UNIVERSITY OF CALIFORNIA PUBLICATIONS

IN

AGRICULTURAL SCIENCES

Vol. 4, No. 10, pp. 245-337, 35 text figures March 22, 1922

EQUILIBRIUM STUDIES WITH CERTAIN ACIDS

AND MINERALS AND THEIR PROBABLE

RELATION TO THE DECOMPOSITION

OF MINERALS BY BACTERIA

BY

DOUGLAS WRIGHT, Jr.

CONTENTS

PAGE

Introduction 245

Object of investigation 249

Method of attack and theory 250

Experimental methods 255

Data 257

Summary 263

INTRODUCTION

The importance of the bacterial population to the soil is well recog-
nized. The role of micro-organisms in the processes of ammonification,
of nitrification, and of nitrogen fixation has been the subject of so much
investigation, and has been reviewed so often in the literature that it is
generally accepted as fact. The influence of bacterial life, or of the end-
products resulting therefrom, causing as it does the solution of necessary
plant nutrients from the mineral particles within the soil, has been the
object of much speculation, some of which has been substantiated by
experiment. Aside from this effect of bacteria upon the mineral particles
within the soil, there is some reason for believing that rocks may undergo
disintegration and degradation into soil through the action of bacteria.
This subject has been discussed and investigated at some length by
various writers, whose work will be mentioned later.

The formation of the mineral portion of the soil is due to the opera-
tion upon the rock mass of three general factors, namely, changes in

246 University of California Publications in Agricultural Sciences [Vol.4

physical environment, chemical action, and biological activity. The first
of these exerts so apparent an influence upon rocks that it has long been
recognized and subjected to careful investigation by geologists. As
applied to soils, these effects belong in the realm of the soil physicist and
therefore will not be considered in this paper.

The chemical agencies chiefly instrumental in breaking down and
dissolving mineral material are water, solutions of varying amounts of
NH3 and C02, various salts, organic acids, and organic compounds.
The effect of solutions, especially of neutral salts, has been the subject
of extensive investigation. This work will be reviewed later in the
section of this paper dealing with method of attack and theory.

Certain biological activities are generally acknowledged to be op-
erative in breaking down the rock mass and preparing it for use as a
suitable medium for the growth of plants. Some of these are mechanical,
such as the manifest action of roots in prying apart portions of rock.
Other effects on rocks are far less easily discernible, due to the slight
action of a vast population of microscopic flora found upon rock in all
stages of its decomposition. The growth of algae, both alone and in
their symbiotic relationships with the lichens, may aid, through the
effect of respiration products, in the solution of minerals. It is likely,
however, that the more important office of these simple green plants is
to serve directly or indirectly as a source of energy for the growth of the
still smaller organisms — the bacteria — in situations where the supply of
organic materials is limited.

A statement concerning the effect of bacteria in rock decomposition
was made by Muntz1 as early as the year 1890. He found bacteria "in
the denuded rocks of the Alps, the Pyrenees, the Auvergne, and the
Vosges comprising the most varied mineralogical types: granites, por-
phyries, gneiss, mica schist, volcanic rocks, limestones, and sandstones,
. . . Often the action is not confined to the surface, but extends into
the depth of the rock mass. This is the case with the so-called rotten
rocks of which the particles become disengaged and separate as is often
seen in limestones, schists, and granites. ... In decomposed rocks
I have always verified the presence of nitrifying organisms."

Branner2 takes issue with Muntz's assumptions, citing the" need of
bacteria for a large supply of oxygen and nitrogen, and their sapro-
phytic habit as prohibitive of their growth to any extent upon or in
rocks. J bid Branner's statements been made some years later, they
undoubtedly would have been modified by recent information con-
cerning the nitrogen compounds of the fundamental rocks. The in-
vest igations of IIa.ll and Miller3 show that part of the nitrogen in certain

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 247

clay soils may have been derived from the nitrogen compounds in the
rocks from which those soils were formed.

Merrill4 mentions bacteria as possible agencies in the decomposition
of rocks.

Renault5 found bacteria present in coal, and postulates their action
in coal beds as that of the transformation of carbonaceous material
into methane and hydrogen.

Holland6 suggests that the phenomenon of laterization may be due
to the action of bacteria, possibly to some specific organism allied to the
sulfur and iron bacteria, and gives certain observations which lead to
this belief.

Lacroix7 makes the following statement: "The bare rocky islet of
Cabras, near San Thome in the Gulf of Guinea, is covered with a mantle
of slightly ferruginous aluminum phosphate which is sometimes several
centimeters thick. This has originated from the interaction of some of
the products of bird guano and the underlying rock, aided, doubtless,
by microbes."

All the conclusions in the literature mentioned thus far are of a
conjectural character and are the result of observation only, no con-
trolled or investigational work having been presented in support of the
opinions offered. The most important systematic investigation of the
action of bacteria on rocks was undertaken by K. Bassalik8, and is
reported by him in two papers, The Decomposition of Silicates by Soil
Bacteria, and The Decomposition of Silicates by Soil Bacteria and Yeasts.

The first of these papers is more or less preliminary, the author
drawing the conclusion that bacteria are able to derive their necessary
mineral nutrients from the feldspars, and that appreciable quantities of
unweathered orthoclase are dissolved by bacteria, probably by means
of C02 produced by the latter.

The second paper reports an elaborate study of the effect of the
growth of several organisms upon various minerals. B. extorquens,
several of the nitrifying organisms, butyric acid bacteria, and yeasts
were tried upon twelve widely varying silicates and upon apatite. A
partial summary of Bassalik's results is given here:

1. Bacteria are able by means of their products of respiration to cause a
significant solubility of pulverized silicates.

2. Those which produce organic acids, as Clostridium Pasteurianum, influence
more strongly the solubility of the silicates.

3. In the action of micro-organisms upon rocks, the intensity of contact of
the organism and the mineral to be dissolved is of greater importance than the
various agents of solubility.

4. Thus, B. extorquens, which produces only C02, has the strongest solvent
effect through its close and firm envelope of the mineral particles.

248 University of California Publications in Agricultural Sciences [Vol. 4

5. Yeasts, which produce much more C02 in cultures than B. extorquens ,
cause a smaller solubility because of the absence of the close contact with the mineral
particles.

6. The nitrite bacteria are also able to effect a significant solubility of silicates
as the result of their physiological property of oxidizing NH3, but they affect those
minerals rich in alkaline earths much more than those rich in silicates.

7. The significant solubility of apatite seems to be a property only of those
bacteria which produce organic acids, for this mineral is dissolved only in moderate
degree by those organisms which produce C02.

8. In the filtrates of the bacterial cultures, especially with B. extorquens, can
be recovered all the chemical constituents present in the minerals experimented
with. Those most easily going into solution are the alkalis, then the alkaline earths
and iron, silicic acid much less, and clay the least.

This summary presents some interesting conclusions; and a close
review of the paper shows that they are the result of careful work.
Bassalik, however, does not get at the fundamental causes of the
differences in the effects of organisms. This investigator refers, in
conclusions 3, 4, and 5, to the closeness of contact of organisms to the
mineral as an important factor in determining the magnitude of the
action of B. extorquens; but he does not offer plausible proof of this
assumption, and it would seem that his conclusion concerning this
point may be erroneous. If we have in solution H2C03 from the pro-
duction of CO2 by B. extorquens, the concentration of the acid should
depend upon the partial pressure of the C02 above the liquid and the
rate of C02 production by the organism. The same should be true
with the yeast, and as the yeast, according to Bassalik's own state-
ment, produces C02 more rapidly than does B. extorquens, and if,
as he also states, the solubility is effected by the concentration of C02,
the yeast should effect the greater solution of the mineral. This should
be true, both in the solution culture and in the solution film surrounding
the mineral particles, where the organisms are grown upon the moist
mineral. Thus it would seem that any greater effect of B. extorquens
should be attributed to some specific action on the mineral, such as
oxidation, hydration, etc., rather than to C02. Furthermore, the bac-
terial envelope, which is referred to as enclosing the mineral particles,
may consist of a gelatinous coating produced from the mineral particle
itself, rather than of an aggregate of bacteria (this coating being greater
where the action upon the mineral is greater).

In 1915 T. Kawamura9 described an organism found in some
volcanic material upon one of the mountains of Japan, at an altitude of
6,600 feet. This organism is of special interest as one which has a
specific ad ion upon a silicate material. It forms a zoogloeic mass, the
ash of which contains an unusually large amount of silica, 8.873 per
cent. Kawamura proposed the name Volcanothrix silicophila for the
organism.

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 249

A comprehensive discussion of the action of bacteria upon minerals
would not be complete without some reference to the action of certain
organisms upon the iron, sulfur, and phosphorus compounds found in
rocks and soils. However, since it is the purpose of this paper to deal
with an entirely different phase of the subject, a brief reference to the
bacterial processes affecting these compounds will suffice.

Lipman and McLean10 studied the effect of the oxidation of sulfur
upon rock phosphate and found appreciable amounts of the phosphate
dissolved through the action of the resulting acid.

Stoklasa11 found marked solubility of bone meal through the action
of soil bacteria and attributed it to the action of enzymes upon the
bone meal.

