VOL 5, No. 12
HYDROGEN-ION CONCENTRATION
1647
HYDROGEN-ION CONCENTRATION R. H m w ASHLEY, TUFTS COLLEGE, BOSTON, MASSAWSB~YTS
As this topic involves the designation of magnitudes by the system of powers of ten, a few remarks about this way of designating magnitudes may be pertinent. Notation by Powers of Ten In this system the units place is taken as the center of symmetry and all numbers are written in this place followed by ten raised to the appropriate power. In the units place the power of ten is zero, that is, 1= 100, consequently a magnitude between 1and up to 10 need not be followed by the ten factor; all other magnitudes will call for a ten factor. In this system, instead of writing 88 49W 0.0000725 968.45 0.326
write 8 . 8 X 10' write 4 . 9 X loa write 7.25 X write 9.6845 X 10' mite 3.26 X lo-'
To transform a magnitude written in the system of notation by powers of ten to the usual system, reverse the above process. Thus, to convert 8.425 X 10%into the ordinary notation, the factor 10%becomes 100, hence 8.425 X 10%becomes 8.425 X 100 = 842.5. For example: 9.62 X lo5 becomes 96ZW0 8.79 X 10-I becomes 0.879 4.53 X becomes 0.0000453
The conversion of numbers into the system of notation by powers of ten and vice versa will be easily remembered by those accustomed to logarithms. When a number is written in the usual notation, in order to convert it into the system of notation by powers of ten, write the number with the first significant figure in the units place, followed by the decimal point and the other significant figures. Multiply this by the appropriate power of ten. When the original number was greater than 1, and less than 10, no power of ten is called for; if greater than 10, the power of ten to employ is positive and is the same as the characteristic of the logarithm of the number. When the original number is less than 1, the power of ten to employ is negative and is the same as the characteristic of the logarithm of the number. Equilibrium An acid may be typified as HA in which H is the ionizable hydrogen and A the acid radical. On going into solution ionization takes place according to the equation:
HA-&H++
A-
Applying the mass law to this equilibrium:
A few remarks about tlie above expression: a symbol, formula, or radical enclosed in a square bracket bas a special significance. A symbol or formula written without the bracket stands for a definite weight of substance, equal numerically to the atomic or molecular weights of the substances designated. When a svmbol or formula is enclosed in a sauare bracket it has the added significance of concentration. Thus, the symbol H + represents 1.008 parts by weight of hydrogen ions, while [H+1 is used to represent the concentration of hydrogen ions. As the unit of weight in chemical measurement is the gram and the unit of volume is the liter, then [H+] represents the number of gram molecules of hydrogen i o ~ in s each liter of the solntion. The molar system of expressing concentration is based on these units, a unit molar solution being one which contains one gram molecular weight of the dissolved substance disseminated in a liter of the solution. Any given solution may be a multiple or sub-multiple of the molar unit. For example, the formula of acetic acid being HGHaOe, the molecular weight is 60.042, hence if this weight of acetic acid in grams (one gram molecular weight) is dissolved or present in a liter of solution, the solution is of molar concentration. On going into solution, only a small portion of the molecules of acetic acid break up into ions. In a molar solution, out of every ten thousand molecules of the original acetic acid molecules,. only42 . are in the ionic condition. Forty-two parts in 10,000 may be represented as 0.0042 or 4.2 X 10-3. If the acid of equation (1) is molar acetic acid then the numerical value of [H+] in this expression is [H+] = 4.2 X lo-=. The term K. has a special significance: it is a constant. No matter how the values of [H+], [A-] or [HA] may be changed, the equilibrium will adjust itself either by an increase or decrease of ionization until the value of K. is regained. While the concentration factors on the left side of the equation may be varied, no variation of K. is possible, it is a constant of
-
VOL. 5, No. 12
HYDROGEN-ION CONCENTRATION
1649
