ANALYTICAL EDITION
192
Vol. 3, No. 2
Interpretation of Water Analysis Equilibrium Considerations Determining Activities and Concentrations of Ions' D. S. McKinney POWER STATIONS DEPARTMENT,
Introduction2
DUQUESNE b G H T CO., PITTSBURGII,
Defects in the methods now in use for determining the alkaline ions in water are pointed out. Two methods of calculating the anions of carbonic and orthophosphoric acids are presented in which the relations between the pH value, the dissociation constants of these acids, and the dissociation constant of water are used to calculate the concentrations of the various alkaline ions at 25' C. The more accurate method utilizes the simplified Huckel and Debye equation to calculate the ion concentrations from the ion activities, and requires complete analysis of the water. The less accurate method assumes that ion activities and concentrations are equal, and requires the determination of pH, total phosphate, and a titration from pH 5.0 to pH 8.5. Tables are presented which reduce the calculations to simple arithmetic, and the method of calculation is illustrated by an example. The need for data at high temperatures is indicated.
T IS an interesting observation that the results of studies of the physical chemistry of dilute aqueous solutions have found meager applications to the analytical and applied chemistry of industrial water supplies. Methods of analysis, stoichiometric in character, and developed primarily for the exa m i n a t i o n of concentrated solutions, have been and still are applied to the exa m i n a t i o n of i n d u s t r i a l waters. These methods are employed to obtain data from which it is attempted to intermet the mechanism of corro;ion and scale formation, and for the conditioning of water to prevent corrosion and scale formation. The customary methods are those prepared jointly by the AMERICANCHEMICAL SOCIETY and the American Public Health Association, and published by the latter as standard methods, These have been used for lack of more appropriate ones, for the complete analyses of natural, conditioned (chemically and thermally) , and concentrated boiler waters. They have been used in the field for control of conditioning systems, and other studies. Inconsistencies have been observed in the results obtained, not wholly explained by lack of accuracy in the analytical procedure. For example, in the complete analyses of water, apparently containing bicarbonate, the content of this anion appeared materially in excess of the sum of the cations. I n distilled water, the inclusion of the determined bicarbonate completely upsets the analysis. No hydroxide was registered in boiler waters treated with trisodium phosphate, although the pH value was in excess of 9.0. The application of some studies of the physical chemistry of dilute aqueous solutions was prompted by an attempt to explain the apparent confusion resulting from the use of existing methods. It was further believed that the relation existing between the H-ion concentration of a water and the quantities of ions present could be utilized in the control and treatment of concentrated water and would provide data for use in a more rational explanation of corrosion phenomena occurring in the steam and water cycle. A further purpose of the study by the author was a more exact evaluation of free carbon dioxide and the anions which produce alkalinity in water. It is apparent from the following development of the application of ion activities that a new procedure is available for the conditioning of water for both scale prevention and inhibition of corrosion.
I
1 f
pany.
PA.
Received December 19, 1930. By Mas Hecht, Power Stations Department, Duquesne Light Com
The pH determination ha5 been considered as a separate item in the u s u a l w a t e r analysis. As will be noted in the discussion, the relation of the H-ion concentration of the water and the quantities of the ions present is necessary. If the s t o i c h i o m e t r i c methods of analysis now in use fail to evaluate correctly the c o n c e n t r a t i o n of the weakly dissociated acids in water, it must be concluded that the interpretations of the data are erroneous. Water t e c h n o l o g i s t s need, then, to recognize the application of physical chemistry to the chemistry of water if the evaporative industries are to avoid economic losses, the results of corrosion, and scale formation. General Considerations
The determination of the correct ion concentration and activities in water is necessary in industrial processes to prevent corrosion and the formation of deposits. The ion concentrations determine the possible quantity of metal corroded, of deposit formed, and of reagents required to produce a given amount of desired precipitate. The ion activities determine corrosion rates (except as modified by the use of inhibitors or by the phenomenon of passivity), the character of deposit which will precipitate from a particular water, and the amount of excess reagent required to produce a desired precipitate. Present methods of determining the anions of the slightly dissociated acids (carbonic and phosphoric and their salts) are stoichiometric, and disregard the equilibria which control the relations of these anions and of hydrogen and hydroxyl ions. Therefore, they give the operator a false impression of the quantities of each anion present. For example, a dilute solution of sodium carbonate is considered, stoichiometrically, to contain only the carbonate anion. The pH value of such a solution is approximately 11. Hence, from equilibrium considerations, the hydroxyl-ion concentration must be that. required by the equilibrium constant of water, and the relation of carbonate to bicarbonate ion must be that required by the second dissociation constant of carbonic acid at this pH value. Further, the results obtained by present methods cannot be evaluated when more than one weak acid is present unless unwarranted assumptions are made. For example, in mixtures of silicate and carbonate compounds, the assumption that the silicate is present as silicon dioxide, or in the case of mixtures of phosphate and carbonate compounds, the assumption that the phosphate is present as phosphate (by some operators HP04--).