Koch and Kroeber12 and later Kroeber13 determined the solubility
of different forms of phosphate in the acids produced by the growth of
soil and sewage organisms upon dextrose. Kroeber concluded that the
acids produced by bacteria and yeasts in the soil may be of great im-
portance in rendering phosphate soluble. In cultures where CaC03 was
present little or no phosphate was made soluble.

Sackett, Patten, and Brown14 in a somewhat similar work found
that there was a decided solution of the insoluble phosphate when
bacterial growth was accompanied by acid formation. They believed
that acid is not the sole solvent.

Hopkins and Whiting15 discuss the effect upon rock phosphate of the
nitrous acid produced through the oxidation of NH3 by Nitrosomonas.

OBJECT OF INVESTIGATION

Bacteria may effect the solution and disintegration of minerals in
at least two ways:

1. Through the oxidation or reduction of one or more of the con-
stituents of the mineral by specific organisms.

2. By the action of some end-product of bacterial activity: i. e.,
H ion resulting from acid produced, or OH ion from the production of
NH3.

In the present investigation some of the fundamental considerations
in connection with the second phase of the subject were studied, the
work being limited to the effect of acid end-products. In none of the
work reviewed in the foregoing section have attempts been made to
obtain results which may be used to determine whether the action of
bacteria upon minerals may follow the usual chemical laws, or at least

250 University of California Publications in Agricultural Sciences [Vol. 4

present some constant relationship which may be expressed in an
empirical formula. The work in hand has had for its object the pro-
curement and interpretation of data suitable for the confirmation of
some such relationship.

METHOD OF ATTACK AND THEORY

In order to obtain such data it was found necessary to use a different
method of attack from that usually pursued in a bacteriological problem.
The most common approach to such a problem is by the determination,
either in solution culture, in sand culture, or in culture upon the moist
pulverized mineral itself, of the amount of material made soluble by
the growth of certain organisms. This method gives a series of isolated
results, which, though no doubt interesting in themselves, are entirely
unrelated either among themselves or to any factor which may control
the magnitude of the bacterial effect. In dealing with the phase of the
problem studied in this paper, a different method is employed, a
method by which it is hoped to show a certain relationship between H
ion produced by bacteria and the amounts of bases brought into
solution.

The magnitude of the effect of bacterial end-products upon a mineral
will depend upon the equilibrium involving that end-product and
mineral. As stated before, in this study it is elected to deal with cases
in which acids are the end-products in question. Therefore, it was
deemed necessary first to study the equilibria of certain acids, used
over a wide range of concentrations, with certain minerals. The object
of these equilibrium studies was to compare the H ion concentrations
of the acids, at the various molar concentrations, with the amounts of
material which are brought into solution, so to speak, by these H ion
concentrations. Later, studies were made of the H ion production by
certain organisms, and of the equilibria involving these acids and the
minerals, the H ion and the amounts of material in solution being
determined.

There is an extensive literature dealing with the equilibria
of various soils and minerals in contact with solutions of acids, of
bases, and of salts. This literature deals largely with the absorption of
bases by soils and minerals, and with the exchange of bases between
solution and soil or solution and mineral. In nearly every instance,
however, the data are insufficient to warrant their use for substitution
in formulae.

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 251

The earlier work is so ably and completely reviewed by Sullivan,16
in his consideration of The Interaction between Minerals and Water
Solutions, that it seems advisable to refer the reader to that excellent
resume rather than to attempt a repetition here. This review covers
the work of Thompson,17 Way,18 Eichhorn,19 Henneberg and Stohmann,20
Lemberg,21 Peters,22 Liebig,23 Rautenberg,24 Van Bemmelen,25 Armsby,26
and Boedeker,27 and deals largely with the controversy of the physical
process of adsorption versus chemical reaction as the cause of the
absorption and exchange of bases in soils.

The work of Dittrick28 is not included above. His work is reported
in two papers, and covers experiments with a granite and an amphibole
paridotite, and solutions of KC1, NaCl, NH4C1, CaCl2, MgCl2, KN03,
K2S04, and K2C03, in the concentrations N/1, N/10, and N/100. He
found Ca and Mg dissolved by the solutions, the least by N/1 solution,
more by the N/10 solution, and most by the N/100 solution. The
amount of exchange was greater with the more decomposed rock.
Repeated extraction with solutions removed roughly twice as much
material as a single extraction.

The action of an acid upon a silicate is really an exchange of H ion
for any of the bases which come into solution through its action. This
exchange is a reversible chemical reaction, and as such should conform
with the chemical laws applicable to such reactions.

Let us consider a simple case of reversible reaction, or balanced
action, that of the union of hydrogen and iodine to form hydriodic
acid: H2+I2-2HL

In this reaction there is a point of equilibrium which is represented
by the equation :

Ch2 X C12 _ ki _ „

Chi K

This is an example of homogeneous equilibrium, involving the
gaseous phase only.

A somewhat different case is encountered with the decomposition
of calcium carbonate into carbon dioxide and calcium oxide:

CaC03 =0= CaO + C02.

Here we have both gaseous and solid phases. The amount of gas
taking part in the reaction may be measured by its pressure, but the
solid must be considered in a different light. This reaction may be
considered as taking place in the gaseous phase, the solids present fur-
nishing a constant supply of CaC03 and CaO vapor. Then if C is the

252 University of California Publications in Agricultural Sciences [Vol. 4

pressure of CaC03, Ci the pressure of CaO, and c the pressure of C02
at equilibrium, the equation at equilibrium is:

kC = kiCiC, or c = r-~r = K

Going farther we have the following as a reaction in which we have
a solid and a gas on both sides of the equation :

H20 + Fe - FeO + H2

Let c be the concentration of H20, C that of Fe, Ci of FeO, and Ci of
H2. At equilibrium we then have the equation:

kcC = ki Ci Ci.

, c ki Ci T^
and — = -j— ft = &
Ci kC

or — = K

Ci

Now applying this last equation to a case where we have a solution
of a salt acting upon a solid to form another salt in solution and a
solid we will take the following reaction:

BaS04 + Na2C03 =c= Na2S04 + BaC03.

Let C, c, Ci and Ci be the respective concentrations of the reacting
substances. Then from the above equation

-=K,

Cl

CNa2CQ3 _ T7-

Cn,i2&04

This last equation shows that the equilibrium point is measured by the
ratio of concentrations of the soluble reacting materials. As stated by
Walker:29 "The active masses of the barium salts may be accounted
constant in the reaction, for although they are generally spoken of as
' insoluble ', they are in reality measurably soluble in water. The aqueous
liquid in contact with them will be and remain saturated with respect to
them, i.e., their concentration and active mass in the solution will be
constant. The equilibrium will thus be determined by a certain ratio
of the concentrations of the soluble sodium salts, independent of what
the actual values of the concentrations may be."

A mineral in contact with an acid solution is very similar to the last
case cited above, and at any concentration of the acid the equilibrium
should be measured by the ratio

concentration of the acid

concentration of the material in solution
when these are measured at equilibrium.

= K

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 253

The H ion is usually assumed to be the measure of the active acid.
In acid solution the H ion concentration is some function of the molar
concentration of the acid. Since gas chain measurements yield values
which approach the theoretical H ion concentration, determinations of
the H ion concentrations, Ch, by this method may be substituted for
" concentration of acid" in the above formula and the ratio

^material in solution

will be constant.

When dealing with materials as complex in their chemical structure
as are minerals, it is recognized that a rigid adherence to the theoretical
laws can not be expected, and it becomes necessary, therefore, for a
comprehensive knowledge of such reactions as are considered in this
paper, to resort to certain empirical formulae. It is obviously imprac-
ticable to attempt to consider in the term " concentration of material
in solution," as used in the formula above, all the bases which may be
present in the solution in contact with the mineral at equilibrium.
These considerations lead to the assumption that any one of the bases
may be taken as measuring the magnitude of the action of the acid on
the mineral. Consequently, it is suggested that the formula thus far
developed theoretically, be changed to the empirical formula

— h = K
Ca ^

where Ch is the concentration of hydrogen ion, and Ca represents the
molar concentration of Ca, Mg, Fe, or K in solution at equilibrium
with the acid.

Since it is desired to study the initial H ion concentration with
respect to Ca, Mg, Fe, or K in solution, it becomes necessary to add a
still further modification to the empirical formula — namely, the expres-
sion of the initial H ion concentration in terms of, or as some function
of, the H ion concentration at equilibrium. It is found that this is an
exponential function of the H ion concentration at equilibrium. (See
fig. 0.) ' In this figure, log. Ch of the acid alone is plotted against log.
Ch of acid in contact with the mineral. The resulting graph is a straight
line, indicating that the ratio is constant, at least over a certain range
of concentrations. Thus Ch of the acid alone is a logarithmic or ex-
ponential function of Ch of the acid in contact with the mineral, or

C Cx

Ch = Ch • Then the equation — = K becomes — = K, where Ch is the

254 University of California Publications in Agricultural Sciences [Vol.4

initial H ion concentration of the acid, Ca the concentration of Ca, Mg,
Fe, or K in solution at equilibrium, and K is a constant. This equation
is the one used in the consideration of the data contained in this paper.

