On the Equilibrium Concentration Ratio of Carbonic Acid Substances Dissolved in Natural Water —A Study on the Metabolism in Natural Waters (II)—

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551. 464. On the Equilibrium Concentration Ratio of Carbonic Acid Substances Dissolved in Natural Water —A Study on the Metabolism in Natural Waters (II)—

K. Saruhashi Meteorological Research Institute (Received May 31, 1955)

Abstract

It is of importance to study the behaviour of carbonic acid substances dissolved in natural water in order to know the chemical properties of the water. Acidity or alkalinity method has been gen- erally used for this purpose for a long time. But this method often leads to erroneous results. The present author proposed that a better way is to determine first the amount of total carbonic acid, pH and temperature, and then to calculate theoretically the amount of H7CO3, HCO3- and CO3- using equilibrium constants between them. However, such a calculation is too laborious for every analyst, and therefore the author completed tables convenient for use containing calculated values of molar fractions of each carbonic acid substance for different temperature and pH in fresh water and sea water. In these tables, one can find any necessary values of molar fraction when the total amount of carbonic acid, temperature and pH of waters are given. By the use of this method, exact determination of the amount of each carbonic acid substance in water is made possible.

1. Introduction To know the chemical properties of natural water, it is important to investi- gate especially the behaviour of carbonic acid matter, that is, free carbonic acid, bicarbonate and carbonate ions, dissolved in it. For this purpose, it is necessary above all to determine accurately the amount of each form of carbonic acid substances in water. As already mentioned in my previous paper [1], there have been many methods for determining the concentration of carbonic acid substances dissolved in water. Among them, the neutralization titration method is most widely used and the concentrations of 1-12CO3,HCO3- and CO3= are calculated by using the values of acidity or alkalinity of water obtained in this way. But, needless to say, the acidity or alkalinity is defined by the equivalent amount of hydrogen ion required to make free weak acids of any kind dissolved in water of 1 litre. Therefore, it is related to all kinds of weak acids contained in water. Since different kinds of acid substance such as silicate, borate, phosphate and organic acid (humic acid, 1955Equilibrium Concentration Ratio of Carbonic Acid Substances39

etc.) may exist in water and affect the acidity or alkalinity, it is by no means a correct way to estimate the concentration of each carbonic acid substance by use of the values of the acidity or alkalinity. In fact, according to MACHIDA [2] and OANA [3], the amount of carbonic acid substances calculated from the acidity or alkalinity is usually overestimated up to 1.2-2.5 times of the actual values. The present author believes that the best way to obtain the exact amount of each carbonic acid substance in water is to determine first the amount of total carbonic acid, pH and water temperature, and then to calculate theoretically the amount of H2CO3, HCO3- and CO3 using equilibrium constants between them. As is well known, besides temperature, the equilibrium dissociation constants are affected by the presence of other electrolytes dissolved in water. Therefore, the latter effect must also be taken into consideration when sea water is chosen as a sample. However, since it is rather laborious task to calculate each value of molar fraction of carbonic acid substances every time it is necessary, the present author intends to prepare the tables containing the calculated values of molar fractions in percentage of H2CO3, HCO3- and CO3= in fresh and sea water, taking the amount of the total carbonic acid as a unit. By these tables one can find easily the fraction of each carbonic acid substance, knowing the total amount of carbonic acid, pH and water temperature in a water sample. There is already a graph prepared by SCHWARTZ[4] showing the molar fraction of H2CO3, HCO3- and CO3= in fresh water based on MOORE'S calculation [5], but he did not take into consideration the effect on the equilibrium dissociation constants with the water temperature.

2. The equilibrium of the carbonic acid substances dissolved in water The following equilibriums exist among carbonic acid substances dissolved in water.

Though a smaller part of free CO, is hydrated forming H2CO3, the concentration of free CO, plus H2CO3 is usually expressed as H2CO3. CO, dissolved in water is in an equilibrium state of partition with gaseous CO, in the air when the water contacts with the latter. Therefore, we may express the relation as follows :

where, Pco2 is the partial• pressure of CO, in the air, and c is the partition coefficient, varying with the temperature and concentration of other electrolytes dissolved in water. The equilibriums between H2CO3 and HCO3-, and HCO3- and CO3= can be expressed in the following ways :

where, K1 and K2 are respectively the first and the second dissociation constant of carbonic acid dissolved in water which are affected by the temperature and 40K. SaruhashiVol. VI No. 1

the presence of other electrolytes.,r1rrrand ,7;2 T3 are the activity coefficients of H+, 119CO3, HCO3- and CO3= respectively.