nature. The numerical value of K. changes with the acid under consideration and with the temperature, hut in general is independent of the dilution. As it is conventional to write the equilibrium equation of an eledrolyte with the concentration of the ions in the numerator, a tabulation of the values of K , will be a measure of the strength of the acids tabulated. As the strength of an acid depends on the concentration of the hydrogen ions it follows that the larger the value of K,, the stronger is the acid. Strong electrolytes, in this case strong acids, do not give a constant value for K. for all dilutions and are not included in this discussion. To calculate the value for K , for acetic acid: the concentration of the hydrogen ions is [H+] = 4.2 X 10W3,and the concentration of the acetate ions is thesame, for each acetic acid molecule on ionizing produces one hydrogen ion and one acetate ion. The concentration of the unionized acetic acid is 1.000 - 0.0042 = 0.9958 = 9.958 X lo-'. Substituting these values in equation (2) gives
from which K, = 1.8 X lo-' for acetic acid. These constants are called dissociation or ionization constants. The ionization of a base may be represented: BOH 3B+
+ OH-
the equilibrium expression of which comes to
The value of Kb gives information about the degree of ionization of the base at different dilutions and the same remarks apply to Kb as were given with K,. Following are a few dissociation constants for acids and bases: Class
I
Strong acid Moderately strong acid Weak acid Very weak acid
Strong base Weak base Very weak base
Compound
I
Hydrochloric acid Oxalic acid Acetic acid Boric acid
Sodium hydroxide Ammonium hydroxide Aniline
Ka
Not well de6ned
1
1.1 X 10-I 1.8 X 10-5 6.5X10-10
Not well defined 1.8 X 4.6 X
lo-'
1
Soluble salts are ionized and a constant K , might be worked out in the same manner as for acids and bases. It may be said roughly that salts are generally highly ionized, those of the weak acids and weak bases included. Dissociation of Water Water is slightly dissociated into H f and OH- according to the equilibrium: HOH c;H+ + OH-
The equilibrium expression is
As the dissociation of water is so slight the concentration of the undissociated molecules of water may be taken as a constant: call it K z ; then
and [H+] X [OH-]
=
K , X K* = K .
(5)
Values of the constant K , determined by various methods agree very well, the accepted value being, K , = 10-14. From the above i t is apparent that the concentration of the H+ ions varies inversely with the concentration of the OH- ions; hence, in every water solution of an acid, a base or a salt, both H+ ions and OH- are always present. Take, for example, a solution of a base which is 0.01N* (normal) in respect to OH- ions. From (5) the concentration of the H+ ions is
Knowing the concentration of OH- ion to be 0.01N, then [OH-] = 10P and substituting in (6) gives
From the above it is apparent that the concentration of a base or an acid may be expressed in terms of the concentration of H+ ions. The Ionization of an Acid The equilibrium equation (2) being
* A normal solution is one which contains onc gram epuivalnt af replaceable hydro-
-Zen ions. or that weirrht . of element. or radical, which will react with or replace one gram
equivalent of hydrogen ions, in a liter of solution. When we are dealing with H A or OH- ions, we are dealing with monovalent substances, and in such cases the normal solution and molar solution are of the same concentration.
may be rearranged to
Multiplying both sides by
rA-1 gives -[HA]
Taking logarithms gives 1 1 log - = log -
LH+l
K.
[A-I + log (HA1
(7)
The term, log - has a special significance for this discussion and is
W+I'
designated pH. That is,
In words, pH is the logarithm of the reciprocal of the concentration of the hydrogen ions. The term [H+] is often written CH. The Titration of Acetic Acid with Sodium Hydroxide Ordinary analytical titrations of acids and bases take account only of the end point or point of equivalence, the changes in concentration of the add or base not being accounted for during the course of the titration. Suppose 10cc. of 0.2N acetic acid is titrated with 0.2N sodium hydroxide. The alkali is in the buret and the acid in the beaker, the changes of [H+] of the latter will be followed. Acetic acid is a weak monobasic acid, the This shows a slightly dissociation constant for which is K, = 1.82 X lo-'. dissociated acid; in 0.2N solution only 0.9% of the acetic acid molecules being ionized, the remainder being in molecular form. As sodium hydroxide is added from the buret, sodium acetate is formed, the latter being highly dissociated into ions. This sodium acetate is the source of most of the acetate ions, C2Hs02- correspondinp - to the A- ions of equation (1). . . [Salt] [*-I in equation (7) approximates This being the fact, the factor [HA1 [Acid]' Substituting this in equation (7) gives 1 1 log -= pH = log --
LHf1
K.