The formation of acid as the end-product of bacterial activity is a
property common to many organisms including many which are com-
monly found in soils. Acid production by bacteria has been the subject
of many investigations. It is used as a means for identifying the
various members of the Colon group of bacteria, and consequently the
fermentation of sugars by this group has been widely studied. A
review of the entire field will not be attempted, but it is well to mention
work having a more or less direct bearing upon the subject in hand.

Harden30 studied the Chemical Action of B. coli communis and Similar
Organisms on Carbohydrates and Allied Compounds. He found that the
lactic acid produced never exceeds one-half of the sugar fermented. The
amount of acid formed varies with the different sugars.

In a later study with Penfold 31 he used B. coli on a medium com-
posed of 2 per cent glucose and 1 per cent peptone. He gets of alcohol,
acetic acid, formic acid, C02, lactic acid, and succinic acid, respectively
17.22 per cent, 20.60 per cent, 2.55 per cent, 17.30 per cent, 40.60 per
cent, and 4.80 per cent of the sugar used. With a selected strain of
B. coli, the lactic acid reaches 70 per cent of the amount of sugar used.

Michaelis and Marcora32 find that the highest degree of acidity
produced by B. coli at 37° C. is 1 x 105.

In the lactic acid fermentation of sugars, Claflin33 notes the formation
also of formic, propionic, and acetic acids, the acetic acid formation
depending upon the degree of aeration. Ninety-five to 97 per cent of
the sugar may be converted into lactic acid, with a very low production
of volatile acids, not over one-half per cent. He claims that the nature
of the acid produced depends upon the organism and not upon the
nature of the medium.

In the present work it must be shown what is the amount of acid, or
rather the H ion concentration, produced by the organisms upon the
carbohydrate media used, and what is the effect of this concentration
upon the minerals. Is this effect similar to that of the acids alone?

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 255

EXPERIMENTAL METHODS

As suggested in the foregoing section, the experimental work is
divided into two parts, the first consisting of the equilibrium studies
with the minerals and acid solutions, the second of bacteriological
studies.

Equilibrium studies. — The acids used were hydrochloric, sulfuric,
oxalic, phosphoric, lactic, formic, and acetic. It will be observed that
these acids vary in the degree of dissociation for any given concentra-
tion, hydrochloric acid being the most highly dissociated, and acetic
acid being the least ionized. The minerals were calcium silicate, ortho-
clase feldspar, biotite, and granite. They were ground in a ball mill to
pass a 200-mesh sieve. The acids were used in the concentrations : N/5,
N/25, N/50, N/100, N/250, N/500, N/1,000, N/2,000, N/5,000, and
N/10,000.

The work was carried on at room temperature. The equilibrium
studies were arranged in four series, one for each mineral, and each
series contained a sub-series for each acid. 200 cubic centimeters of
solution were thoroughly shaken with 5 grams of mineral, Jena glass-
ware being used. The solutions were allowed to remain in contact with
the mineral for three days, which time is shown in the following table
to be sufficient for equilibrium.

Table Showing the Effect of the Time of Contact
upon the H ion Concentration.

Orthoclase + N 5 HC1

Days H ion concentration

1 709 xlO-1

2 636X10-1

3 615X10-1

4 656 x 10-1

5 615 x 10-1

As much as possible of the supernatant solution was then pipetted
off and filtered through a Whatman No. 42 filter paper, an unfiltered
portion being taken, however, for the H ion determination. In an
aliquot of the filtered solution, calcium, iron, magnesium, and potassium
were determined, the calcium and iron by titration with potassium
permanganate, the magnesium and potassium gravimetrically as the
pyrophosphate and chloroplatinate respectively.

256 University of California Publications in Agricultural Sciences [Vol. 4

The H ion determinations were made by the use of the hydrogen
electrode, with the same modifications as were used by Sharp and
Hoagland34 for soils. These determinations are made both on the acid
solutions, and on the acids in contact with the minerals.

A question arose as to the possibility of the formation of a gelatinous
coating upon the surface of the mineral, which would hinder the further
action of the acid, and prevent attainment of equilibrium. In order
to ascertain whether the amount of shaking had been sufficient to
remove this film and allow the reaction to come to equilibrium, the fol-
lowing experiment was proposed. A 5-gram portion of mineral was
shaken with 200 cc. of N/5 HC1, as in the experimental procedure.
The mineral and solution were then poured upon a filter paper, and the
mineral was dried and then ground in a mortar. H ion determinations
were made upon the filtrate. The filtrate was poured upon the dried
mineral and allowed to remain for three days with frequent shaking.
H ion determinations were again made. The following data show that
there is no significant change in H ion concentration in the second
contact of the solution with the mineral :

H ion Cone.

Calcium silicate +N 5 HCl....lst contact 0.607 x 10"1

Calcium silicate +N 5 HC1....2d contact.. . . 0.607 x 10"1

Labradorite +N 5 HCl....lst contact 0.797 x 10"1

Labradorite +N 5 HC1....2d contact 0.828 x 10"1

Bacteriological work. — Three organisms were used, Azotobacter,
Bacillus coli, and B. lactis acidi. The first of these was chosen because
of the very high H ion concentration which it produced upon dextrose
solution, nearly 1. x 10_1 as determined by Dr. Waynick in this labora-
tory. B. coli is referred to in the literature previously cited as producing
large amounts of acid, and B. lactis acidi was taken as a typical acid
producer. Azotobacter were grown upon 2 per cent dextrose solution,
B. coli in a solution of 2 per cent dextrose and 1 per cent peptone as
used by Penfold, and B. lactis acidi in 1 per cent dextrose. The work
was arranged in three series, one for each organism. Each series con-
tained five cultures, each culture containing 1,000 cc. of solution in
1,200 cc. Florence flasks. One culture contained no mineral. The other
cultures contained 25 grams of mineral each, one with calcium silicate,
one with orthoclase feldspar, another with biotite, and one with granite.
These cultures were run for a total time of sixteen days, H ion determina-
tions being made at 1, 2, 3, 5, 7, 9, 11, and 16 days, and on each of these
days 100 cc. of solution was removed for the determination of calcium,
iron, magnesium, and potassium. The cultures were grown at a tem-
perature of 28° C. and the customary bacteriological precautions were
observed throughout the work.

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 257

DATA

The data obtained by the methods given above are reported in
tables 1 to 38 inclusive. The amounts of calcium, magnesium, iron, and
potassium are calculated and expressed as moles per liter. Both the
initial and final H ion concentrations are also reported as gram mole-
cules per liter. For the convenience of the reader, the logarithms of
these numerical values are given in adjacent columns.

Accompanying each table is a graphical representation of the rela-
tion between certain series of values given in that table. (Owing to a
loss of material during the analysis, tables 3, 9, and 22 are incomplete;
there are, therefore, no graphs for these tables.) The logarithms
of the H ion concentrations, log. Ch, are plotted along the ordinates,
and the logarithms of the concentrations of Ca, Mg, Fe, or k, log. Ca,
along the abscissas, and the average curve is drawn through the points
thus obtained.

In the section of this paper dealing with " Method of Attack and
Theory," certain assumptions are made and ultimately expressed in the

Cx

empirical formula, — = K. By substitution of the experimental data

Ca

in this formula, the values of the constants x and K may be calculated.
If these values of x and K are constant for a given series, then the ratio,

— , is constant for that series, and the plotted graph representing that

Ca

ratio will be a straight line, or conversely, a straight line curve indicates
that x and K are constant. The straight line graph expresses a direct
ratio between series of values, these values being, in this case, the
logarithms of Ch and of Ca.

The exponential constant x and the reasons for its use have been
discussed previously. It expresses the relation of H ion at equilibrium
to the initial H ion concentration of the acid. That this relationship is
of an exponential character may be due to chemical reaction, to ad-
sorption, or to a combination of these phenomena. It is not proposed,
however, to differentiate here between adsorption and chemical re-
action, the purpose of this work being to provide a means, empirical if
necessary, of accounting for the magnitude of the action of acids upon
minerals.

The constant K is the numerical expression of the ratio of the
logarithm of the initial H ion concentration to the logarithm of Ca, Mg,

258 University of California Publications in Agricultural Sciences [Vol. 4

Fe, of K brought into solution, so to speak, by that H ion concentration.
The numerical magnitude of K for any table represents the slope or
inclination of the graph plotted from that table. The range of values
for K may be very large, varying from infinity, for a horizontal line,
to zero, for a vertical line.

Since it is possible to draw a straight line averaging the points
plotted from the experimental data, the graphical method is employed
for obtaining values of log. Ch and log. Ca for substitution in the equation
for the calculation of x and K. By this means average values of x and
K may be computed without resorting to a calculation of all the possible
combinations of equations for which data are available. The use of this
procedure eliminates a large part of the tedious mathematical routine,
and it is recognized as yielding averages sufficiently close to the statis-
tical average to serve the purpose contemplated in this paper. If the
above preliminary remarks are borne carefully in mind, the following
consideration of the groups of tables and graphs will be clear.