A. The equilibrium of the carbonic acid substances dissolved in fresh water. In fresh water which may be considered as an extremely diluted solution of electrolytes, the activity coefficients, To,ri, 12 and 13 in equations (2) and (3) may be considered approximately as unity. Then, equations (2) and (3) may be sim- ply expressed as follows :

where, K3 and K2 depend only on water temperature. SHEDLOVSKYand MACINNES[6], and HARNEDand DAVIS[7] determined the first dissociation constant K1. According to SHEDLOVSKYand MACINNES,the relation between pK1 and water temperature T(absolute) is, plki —17.052/T+215.21 log T —0.12675T —545.560. On the other hand, HARNEDand DAVISexpressed the relation between pK1 and water temperature T(absolute) as follows : pK1=3405/T+O.0328 T —14.84. However, since the difference between values of K1 for different temperature are practically small, either of these equations may be used for calculation. Values of K1 and pK1 obtained by SHEDLOVSKYand MACINNES,and by HARNED and DAVISare shown in Table 1. Table 1. Relation between dissociation constants of carbonic acid and temperature (Fresh water).

HARNED, SAMUEL and SCHOLEStried a determination of the second dissociation constants K2 [81. According to these authors the relation between pK2 and water temperature T(absolute) is as follows 1955Equilibrium Concentration Ratio of Carbonic Acid Substances41

—131.(2——2902.39/T —0.02379 T+6.4980 K2 and pK2 determined by HARNED,SAMUEL and SCHOLESare given also in Table 1. Thus, by using the values in Table 1, the molar fraction of H2CO3, HCO3- and CO3= (total carbon dioxide is taken as a unit) can be calculated for different water temperatures and hydrogen ion concentration by the formulae (4) and (5). Here, the present author performed the calculation of each molar fraction in percentage of H2CO3, HCO3- and CO3= for pH from 5.4 to 10.4 at an interval of 0.1 and for temperatures from 0° to 30°C at an interval of 2°C based on these data. The results are given in Table 2. B. The equilibrium of carbonic acid substances dissolved in sea water. As sea water contains a larger amount of salt, the activity coefficient To, Ti, 12 and 13 in formulae (2) and (3) have different values from those in fresh water.

Ki' and K2' in the above equations are values corresponding to the apparent dissociation constants of free carbon dioxide and bicarbonate ion in sea water respectively, which also vary with water temperature and salinity. Values of K1', pl-Cif, K2' and pK2' determined recently by Bum {9] are given in Table 3. When we know K1' and K2' in Table 3 after measuring water temperature, salinity and [CO31----ionconcentration hydrogen , molar or ionic rations-[H[HC0CO31-]andin[HCO sea 31 water can be estimated by the formulae (6) and (7) as in the case of fresh water. According to Bum, at 20°C the relation between the first dissociation constant in sea water K1' and chlorinity Cl()% is as follows : and the temperature corrections in the case of Cl 19% are,

where 40 denotes the temperature difference. As to the effect of hydrostatic pressure, where 4z is expressed by means of the depth in meters. 42K. SaruhashiVol. VI No. 1

