resources of the San Antonio area, Texas: Texas Board Water Engineers Bull. 5608, v. II, pt. III, 

pages unnumbered. 
D-14 GEOCHE~STRY OF VVATER 

Shedlovsky, Theodore, and Macinnes, D. A., 1935, The first ionization constant 

of carbonic acid, 0° to 38° from conductance measurements: Am. Chem. 

Soc. Jour., v. 57, no. 9, p. 1705-1710. 

Walker, E. H., 1956, Ground-water resources of the Hopkinsville quadrangle, 

Kentucky: U.S. Geol. Survey Water-Supply Paper 1328, 98 p. 

0