Tables 1 to 7 contain the data for the equilibria between calcium
silicate and the acids. The figures accompanying these tables are
sufficient to show that the graph for any given series is a straight line.
As stated before, this signifies that x and K are constant for each series,
and that the reaction of the acid with the mineral takes place in accord-

ance with the formula — = K. The slope of the graphs, however, seems

Ca

to become less for the equilibria involving the less dissociated acids, the
slope for acetic acid being much less than that for hydrochloric acid.
As explained before, this difference in slope is indicated by the
following numerical values for the constant K calculated from the
graphs, the slope becoming less as K increases :

HC1 K = 0.01391

Sulfuric acid K = 0.2642

Phosphoric acid K = 0.4448

Lactic acid K = 14.86

Formic acid K = 335.5

Acetic acid K = 941.2

Since, as stated before, the graphs represent ratios of log. Ch to
log. Ca, and since this ratio varies with the slope of the graph, it would
seem, from a comparison of the curves for HC1 and acetic acid, that
an acid such as HC1, which is highly ionized, brings smaller amounts of
materia] into solution per unit increase of H ion than do those acids,
acetic for instance, which have a lower ionization constant. This
apparent difference in the action of various acids is due undoubtedly to

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 259

the fact that the commercial calcium silicate was used for this work,
and that it contained considerable quantities of CaC03, as shown by
the marked effervescence which occurred when the acid was added to
this material. The loss of C02 from the system undoubtedly affected
the true equilibrium, and this apparently greater action of the less
dissociated acids is the result. As will be seen in the considerations
which follow, this difference in effect between various acids occurs
only with calcium silicate.

In tables 1 to 7, as well as in those which follow, there are no
data for calcium where oxalic acid is used, because of the insolubility of
the resulting calcium oxalate. This fact is mentioned again, and its
importance is emphasized further, in connection with a general state-
ment corcerning the action of the H ion concentration of acids upon
minerals.

The data for the various acids and orthoclase are found in tables 8
to 12 inclusive. From a comparison of the corresponding graphs,
it is seen that they are quite steep, and that all have approxi-
mately the same slope. This observation is verified by a consideration
of the constant, K, as calculated for the various members of this group
of tables. The fact that K is very small is evidence that the graphs
approach the perpendicular, and when it is remembered that the values
for K range from zero to infinity for a change of 90 degrees in slope, it
is obvious that the very small range of values for K given here,
0.00002661 to 0.000001427, represents a very small difference in the
slopes of the various curves. The fact that K is constant for each
series, and that the corresponding graph is a straight line, goes to show
that the calcium coming into solution is a logarithmic function of the
initial H ion concentration of the acid, and that the assumptions ex-

Cx

pressed in the formula — = K are verified by experimental evidence .

Further proof of these assumptions is offered in the next group of
tables, numbers 13 to 19 inclusive, which give the data for the acids in
equilibrium with biotite. Data for calcium, magnesium, and potassium
in solution are reported. As in the previous series of tables, the graphs
for calcium are straight lines and have about the same slope, the extreme
range of values for K being from 0.00005790 to 0.000001071. The
constant K for the magnesium determinations is more variable, but
still no large discrepancy is apparent, the values ranging from 0.04373
to 0.000008395.

A deviation from the straight line graph is encountered in the
figures and tables expressing the equilibria for granite and the acids,

260 University of California Publications in Agricultural Sciences [Vol. 4

tables 20 to 26 inclusive. When the logarithms of the data for iron are
plotted against the logarithms for H ion concentrations and the lines
are drawn through the points thus obtained, the resulting curves are
not straight lines. (See figures 20 to 26.) The flatter portion of the
curve occurs in every instance at approximately the value, 3.0, repre-
sented by that logarithm of the H ion concentration, and probably is
due to the formation of another compound of iron at that concentra-
tion. Since these curves are not straight lines, it is obvious that no
constant values for x and K may be calculated therefrom, and further-
more it may be inferred that any iron compounds in the mineral do not
react with the acids in accordance with the proposed formula. The
curves for calcium, however, are straight lines, thus affording still
further proof that the assumptions regarding the nature of such re-
actions are correct as far as calcium is concerned. The graphs have
nearly the same slope throughout the series of figures, the values for
K ranging from 0.000001328 to 0.000007799.

In a general survey of the graphs thus far discussed, instances may
be observed in which certain plotted points are far from coincident with
the straight line graph. In certain cases, these discrepancies represent
error in the determinations. Where they appear in the lower portion
of the graph, however, the last two -or three points dropping below the
curve, they occur because the lower limit of the determination has been
reached, and no smaller amounts can be determined with any degree
of accuracy.

A consideration of the meaning and the possible relationships of the
results thus far reviewed is not inappropriate at this point. It is the
opinion of the writer that that type of investigation is the most valuable
which has for its object the procurement of data which are related,
either among themselves, or to certain controllable factors, and which
may be taken as the basis for, or in verification of, some general law
suitable either for the explanation of certain phenomena or for direct
application in the prediction of future results. Thus a general con-
sideration of the tables and figures leads to the following remarks.

All the straight line graphs for a given mineral, excepting calcium
silicate, the deviation of which has been explained, have practically the
same slope and give nearly the same values for x and K. It follows
therefore, that if the curves for one mineral in contact with the various
acids be superimposed one upon the other, they will all fall practically
in the same straight line. This would seem to indicate, for a given
mineral, and within the limits of the concentrations used, that the amount
of calcium, magnesium, or potassium coming into solution is a function

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 261

of the H ion concentration of the acid, regardless of the nature of the
acid used, except, and this exception is extremely important, in those
cases where the acid forms compounds which are less soluble at any
given H ion concentration than the compounds in the mineral itself.
The importance of this exception must be emphasized, and it is illus-
trated in a very striking manner by the different series with oxalic acid
where only traces of calcium are found in solution. It is recognized
that this illustration represents an extreme case and that other so-
called insoluble compounds may approach the mineral compounds in
solubility.

The objection was raised to the foregoing generalization that a
N/100 solution of acetic acid, for instance, contains the same total
molar concentration of hydrogen as a N/100 hydrochloric acid solution,
regardless of the relative H ion concentration of these acids. The hydro-
chloric acid is, of course, the more highly dissociated acid, but will not
the slightly dissociated acetic acid continue to give off H ion as that
already in solution combines with the mineral, and should not the ulti-
mate result be the same with the acetic as with the hydrochloric acid
for a given molar concentration? That this objection is not sub-
stantiated by fact is due doubtless to the following reason. In general
the salts of acetic acid are much more highly dissociated than is the
acid itself. Consequently, the acetates formed by the contact of acetic
acid with the mineral will be fairly highly dissociated, thus supplying
the solution at equilibrium with a certain concentration of acetic ion.
The presence of this acetate ion will depress or prevent the further
ionization of the acetic acid in solution, and thus practically limit the
action of the acetic acid to its original H ion concentration. This same
explanation will hold for other slightly dissociated acids.

The general relation existing between the H ion concentration of
acids and the amounts of Ca, of Mg, or of K in solution, may have the
following practical application. It is desired to determine the effect of
certain acids upon a mineral. This mineral may be studied in equi-
librium with different concentrations of HC1, and the logarithmic
graph constructed as in the foregoing mineral series. Any point on this
graph represents a ratio of log. H ion to log. Ca, or whatever base it is
desired to consider, in solution. Thus, by determining the H ion con-
centration of the acid whose action it is desired to predict, we may, by
referring to the graph, estimate the magnitude of the effect of the acid
upon the mineral, at least within certain limits already discussed. The
application suggested above may be made to the effect of acids produced
by bacterial growth, and in the prediction of their action upon a given
mineral.

262 University of California Publications in Agricultural Sciences [Vol. 4

The above application is suggested merely as a possibility, and it is
fully recognized that there is room for much further study and research
before the existence of such a general relationship can be definitely
established. It must be emphasized also that the constants for one
mineral and one set of conditions can not be applied directly to another
mineral and a different set of conditions. The constants must be de-
termined, and the resulting graph constructed for every application of
the relation suggested.

The data obtained from the bacterial series still await consideration.
As expressed in tables 26 to 38, and in the corresponding figures, the
action of the acids produced by bacteria seems to differ in magnitude
from the action of the acids used in the foregoing series. In regard to
this difference, it should be observed that Ch, the H ion concentration,
was determined, for the bacterial series, in solution cultures with no
mineral present. Had the bacterial growth been stopped immediately
following the H ion determination, and had this solution then been
brought into contact with the mineral, the magnitude of the effect
should have been comparable with that of the acid series. Instead, the
amounts of material coming into solution were determined in a series
parallel with the above, wherein bacteria were grown in solution in
contact with the minerals. It had been assumed that the rate of H ion
production would be the same, both in solution culture and in solution
in contact with the mineral. This assumption was found to be incorrect.
In the mineral cultures the acid was partly neutralized as produced,
and the growth of the organism was not inhibited by the increasing
concentration of acid as it was in the dextrose solution with no mineral.
Consequently, the total H ion as produced in the mineral cultures, and
indicated by the large relative amounts of material coming into solution
in these cultures, was much greater than that produced in the parallel
series without mineral. Since the data for H ion, Ch, as expressed in
the tables, were obtained from the latter series, it is obvious that the
graphs plotted from a ratio of H ion, as determined in dextrose solution,
to material in solution, as determined in the mineral cultures, are not
directly comparable with the graphs for the equilibria between acids and
minerals.