The relation between the second dissociation constant K2' in sea water of 20°C and chlorinity C1(19%) is expressed by the next equation. pK,' = 10.38 —0.510VC1, Temperature corrections are as follows : near 5°C —0.001240, near 20°C 4pK2P-0.0011JO, and the pressure correction is, 4pK2' — 0.18 x 10-44z. Thus, the present author calculated the molar fraction of H2CO3, HCO3- and CO3- in percentage based on studies by K. BUCH for cases when pH is from 7.4 to 8.4 at an interval of 0.1 and temperature, from 0° to 30°C at an interval of 2°C. The results of calculation are shown in Table 4. The pressure effect was not considered in the table, since it is very small for shallow waters. But it must naturally be taken into consideration when pH is smaller and the depth exceeds 1000 M. 4. Conclusion To obtain reasonable values of concentrations of H2CO3, HCO3- and CO3--- dissolved in natural water, we can not rely on the determination of the alkalinity and the acidity as has usually been done for a long time, because such a method often leads to erroneous results. An alternative and better way consists in the determination of the total carbonic acid followed by calculation of each molar fraction of H2CO3, HCO3- and CO3=, taking the change of dissociation constants with temperature and ionic in- tensity of the solution etc. into consideration. However, such a calculation being rather laborious for every analyst to do, complete tables convenient for use containing calculated values of molar fractions of each carbonic acid substance for different pH and temperature would be desir- able. The present author completed such tables using the most reliable data up to now in the case of fresh water as well as sea water. One can easily find any necessary value of molar fraction in these tables, by which exact determination of the amount of each carbonic acid substance is made possible.

Acknowledgements------The author wishes to express her hearty thanks to Dr. Y. MIYAKE for his kind guidance throughout the study. Her thanks are also ex- tended to Prof. K. BucH who kindly sent her a copy of his recent study.

References

[1] SARUHASIII,K., 1953: On the Total Carbonaceous Matter and Hydrogen Ion Concentra tion. Papers in Meteorology and Geophysics, 3, p. 202. [2] MACIIIDA, Y., 1953: Some Notes on the Method of Alkalinity Determination. Jour. Japanese Society of Scientific Fisheries, 19, p. 703. [3] OANA, S., 1954: Chemical Analysis of Gases in Water. Japan Analyst, 3, p. 522. [4] SCHIV..ARTZ,M.C., 1946: Standard Method for the Examinations of Water and Sewage. 9th Ed., p. 31, Am. Public Health Assoc. and Am. Water Works Assoc., New York. [5] MOORE, E.W., 1938: J. Am. Water Works Assoc., 30, p. 108. [6] SHEDLOVSKY,T. and MACINNES,D.A., 1935 : The First Ionization Constant of Carbonic Acid, 0° to 38°, from Conductance Measurements. J. Am. Chem. Soc., 57, p. 1705. [7] HARNED, H.S. and DAVIS, R., 1943 : The Ionization Constant of Carbonic Acid in Water and the Solubility of Carbon Dioxide in Water and Aqueous Salt Solutions from 00 to 50°. J. Am. Chem. Soc., 65, p. 2030. [8] HARNED, H.S. and SOHOLES,S.R., 1941 : The Ionization Constant of HCO3- from 0° to 50°. J. Am. Chem. Soc., 63, p. 1706. [9] BUCH, K., 1951 : Das Kohlensdure Gleichgewichtssystem im Meerwasser Kritische Durchsicht und Neuberechnungen der Konstituenten. Merentutkimuslaitoksen Jul- kaisu Havaforskningsinstitutets Skrift, No. 151, Helsinki. BucH, K., 1938 : New Determination of the Second Dissociation Constant of Carbonic Acid in Sea Water. Acta Academiae Aboensis Math. et Phys., XI 5. Abo. Finland. 44K. SaruhashiVol. VI No. 1

Table 2. Percentage molar fraction of free carbonic acid (F), bicarbonate ion (B) and carbonate ion (C) at different temperature and pH (Fresh water). 1955Equilibrium Concentration Ratio of Carbonic Acid Substances45 46K. SaruhashiVol. VI No. 1 1955Equilibrium Concentration Ratio of Carbonic Acid Substances47 48K. SaruhashiVol. VI No. 1

Table 3. Relation between dissociation constants of carbonic acid and temperature (Sea water, Cl: 15-21%) (K. Bumf). 1955Equilibrium Concentration Ratio of Carbonic Acid Substances49 Table 4. Percentage molar fraction of free carbonic acid (F), bicarbonate ion (B) and carbonate ion (C) at different temperature, pH and chlorinity (Sea water) 50K. SaruhashiVol. VI No. 1 1955Equilibrium Concentration Ratio of Carbonic Acid Substances51 52 K. Saruhashi Vol. VI No. 1 1955 Equilibrium Concentration Ratio of Carbonic Acid Substances 53 54K. SaruhashiVol. VI No. 1 1955 Equilibrium Concentration Ratio of Carbonic Acid Substances 55