[Wtl + log -[Acid]
(9)
To give in detail the method by which the change in pH varies with
successive additions of the sodium hydroxide to the acetic acid would expand this article beyond the limit of its intention. The calculation is made by use of equation (9), all the factors of which are easily approximated. When calculated or plotted a curve given in Figure 2 results. Two facts are to be noted concerning this curve. (1) The addition of small amounts of sodium hydroxide at the beginning and at the end of the titration produce very large changes in the pH, and (2) in the middle portion of the curve, the addition of considerable sodium hydroxide changes the pH but slightly. In this middle portion of the curve when the acetic acid is half neutralized, the solution exhibits "buffer" action; that is, it
I
71 0
I
1
FIGWRE 2.-Curve
2
3
4
5
6
7
8
9
/
Cubic Cenfimeferr o f OMNaOH ~dded
0
showing variation of pH with successive additions of NaOH to HGHaOl.
changes but slightly in its pH on the addition of acids or bases. More will be said about this "buffer" action later.
The pH Scale The normal and molar system of expressing the concentration of acids and bases does not distinguish between the quantity of H + ions actually present a t a given dilution and the potential quantity of H+ ions. The pH scale does this and indicates what might be termed the intensity factor; that is, it is a measure of the actual concentration of the H + ions present in the solution. Recollecting that pH = log - it is to be noted that
W+l'
the values are always positive and the higher the concentration of the H + ions, the smaller is the value of pH, while on the contrary, the lower the concentration of the H+ ions, the higher is the value of the pH. There are other advantages. As a change of one unit of pH involves a
VOL.5, NO.12
HYDROGEN-ION CONCENTRATION
1653
ten-fold change in the concentration of the H + ions, the system is more compact. Further, in the actual determination of the pH of a solution as carried out by electrical measurements, many of the relationships are proportional to the logarithm of the hydrogen-ion concentration and are not proportional to the [H+] concentration. The pH Value of Pure Water The value of K, for pure water is 10-14, that is, [HC] X [OH-] = K , = 10-14.
(5)
For every H + ion an OH- ion is simultaneously formed, then as [H+] = [OH-], the expression becomes [H+]Z= 10-16 and [H+] = I-
=
10-7
Hence, the pH of pure water is 7. It is then seen that a neutral solution has a pH of 7, and an acid solution will show a pH less than 7; the greater the acidity the smaller will be the value of pH. So also an alkaline solution will have a pH value greater than 7; the larger the departure upward above 7, the greater the alkalinity. Calculating the Value of pH Suppose a 0.10N solution of acetic acid is ionized to the extent of 1.3%. 0.013 This would mean that it contains -- = 0.0013 gram molecular weights
i--n
(moles) of H + ions per liter or it is 0.0013N in respect to H + ions. The pH of the solution is 1
pH = log
To calculate the numerical value of pH: pH = log 1 - log 1.3 X l O V S log 1 = 0.0000
Subtracting,
log 1.3 x
lo-'
= 3.1139 -
2.8861
from which i t is seen that a 0.10N acetic acid solutionhas a pH = 2.89 to 1
the nearest three figures. Seeing pH = log - = - log CR, another way 2 '-.J-of defining the term pH is to say that it is minus the logarithm of the hydrogen-ion concentration. An alternative method of calculating the pH
..