The lack of agreement between the acid series and the bacterial
series is made evident by a review of the curves and the corresponding
constants for the bacterial series. The graphs are straight lines, but
they have less slope than do those graphs for the corresponding mineral
in equilibrium with the acids. For instance, the constant, K, for ortho-
clase and Azotobacter is 19.77 against a value approaching l(h6 for

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 263

orthoclase and the acids, and the graph for the former has much
less slope than the graph for the latter. The constant, K, for orthoclase
and B. coli is 13,490, against 1CH5 for orthoclase and the acids. B. lactis
acidi, which produced acid very slowly, is represented by graphs which
more nearly resemble those of the acid-mineral series, and the value for
K for calcium from orthoclase, for instance, is 0.0006652. Since dis-
crepancies of the same general nature and magnitude as those just
pointed out, are apparent in the other graphs and constants for the
bacterial-mineral series, the reader is referred to the graphs and tables
for further comparisons.

The important point brought out by the bacterial series is that the
graphs for calcium, for magnesium, and for potassium are straight lines,
and that x and K are constant for a given series. Thus it is shown that
the reactions between minerals and the acids produced by bacterial
growth, conform with the given empirical formula. Since this same
formula has been successfully applied to the chemical equilibria between
various acid solutions and the same minerals, it may be concluded that
the action of bacterial end-products upon minerals, at least when these
end-products are acids, is explainable upon the basis that it is a chemical
reaction.

SUMMARY

Equilibria of certain minerals and various concentrations of acids
are studied.

Equilibria of the same minerals with solutions in which bacteria are
producing acid are also studied.

The data obtained from the acid-mineral series are applied to the

Cx

formula — = K.

Ca

It is found that the reactions occurring in the mineral-acid equilibria
conform with the given formula.

It is suggested that a general -relation exists between the initial
H ion concentration of the acid and the amount of material which the
acid brings into solution when in contact with a mineral.

A practical application of the relation just referred to, is suggested.

The data obtained from the bacterial studies are applied to the

formula — = K.

Ca

The reactions occurring in the bacterial series also conform with the
above formula.

264 University of California Publications in Agricultural Sciences [Vol. 4

It is concluded that the action of acid bacterial end-products upon
minerals is explainable as a chemical reaction.

The author wishes to express his gratitude to Dr. C. B. Lipman
for the suggestion of the problem and for his interest and help during
the progress of the work, and to Professor L. T. Sharp and Dr. D. D.
Way nick for many helpful suggestions.

Transmitted September 2, 1919.

LITERATURE CITED

1 Muntz, A.

1890. Chimie agricole. Sur la decomposition des roches et la formation de la
terre arable. Compt. Rend. Acad, des Sciences, Paris, vol, 110,
pp. 1370-1372.

2 Branner, J. C.

1897. Bacteria and the decomposition of rocks. Am. Jour, of Sci., vol. 153,
p. 438.

3 Hall, A. D., and Miller, N. H. J.

1908. The nitrogen compounds of the fundamental rocks. Jour, of Agric
Sci., vol. 2, pp. 343-345.

4 Merrill, G. P.

1895. Disintegration of the granite rocks of the District of Columbia. Bull.

Geol. Soc. Am., vol. 6, pp. 321-332.

5 Renault, B.

1896. Conclusions from an article by Renault entitled, "Les bacteries et leur

oeuvre geologique." Nature, vol. 55, p. 40.

6 Holland, T. H.

1903. On the constitution, origin and dehydration of laterite. Geol. Mag.,
vol. 40, pp. 59-69.

7 Lacroix, A.

1906. Sur la transformation de roches volcaniques en phosphate d'alumine
sous 1'innuence de produits d'origine physiologique. Compt.
Rend., Acad, des Sciences, Paris, vol. 143, pp. 661-664.

8 Bassalik, K.

1913a. Decomposition of silicates by soil bacteria. Zeitsch. Garungsphysiol.,
vol. 2, pp. 1-32.

19136. Silicate decomposition by soil bacteria and yeasts. Ibid., vol. 3,
pp. 15-42.

9 Kawamura, T.

Studies on "Tengunomugimethi."

10 Lipman, J. G., and McLean, H. C.

1916. The oxidation of sulphur in soils as a means of increasing the availability
of mineral phosphates. Soil Science, vol. 1, pp. 533-539.

11 Stoklasa, J.

1900. Ueber den Einfluss der Baktcrien auf die Knochenzersetzung. Central-
blatt fur Bakt., Abt. 2, Bd. 6, pp. 554-560.

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 265

12 Koch, A., and Kroeber, E.

1906. Der Einfluss der Bodenbakterien auf das Loslichwerden der Phos-

phorsaure aus verschiedenen Phosphaten. Fiihling's Landwirt.
Zeit., vol. 55, pp. 225-235.

13 Kroeber, E.

1909. Ueber das Loslichwerden der Phosphorsaure aus wasserunloslichen
Verbindungen unter der Einwerkung von Bakterien und Hefen.
Jour, fur Landwirt., vol. 57, pp. 5-80.

14 Sackett, W. G., Patten, A. J., and Brown, C. W.

1908. The solvent action of soil bacteria upon the insoluble phosphates of raw
bone meal and natural raw rock phosphate. Michigan Agric.
Exper. Station, Special Bull., No. 43, pp. 363-390.

15 Hopkins, C. G., and Whiting, A. L.

1916. Soil bacteria and phosphates. Illinois Exper. Station Bull. No. 190,
pp. 395-406.

16 Sullivan, E. C.

1907. The interaction between minerals and water solutions with special

reference to geologic phenomena. U. S. Geol. Surv., Bull. 312,
pp. 9-64.

17 Thompson, H. S.

1850. On the absorbent power of soils. Jour. Roy. Agric. Soc, vol. 2, pp. 68-74.

18 Way, J. T.

1850. On the power of soils to absorb manure. Jour. Roy. Agric. Soc, vol. 2,

pp. 313-379.
1852. Idem, Second paper, ibid., vol. 13, pp. 123-143.
1854. On the influence of lime on the absorptive properties of soils. Jour. Roy.

Agric. Soc, vol. 15, pp. 491-514.

19 Eichorn, H.

1858. Ueber die Einwirkung verdunnter Salzlosungen auf Silicate. Pogg.

Ann., vol. 105, pp. 126-133.

20 Henneberg, J. W. J., and Stohmann, F. K. A.

1859. Ueber das Verhalten der Ackererde gegen Losungen von Ammoniak und

Ammoniaksalzen. Jour, fur Landwirt. Gottingen, Bd. 7, (Neue
Folge, Bd. 3), pp. 25-47.
1858. Ueber das Verhalten der Ackerkrume gegen Ammoniak und Ammoniak-
salze. Liebig's Annalen, vol. 107, pp. 152-174.

21 Lemberg, H. J. VON.

1870. Ueber einige Umwandlungen finnlandischer Feldspathe. Zeitschr. der
deutsch. geol. Gesell., vol. 22, pp. 335-372.

22 Peters, E.

1860. Studien ueber den Boden aus dem Laboratorium zu Tharand. Landw.

Versstat., vol. 2, pp. 113-116.

23 LlEBIG, J. VON.

1858. Ueber einige Eigenschaften der Ackerkrume. Ann. chem., vol. 105, pp.
109-144.

24 Rautenberg, F. VON.

1862. Ueber die Absorptionsfahigkeit verschiedener Bodenarten und das
geognostitischen Vorkommen derselben. Jour, fur Landwirt.,
vol. 10, pp. 49-66.

266 University of California Publications in Agricultural Sciences [Vol. 4

25 Van Bemmelen, J. M.

1899. Die Absorption IV. Die Isotherme des kolloidalen Eisenoxyds bei 15°.

Zeitschrift flir anorg. Chemie, vol. 20, pp. 185-211.
1878. Das Absorptionsvermogen der Ackererde. Landwirt. Versstat., vol. 21,

pp. 135-191.
1881. Die Verbindungen einiger fester Dioxydhydrate mit Sauren, Salzen und

Alkalien. Jour, fur prakt. chemie, Ser. 5, Bd. 131-132, pp. 324-

349, 379-395.

26 Armsby, H. P.

1878. Ueber das Absorptionsvermogen des Bodens fur Basen. Landwirt.
Versstat., vol. 21, pp. 397-405.

27 BOEDEKER, C. VON.

1859. Ueber das Verhaltniss zwischen Masse und Wirkung beim Contact
ammoniakalischer Fliissigkeiten mit Ackererde und mit kohlen-
saurem Kalk. Jour, fur Landwirt., vol. 7, pp. 48.

28 DlTTRICK, M. VON.

1901. Chemisch-geologische Untersuchungen ueber "Absorptionserscheinun-
gen" bei zersetzten Gesteinen. Mitt, grossh. bad. geol. Landesan-
stalt, vol. 4, pp. 341-366.

1905. Idem, Second paper, ibid., vol. 5, pp. 1-23.

29 Walker, James.

1913. Introduction to physical chemistry. Macmillan.

30 Harden, A.

1901. The chemical action of Bacillus coli communis and similar organisms on
carbohydrates and allied compounds. Jour. Chem. Soc. London,
vol. 79, pp. 691-698.

31 Harden, A., and Penfold, W. J.

1912. The chemical action on glucose of a variety of Bacillus coli communis
(Escherich) obtained by a culture in presence of chloracetate.
Proc. Roy. Soc. London, vol. 85 B, pp. 415-417.

32 Michaelis, L., and Marcora, F.

1912. Die Saureproduktivitat des bacterium coli. Zeitschrift Immunitats-
forschung u. exper. Terapie, Bd. 14, pp. 170-173.

33 Claflin, A. A.

1912. Products of the lactic fermentation of sugars. Orig. Comm. 8th Intern.
Congress Appl. Chem., vol. 25, Appendix, pp. 343-345.

34 Sharp, L. T., and Hoagland, D. R.

1916. Acidity and absorption in soils as measured by the hydrogen electrode.
Jour. Agric. Research, vol. 7, pp. 123-143.

1922] Wright: Equilibrium Studies With Certain Acids and Minerals

267

NOTE

The following legend refers to all the figures:

+ = Curve for Calcium.

O = Curve for Magnesium.

0 = Curve for Potassium or Iron.

The numbers along the ordinates represent the logarithms of the
H ion concentrations, or log. Ch. Those along the abscissas measure
the logarithms of the concentrations, or log. Ca, of calcium, magnesium,
iron, or potassium.

2.0

3.0

4.0 _

5.0

7.0 6.0 5.0 4.0 3.0 2.0

Fig. 0.

(See Table 8)

Relation of log. H ion, HC1, to log. H ion,

HC1 + Orthoelase.

268

University of California Publications in Agricultural Sciences [Vol. 4

TABLE I

Hydrochloric Acid

and Calcium Silicate

Concentration
HC1

Ch, H ion

Hydrochloric

Acid

Log. H ion

Hydrochloric

Acid

H ion _ Ca, Calcium
Hydrochloric Acid Mols. per
+Calcium Silicate Liter

Log. Calcium
Mols. per
Liter

N5

0.0882

2.94547

0.0313

0.00306

3.485721

N25

0.0218

2.33846

0.00000534

0.00218

3.338456

N50

0.0135

2.13003

0.00000175

0.00121

3.02785

N 100

0.00685

3.83569

0.000000671

0.000685

4.835691

N250

0.00321

3.50651

0.000000131

0.000376

4.575188

N500

0.00114

3.05690

0.0000000842

0.000240

4.380211

N 1,000

0.000677

4.83059

0.0000000587

0.000159

4.201397

N 2,000

0.000281

4.44871

0.0000000965

0.000122

4.086360

N 5,000

0.0000326

5.51322

0.0000000719

0.000120

4.079181

N 10,000

0.0000192

5.28330

0.000000620

0.000117

4.068168

Constants for the equation — = K :

Ca

x = 0.636
K = 0.01391

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 269

2.0

3.0

4.0

5.0

6.0

5.0

4.0

3.0

2.0

Fig. 1.

Hydrochloric Acid and Calcium Silicate.

(See Table 1)

270

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 2

Sulfuric Acid and Calcium Silicate

Concentration

Ch, H ion

Sulfuric

Acid

Log. H ion

Sulfuric

Acid

Hion

Sulfuric Acid
+Calcium Silicate

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.0567

2.75358

0.0300

0.00188

3.274158

N25

0.0186

2.26951

0.00000579

0.00197

3.294466

N50

0.0130

2.11394

0.000000450

0.00115

3.060698

N100

0.00632

3.80072

0.000000203

0.000655

4.816241

N250

0.00296

3.47129

0.0000000810

0.000356

4.551450

N500

0.00162

3.20952

0.0000000719

0.000218

4.338456

N 1,000

0.000931

4.96895

0.000000180

0.000148

4.170262

N 2,000

0.000600

4.77815

0.0000000323

0.000099

5.995635

N 5,000

0.000259

4.41330

0.0000000235

0.000079

5.897627

N 10,000

0.000174

4.24055

0.0000000364

0.000089

5.949390

Constants for the equation

K:

By graphical average :
x = 0.799
K = 0.2642
By calculation:

x = 0.858 ± 0.0074
K = 0.7332 ± 0.0313

v. = 5.99%
v. = 29.05%

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 271

2.0

3.0

4.0

5.0

6.0

5.0 4.0 3.0

Figure 2.
Sulfuric Acid and Calcium Silicate.
(See Table 2)

2.0

>72

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 3

Oxalic Acid and

Calcium Silicate

Concentration

Ch, H ion Log. H ion
Oxalic Oxalic
Acid Acid

H ion Ca, Calcium
Oxalic Acid Mols. per
+Calcium Silicate Liter

Log. Calcium
Mols. per
Liter

N5

0.0218 2.33846

0.0347

N25

0.0110 2.04139

0.0000192

N50

0.00561 3.74896

0.00000175

N 100

0.00347 3.54033

0.000000433

N250

0.00169 3.22789

0.0000000941

N500

0.00105 3.02119

0.0000000778

N 1,000

0.000554 4.74351

0.0000000719

N 2,000

0.000317 4.50106

0.0000000637

N 5,000

0.000132 4.12057

0.0000000544

N 10,000

0.0000785 5.89487

0.000000469

TABLE 4

Phosphoric Acid

and Calcium Silicate

Concentration

Ch, H ion

Phosphoric

Acid

Log. H ion
Phosphoric
Acid

H ion Ca, Calcium
Phosphoric Acid Mols. per
+Calcium Silicate Liter

Log. Calcium
Mols. per
Liter

N5

0.0125

2.09691

0.0498

0.00307

3.487138

N25

0.00632

3.80072

0.00000707

0.000872

4.940516

N50

0.00424

3.62737

0.00000294

0.000525

4.720159

N100

0.00273

3.43616

0.00000054

0.000366

4.563418

N250

0.00144

3.15836

0.000000268

0.000208

4.318063

N500

0.000762

4.88195

0.0000000941

0.000149

4.173186

N 1,000

0.000372

4.57054

0.0000000482

0.000109

4.037426

N 2,000

0.000213

4.32838

0.0000000350

0.000089

5.949390

N 5,000

0.0000642

5.80754

0.0000000235

0.000074

5.869232

N 10,000

0.0000431

5.63448

0.0000000395

0.000074

5.869232

Constants for the equation — — = K:

Ca

x = 0.835
K = 0.4448

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 273

2.0

3.0

4.0

5.0

6.0

5.0 4.0 3.0 2.0

Figure 4.

Phosphoric Acid and Calcium Silicate.

(See Table 4)

274

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 5
Lactic Acid and Calcium Silicate

Concentration

N5
N25
N50
N 100
N250
N500
N 1,000
N 2,000
N 5,000
N 10,000

Ch, H ion

Lactic

Acid

0.00561

0.00252

0.00169

0.00114

0.000677

0.000472

0.000270

0.000189

0.000112

0.0000547

Log. H ion

Lactic

Acid

3.74896
3.40140
3.22789
3.05690
4.83059
4.67394
4.43136
4.27646
4.04922
5.73799

H ion

Lactic Acid
+Calcium Silicate

0.00577

0.000130

0.00000108

0.000000572

0.000000141

0.0000000877

0.0000000719

0.0000000364

0.0000000395

0.000000126

H

Constants for the equation — -

By graphical average:
x = 1.144
K = 14.86
Constants by calculation
x = 1.118 ± 0.0368
K = 12.09 ± 0.326

K:

Ca, Calcium
Mols. per
Liter

0.00308

0.00201

0.00123

0.000812

0.000445

0.000208

0.000148

0.000099

0.000079

0.000074

Log. Calcium
Mols. per
Liter

3.488551
3.303196
3.089905
4.909556
4.648360
4.318063
4.170262
5.995635
5.897627
5.869232

C. v. = 25.9%
C. v. = 12.01%

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 275

2.0

3.0

4.0

5.0

5.0 4.0 3.0

• Figure 5.
Lactic Acid and Calcium Silicate.
(See Table 5)

2.0

276

University of California Publications in Agricultural Sciences [Vol.

TABLE 6
Formic Acid and Calcium Silicate

Concentration

Ch, H ion

Formic

Acid

Log. H ion

Formic

Acid

H ion

Formic Acid
+Calcium Silicate

Ca. Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.00518

3.71433

0.00577

N25

0.00233

3.36736

0.0000635

N50

0.00156

3.19312

0.000000620

0.00119

3.075547

N 100

0.0010

3.00000

0.000000327

0.000694

4.841359

N250

0.000762

4.88195

0.0000000719

0.000365

4.563481

N500

0.000472

4.67394

0.0000000522

0.000208

4.318063

N 1,000

0.000343

4.53529

0.0000000350

0.000138

4.139879

N 2,000

0.000181

4.25768

0.0000000276

0.000119

4.075547

N 5,000

0.0000753

5.87679

0.0000000245

0.000099

5.995635

N 10,000

0.0000398

5.59988

0.0000000719

0.0000248

5.394452

Constants for the equation

C

K:

x = 1.324
K = 335.5

1922] Wright: Equilibrium Studies With Certain Acids and Minerals

277

2.0

3.0

4.0

5.0

5.0 4.0 3.0

Figure 6.
Formic Acid and Calcium Silicate.
(See Table 6)

2.0

278

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 7

Acetic Acid and

Calcium Silicate

Concentration

Ch, H ion

Acetic

Acid

Log. H ion

Acetic

Acid

H ion

Acetic Acid
+Calcium Silicate

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.00224

3.35025

0.000547

0.00285

3.454845

N25

0.000860

4.93450

0.00000797

0.00250

3.397940

N50

0.000677

4.83059

0.00000100

0.00126

3.100371

N 100

0.000454

4.65706

0.000000279

0.000742

4.870404

N250

0.000387

4.58771

0.000000116

0.000347

4.540329

N500

0.000213

4.32838

0.0000000350

0.000178

4.250420

N 1,000

0.000189

4.27646

0.0000000395

0.0000892

5.950365

N 2,000

0.000104

4.01703

0.0000000350

0.0000694

5.841359

N 5,000

0.0000884

5.94645

0.000000116

0.0000694

5.841359

N 10,000

0.0000414

5.61700

0.000000238

0.0000495

5.694605

Constants for the equation

Ca

x =

1.465

K =

941.2

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 279

2.0

3.0

4.0

5.0

5.0 4.0 3.0

Figure 7.