corresponding to a certain [H+] is to note that a solution which is 0.0013N 1v
in respect to H + ions might be expressed as being - The logarithm of 769' . .. 769 is 2.89, which is the pH corresponding to this normality. It is conventional to express [H+] so that the tens factor shall show an integral exponent. Thus, [H+] = 10-11.27would be converted into the form a X l o b in which b is an integer. Thus to find the [H+], or CH, corresponding to pH = 11.27: the problem is to find the unit factor for a such that b is an integer. In the problem given:
The antilogarithm of 0.73 is 5.37, then [H+] = 5.37 X 10-la
Buffer Action Although pure water would show a pH of 7, distilled water prepared under ordinary conditions will show a pH of considerably less than 7 . This is due to several causes; notably, absorption of carbon dioxide forming carbonic acid and also the solvent action of water on the glass of the container. Water containing no dissolved salts is very sensitive to the addition of acids or bases. If to a liter of pure water showing a pH of 7 , one cubic centimeter of 0.01N HC1 is added, the resulting solution would show a pH of 5. On the other hand, if to a liter of beef infusion the same quantity of a d d is added, the change in pH is hardly perceptible. The same might be said if 0.01N NaOH were added. The solution of beef infusion is showing typical "buffer" action previously alluded to. Reference to the curve of Figure 2 will show that in the middle portion of the curve, a t half neutralization, the addition of sodium hydroxide to the acetic acid changed the pH value but slightly, the solution in the beaker exhibiting buffer action. The effects of buffer action may be shown as follows: suppose some methyl orange is added to distilled water and the solution is divided into three parts, one part being reserved for comparison. The solution is yellow. To the other two are added a few drops of dilute acetic acid, imparting a pink color indicating an acid condition. Now to one of the pair is added a few crystals of sodium gcetate. The color reverts to the color of the portion kept as a comparator, showing that the concentration of the H + ion has been reduced by the sodium acetate to below the point where methyl orange will show the presence of H + ions. The addition of a few drops of even a strong a d d does not change the color to the original
strong pink. The sodium acetate is acting as a buffer. Acetic acid is slightly ionized while sodium acetate is ionized to a much greater extent. The sodium acetate providing most of the acetate ions present, disturbs the ionization of the acetic acid, increasing the concentration of the acetate ions which combine with the H + ions to form undissociated acetic acid, and in so doing lowers the H + ion concentration, causing the disappearance of the pink color of the indicator. It was pointed out in connection with Figure 2 that when the acetic acid was half neutralized the solution showed huffer action. Sodium acetate in water solution sets up the equilibrium: Na+
+ CIHsOn- + HzO
?=?
NaC
+ OH+ + H G H 3 0 2
and by itself would produce an alkaline reaction due to the presence of an excess of OH- ions. At half neutralization H + ions are also present due to the unneutralized acid originally taken, and from the curve it is seen that at half neutralization the pH is 4.74, which is acid. If acid be added to this solution, the H + ions are taken up to form undissociated acetic acid, if OH- ions are added the acetic acid reacts with i t to form sodium acetate, thus removing OH-. This solution is then acting as a buffer in the region of pH 4.7. Buffer solutions may be prepared which will exhibit a definite range of pH values by mixing appropriate compounds in definite proportions and concentrations as : DH ran=
Add potassium phthalate and hydrochloric a d d . . ............... 2.2-3.8 Acid potassium phthalate and sodium hydroxide. . . . . . . . . . . . . . . . 4.06.2 Acid potassium phosphate and sodium hydroxide.. .............. 5.8-8.0 Boric acid and sodium hydroxide.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.&10.0
Most of the buffer solutions contain a weak acid or base or a salt of a weak acid or base and mixtures of these. Such solutions by hydrolyzing and by reason of the common ion effect when mixed in definite known proportions give the variation of pH desired and a t the same time provide the buffer effect. Solutions of definite known concentrations of such mixtures may be prepared and the accurate pH measured by potentiometer methods. To obtain a solution of definite pH the huffer solutions, such as listed above, may be made up and standardized by potentiometer methods showing intervals, say, of 0.2 pH. Indicators Indicators are colored bodies, the color of which alters with the concentration of the hydrogen ion. To change from the acid color to the basic color requires a definite change of hydrogen-ion concentration; that is, the pH of the solution must exceed a certain minimum value. The addi-
tion of more base raises the pH of the solution, but beyond a certain point an increase of pH by the addition of more base will not cause any further change in the color of the indicator. Having the solution in this condition with an indicator present, adding acid will lower the pH and a point will be reached a t which the acid color of the indicator appears. The addition of more acid intensifies the acid color, but again a point will be reached when the addition of more acid will not further alter the intensity of the acid color. With most indicators there is a definite range of pH values when both colored forms are present. An elementary explanation of the causes underlying the changes of indicators may be given in the case of methyl orange. This indicator is yellow in neutral and alkaline solution and pink in acid solution. It has two tautomeric forms. I H OH
I/ \
HSO