Acetic Acid and Calcium Silicate.

(See Table 7)

2.0

280

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 8

Hydrochloric Acid and Orthoclase

Concentration

Ch, H ion

Hydrochloric

Acid

Log. H ion

Hydrochloric

Acid

H ion

Hydrochloric Acid
+Orthoclase

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.0882

2.94547

0.0615

0.00159

3.201397

N25

0.0218

2.33846

0.0218

0.001449

3.159567

N50

0 0135

2.13003

0.00836

0.001045

3.019116

N100

0.00685

3.83569

0.00296

0.00094

4.973128

N250

0.00321

3.50651

0.000554

0.000685

4.835691

N500

0.00114

3.05690

0.0000784

0.000565

4.752048

N 1,000

0.000677

4.83059

0.000000935

0.00056

4.748188

N 2,000 .

0.000281

4.44871

0.00000110

0.00040

4.602060

N 5,000

0.0000326

5.51322

0.000000261

0.00038

4.579784

N 10,000

0.00000192 6.28330
Constants for Calcium:

0.00000010

0.000336

4.526339

x =

0.225

K =

0.000006310

1922] Wright: Equilibrium Studies With Certain Acids -and Minerals 281

2.0

3.0

4.0

5.0

6.0

5.0 4.0 3.0 2.0

Figure 8.
Hydrochloric Acid and Orthoclase.
(See Table 8)

282 University of California Publications in Agricultural Sciences [Vol. 4

TABLE 9

Oxalic Acid

AND ORTHOCLASE

Concentration

Ch, H ion

Oxalic

Acid

Log. H ion

Oxalic

Acid

H ion

Oxalic Acid
+Orthoclase

Ca, Calcium
Mols. per
Liter.

Log. Calcium
Mols. per
Liter

N5

0.0218

2.33846

0.0245

N25

0.0110

2.04139

0.00905

N50

0.00561

3.74896

0.00376

N100

0.00347

3.54033

0.000650

N250

0.00169

3.22789

0.00000564

N500

0.00105

3.02119

0.000000735

N 1,000

0.000554

4.74351

0.000000438

N 2,000

0.000317

4.56937

0.000000294

N 5,000

0.000132

4.12057

0.00000294

N 10,000

0.0000785

5.89487

0.00000294

TABLE 10

Lactic Acid

AND ORTHOCLASE

Concentration

Ch, H ion

Lactic

Acid

Log. H ion

Lactic

Acid

H ion

Lactic Acid
+Orthoclase

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.00561

3.74896

0.00441

0.001190

3.075547

N25

0.00252

3.40140

0.00123

0.00094

4.973128

N50

0.00169

3.22789

0.000650

0.00077

4.886491

N100

0.00114

3.05690

0.000372

0.000495

4.694605

N250

0.000677

4.83059

0.000181

0.00073

4.863323

N500

0.000472

4.67394

0.0000414

0.000495

4.694605

N 1,000

0.000270

4.43136

0.00000322

0.000465

4.667453

N 2,000

0.000189

4.27646

0.00000217

0.000475

4.676694

N 5,000

0.000110

4.04139

0.000000282

0.000366

4.563481

N 10,000

0.0000547

5.73799

0.000000261

0.000238

4.376577

Constants for Calcium :

x =

0.324

K =

0.00002661

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 283

2.0

3.0

4.0

5.0

5.0

4.0 3.0

Figure 10.
Lactic Acid and Orthoclase.
(See Table 10)

2.0

284

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 11

Formic Acid

AND ORTHOCLASE

Concentrator

Ch, H ion
Formic
l Acid

Log. H ion

Formic

Acid

Hion

Formic Acid
+Orthoclase

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.00518

3.71433

0.00296

0.000862

4.935507

N25

0.00233

3.36736

0.000677

0.000812

4.909556

N50

0.00156

3.19312

0.000270

0.000723

4.859138

N100

0.0010

3.00000

0.0000957

0.000713

4.853090

N250

0.000762

4.88195

0.0000153

0.000605

4.781755

N500

0.000472

4.67394

0.00000579

0.000535

4.728354

N 1,000

0.000343

4.53529

0.000000197

0.000535

4.728354

N 2,000

0.000181

4.25768

0.000000197

0.000495

4.694605

N 5,000

0 0000753

5.87679

0.000000205

0.000475

4.676694

N 10,000

0.0000398

5.59988

0.0000000923

0.000426

4.629410

Constants for Calcium:

x =

0.142

K =

0.000001427

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 28i.

2.0

3.0

4.0

5.0

5.0

4.0 3.0

Figure 11.
Formic Acid and Orthoclase.
(See Table 11)

2.0

286

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 12

Acetic Acid

AND ORTHOCLASE.

Concentration

Ch, H ion

Acetic

Acid

Log. H ion

Acetic

Acid

H ion

Acetic Acid
+Orthoclase

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

N5

0.00224

3.35025

0.000472

0.000074

4.869232

N25

0.000860

4.93450

0.000132

0.000058

4.763428

N50

0.000677

4.83059

0.0000696

0.00062

4.792392

N100

0.000454

4.65706

0.0000431

0.00065

4.812913

N250

0.000387

4.58771

0.0000179

0.00051

4.707570

N500

0.000213

4.32838

0.00000745

0.00048

4.681241

N 1,000

0.000189

4.27646

0.00000225

0.00043

4.633468

N 2,000

0.000104

4 01703

0.000000627

0.00039

4.591065

N 5,000

0.0000884

5.94645

0.000000438

0.00033

4.518514

N 10,000

0.0000414

5.61700

0.000000261

0.00029

4.462398

Constants for Calcium :

x =

0.235

K =

0.000006966

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 287

2.0

3.0

4.0

5.0

5.0

4.0 3.0

Figure 12.
Acetic Acid and Orthoclase.
(See Table 12)

2.0

288 University of California Publications in Agricultural Sciences [Vol. 4

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2.0

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Figure 13.
Hydrochloric Acid and Biotite.
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2.0

290

University of California Publications in Agricultural Sciences [Vol. 4

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2.0

3.0

4.0

5.0

5.0

4.0 3.0

Figure 14.
Sulfuric Acid and Biotite.
(See Table 14)

2.0

292

University of California Publications in Agricultural Sciences [Vol. 4

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Figure 15.

Oxalic Acid and Biotite.

(See Table 15)

2.0

294 University of California Publications in Agricultural Sciences [Vol.4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 295

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Phosphoric Acid and Biotite.
(See Table 16)

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 297

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Lactic Acid and Biotite.

(See Table 17)

2.0

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Formic Acid and Biotite.

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 301

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Acetic Acid and Biotite.

(See Table 19)

2.0

302 University of California Publications in Agricultural Sciences [Vol.4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 303

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Hydrochloric Acid and Granite.

(See Table 20)

2.0

304

University of California Publications in Agricultural Sciences [Vol. 4

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Figure 21.
Sulfuric Acid and Granite.
(See Table 21)

2.0

306

University of California Publications in Agricultural Sciences [Vol.4

TABLE 22
Oxalic Acid and Granite

Concentration

Ch, H ion

Oxalic

Acid

Log. H ion

Oxalic

Acid

N5

0.0213

2.33846

N25

0.0110

2.04139

N50

0.00561

3.74896

N 100

0.00347

3.54033

N250

0.00169

3.22789

N500

0.00105

3.02119

N 1,000

0.000554

4.74351

N 2,000

0.000317"

4.50106

N 5,000

0.000132

4.12057

N 10,000

0.0000785

5.89487

H ion

Oxalic Acid
+Granite

Ca, Iron
Mols. per
Liter

Log. Iron
Mols. per
Liter

0.0255

0.00772

0.00226

0.00000129

0.0000141

0.00000254

0.000000863

0.000000421

0.000000241

0.000000261

TABLE 23

Phosphoric Acid and Granite

Concen-
tration

Ch, H ion

Phosphoric

Acid

Log. H ion
Phosphoric
Acid

H ion

Phosphoric Acid
+Granite

Ca, Iron
Mols. per
Liter

Log. Iron
Mols. per
Liter

Ca, Calcium
Mols. per
Liter

Log. Calci-
um Mols.
per Liter

N5 .

0.0125

2.09691

0.001

0.00496

3.695482

0.00174

3.232996

N25

0.00632

3.80072

0.00296

0.00410

3.612784

0.000119

4.075547

N50

0.00424

3.62737

0.0001

0.00351

3.545307

0.000178

4.250420

N 100

0.00273

3.43616

0.0000486

0.00716

3.334454

0.000515

4.711807

N250

0.00144

3.15836

0.00000461

0.000675

4.829304

0.000505

4.703291

N500

0.000762

4.88195

0.000000232

0.000308

4.488551

0.000416

4.619093

N 1,000

0.000372

4.57054

0.000000117

0.000188

4.274158

0.000436

4.639486

N 2,000

0.000213

4.32838

0.0000000787

0.000159

4.201397

0.000386

4.586587

N 5,000

0.0000642

5.80754

0.0000000961

0.000148

4.170262

0.000297

4.472756

N 10,000 0.0000431

5.63448

0.000000222

0.000119

4.075547

0.000376

4.575188

Constants for Calcium:

x = 0.136

K = 0.000001987

•

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 307

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Figure 23.
Phosphoric Acid and Granite.
(See Table 23)

2.0

308 University of California Publications in Agricultural Sciences [Vol. 4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 309

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Figure 24.

Lactic Acid and Granite.

(See Table 24)

2.0

310

University of California Publications in Agricultural Sciences [Vol. 4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 311

2.0

3.0

4.0

5.0

5.0

4.0 3.0

Figure 25.

Formic Acid and Granite.

(See Table 25)

2.0

312

University of California Publications in Agricultural Sciences [Vol. 4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 313

2.0

3.0

4.0

5.0

5.0

4.0 3.0

Figure 26.

Acetic Acid and Granite.

(See Table 26)

2.0

314

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 27.

Obthoclase and

AZOTOBACTER.

Time
Days

Ch, H ion
Dextrose
+Azotobacter

Log. H ion

Dextrose

+Azotobacter

H ion

Orthoclase

+Azotobacter

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

0

0.00000282

6.450249

0.000000962

0.000238

4.376577

1

0.00000261

6.416641

0.000000787

0.000675

4.829304

2

0.00000331

6.519828

0.00000161

0.000455

4.658011

3

0.00000359

6.555094

0.000000887

0.000575

4.774517

5

0.00000421

6.624282

0.000000887

0.000852

4.930440

7

0.00000534

6.727541

0.00000197

0.00107

3.029384

9

0.00000627

6.797268

0.00000251

0.00404

3.606381

11

0.00000935

6.970812

0.00000331

0.00198

3.296665

16

0.0000177

5.247973

0.00000389

0.00119

3.075547

Constants for Calcium :

x =

1.804

K =

19.77

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 315

4.0

5.0

6.3

4.0

3.0

Figure 27.

Orthoclase and Azotobacter.

(See Table 27)

316

University of California Publications in Agricultural Sciences [Vol.4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 317

4.0 _

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Figure 28.
Biotite and Azotobacter.
(See Table 28)

318 University of California Publications in Agricultural Sciences [Vol.4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 319

4.0

5.0

6.3

4.0

3.0
Figure 29.
Granite and Azotobacter.
(See Table 29)

320

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 30

Calcium Silicate

AND AZOTOBACTER

Time
Days

Ch, H ion
Dextrose

+Azotobacter

Log. H ion

Dextrose

+Azotobacter

H ion

Calcium Silicate

+Azotobacter

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

0

0.00000282

6.450249

0.0000000778

0.00142

3.152288

1

0.00000261

6.416641

0.0000000778

0.00201

3.303196

2

0.00000331

6.519828

0.0000000912

0.00186

3.269513

3

0.00000359

6.555094

0.0000000912

0.00196

3.292256

5

0.00000421

6.624282

0.0000000112

0.00279

3.445604

7

0.00000534

6.727541

0.0000000941

9

0.00000935

6.797268

0.000000107

0.00396

3.597695

11

0.00000935

6.960812

0.0000000778

0.00396

3.597695

16

0.0000177

5.247973

0.000000731

0.00406

3.695482

Constants for Calcium:

x =

1,280

K =

0.03381

1922] Wright: Equilibrium Studies With Certain Acids and Minerals

321

4.0

5.0

6.3

4.0 3.0

Figure 30.
Calcium Silicate and Azotobacter.
(See Table 30)

322

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 31

Orthoclase

and B. Coli

Time

Days

Ch, H ion
Dextrose
+B. Coli

Log. H ion
Dextrose
+B. Coli

H ion

Orthoclase
+B. Coli

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

0

0.00000261

6.416641

0.000000962

0.000694

4.841359

1

0.000301

4.478566

0.000141

0.000753

4.876795

2

0.000486

4.686636

0.000267

0.00206

3.313867

3

0.000505

4.703291

0.000339

0.00230 .

3.361728

5

0.000505

4.703291

0.000289

0.00224

3.350248

7

0.000467

4.669317

0.000278

0.00270

3.431364

9

0.000414

4.617000

0.000237

11

0.000467

4.669317

0.000313

0.00282

3.450249

16

0.000431

4.634477

0.000179

0.00271

3.432969

Constants for Calcium:

x =

1.690

K =

13,490.0

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 323

4.0

5.0

4.0

3.0
Figure 31.
Orthoclase and B. Coli.
(See Table 31)

324 University of California Publications in Agricultural Sciences [Vol.4

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Figure 32.
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326 University of California Publications in Agricultural Sciences [Vol.4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 327

4.0

5.0

4.0

3.0
Figure 33.
Granite and B. coli.
(See Table 33)

328

University of California Publications in Agricultural Sciences [Vol.

TABLE 34

Calcium Silicate

and B. Coli

Time
Days

Ch, H ion
Dextrose
+B. coli

Log. H ion
Dextrose
+B. coli

H ion

Calcium Silicate

+B. coli

Ca, Calcium
Mols. per
Liter

Log. Calm
Mols. per
Liter

0

0.000000261 6.416614

0.000000220

0.00337

3.527630

1

0.000301

4.478566

0.0000716

0.0108

2.033424

2

0.000486

4.686636

0.0000564

0.0397

2.598791

3

0.000505

4.703291

0.0000687

0.0526

2.720986

5

0.000535

4.728354

0.0000806

0.0723

2.859138

7

0.000567

4.753583

0.0000745

0.0848

2.928396

9

0.000584

4.766413

0.0000716

0.0972

2.987666

11

0.000597

4.775974

0.0000716

0.1018

T.007748

16

0.000579

4.762679

0.0000635

0.1238

1.092721

Constants for Calcium:
x = 5.070
K = 1,667. X 1011

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 329

4.0

5.0

3.5

2.0

Figure 34.

Calcium Silicate and B. coli.

(See Table 34)

1.0

330

University of California Publications in Agricultural Sciences [Vol. 4

TABLE 35

Orthoclase and

B. Lactis Acidi

Time
Days

Ch, H ion Log. H ion

Dextrose Dextrose

+B. lactis acidi +B. lactis acidi

H ion
Orthoclase
+B. lactis acidi

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

0

0.00000421

6.624282

0.000000354

0.00147

3.167317

1

0.0000157

5.195900

0.00000935

0.000912

4.959995

2

0.000228

4.357935

0.00000967

0.000852

4.930440

3

0.000398

4.599883

0.00000967

0.00162

3.209515

5

0.000642

4.807535

0.0000217

0.00228

3.357935

7

0.000696

4.842609

0.0000170

0.00235

3.371068

9

0.000696

4.842609

0.0000192

0.00249

3.396199

11

0.000789

4.897077

0.0000244

0.00271

3.432969

16

0.000642

4.807535

0.0000286

0.00210

3.322219

Constants for Calcium :

x =

0.867

K =

0.0006652

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 331

4.0

5.0

4.0 3.0

Figure 35.

Orthoclase and B. lactis acidi.

(See Table 35)

332 University of California Publications in Agricultural Sciences [Vol.4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 333

3.0
Figure 36.
Biotite and B. lactis acidi.
(See Table 36)

334 University of California Publications in Agricultural Sciences [Vol. 4

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1922] Wright: Equilibrium Studies With Certain Acids and Minerals 335

4.0

5.0

4.0

3.0
Figure 37.
Granite and B. lactis acidi.
(See Table 37)

336

University of California Publications in Agricultural Sciences [Vol.4

TABLE 38

Calcium Silicate and B. Lactis Acidi

Time
Days

Ch, H ion
Dextrose
+B. lactis acidi

Log. H ion

Dextrose

+B. lactis acidi

H ion

Calcium Silicate

+B. lactis acidi

Ca, Calcium
Mols. per
Liter

Log. Calcium
Mols. per
Liter

0

0.00000421

6.624282

0.0000000877

0.00229

3.359835

1

0.0000157

5.195900

0.000000136

0.00248

3.394452

2

0.000228

4.357935

0.000000142

0.00475

3.676694

3

0.000398

4.599883

0.0000000778

0.00416

3.619093

5

0.000642

4.807535

0.0000000778

0.00486

3.686636

7

0.000696

4.842609

0.0000000411

0.00554

3.743510

9

0.000696

4.842609

0.0000000544

0.00545

3.736397

11

0.000789

4.897077

0.0000000544

0.00525

3.720159

16

0.000642

4.807535

0.0000000544

0.00565

3.752048

Constants for Calcium :
x = 0.170
K = 0.0000002710

1922] Wright: Equilibrium Studies With Certain Acids and Minerals 337

4.0

5.0

4.0 3.0

Figure 38.
Calcium Silicate and B. lactis acidi.
(See Table 38)