IjVD USTRIAL A!VD ENGINEERING CHEMISTRY
April 15, 1931
193
Derivation of Formulas
A method and tables for the calculation of the activities and concentrations of the ions of carbonic and orthophosphoric acids a t 25" C. is outlined. This method may be applied to any other weak acids, if their dissociation constants are known. The data obtained below are applicable only to the treatment of water a t room temperature. The method, however, is applicable to the treatment of water at any temperature if the necessary constants are known at the desired temperature. In the following, a represents molal activity-i. e., the limit of the molality (c) as the total concentration approaches zero equals the activity. Carbonic acid dissociates as follows:
A IO
09 08 A. -
8 07
Also UH+.UOH-
=
K, = 10-1'
Hence, since UH+ =
lo-',
QOH =
10('-''J
If we let
+
+ aces--
~ H Z C O ~ ~ H C O ~ -
= ac
and
+
+
~ H ~ P O , aH2P04-
aHPo4--
+
ape,--- = a p
the formulas of Table I may be obtained. The fractional activitv of each ion mav be calculated from the formulas of Tible I. These frackons have been calculated for each 0.1 pH from a pH of 1 to a pH of 13, and are given together with the activities of hydrogen and hydroxyl in Table 11. Linear interpolation between these values will be sufficiently accurate for the purposes of water analysis. The data of Table I1 are shown graphically in Figure 1.
2
U 06
cE0 5 4
04
4 03 02
O/ nn -..
2
3
+
5
6 7 8 9 / O N 1.2 /3PH Figure 1-Relation of Activity Fractions of Anions of HzCOt a n d HzPO4, a n d Activity (X100) of € aI n+ d OH- t o pH (Read scale A for all values except activity of Hf at pH 1 to 3, and OH- at pH 11 to 13)
From the la8wof mass action
The dissociation constants of carbonic acid (8)are K, = 3.5 X lO-'and K? = 5.4 X 10-11 Note-Walker, Bray, and Johnston [ J . A m . Chem. Sac., 49, 1236 (1927)] obtain Kz = 3.88 X 10-1l. Since an error of only 0.025 in the pH value will produce a difference equal to that between the two values for KI, and industrial measurements are seldom made with this accuracy, Tables I and I1 have not been recalculated.
These relations may be expressed
++
27.92 8.99 20.04 12.16 Mg,'+ 23.00 39.096 1.008 H+ 17.008 OH44.00 COtb 61.01 HCOsP. p. m. X fi = milliequivalents per liter. Milliequivalents per liter X ft = p. p. m. b P. p. m. X f i = millimols per liter. Millimols per liter X fz = p. p. m. Millimols X valence = mlliequivalents.
;+++
Ca++
p+
Let x = pH = log
-.1
aH+'
then ag+ = lo-"
Substituting lo-" for aH+in proportion (1) we obtain aHzC04:aH003-:ac0s--
= 1:3.5.10(2-7): 1.89~1OP-l7)
Proceeding in a like manner for orthophosphoric acid, whose dissociation constants (4) are K, = lo-*, Kt = 1.95 X lo-', and Ks = 3.6 X we obtain,
A study of the above will show that the pH value determines the activities of hydrogen and hydroxyl and the ratios of the activities of the various ions of carbonic and phosphoric acids. I n order to obtain the ion concentrations and activities, it is necessary to know the activity coefficient. The relation between the activity and the concentration may be expressed:
Vol. 3, No. 2
ANALYTICAL EDITION
194 Table 11-Activity PH
Fractions-HsPO4, HzCOs, and HnO for Phosphoric and Carbonic Acids a n d Water
aces--
aHsPO4 UP
0.9091 0.8882 0.8632 0.8337 0.7992 0.7598 0.7153 0.6661 0.6131 0.5673 0.5000 0,4427 0.3868 0,3339 0.2847 0.2403 0.2008 0,1663 0.1366 0.1118 0,0909 0,0736 0,0593 0.0477 0.0383 0,0306 0,0246 0,0195 0.0156 0.0124 0,0099 0.0079 0.0063 0.0050 0,0039 0,0031 0.0025 0,0020 0.0016 0,0012 0.0010 0.0008 0.0006 0.0005 0,0004 0,0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000
0.0000
0.0000 0.0001 0.0001 0.0001 0 IO001 0.0002 0,0002 0 I0003 0.0004 0.0005 0.0006 0,0008 0.0010 0,0012 0.0015 0.0019 0.0024 0.0031 0.0039 0,0049
0.00til 0,0077 0,0097 0.0121 0.0152 0,0191 0.0239 0.0300 0.0374 0.0467 0.0581 0,0720 0,0890 0.1095 0.1341 0.1632 0.1971 0.2361 0.2801 0.3287 0.3814 0.4370 0.4942 0.5516 0.6076 0.6610
a = ffc wherea = activity 01 = activity coefficient c = concentration (molality)
This coefficient may be obtained by calculation from the complete water analysis by means of the, simplified equation of Debye and Hiickel as modified by Noyes ( 5 ) . log 01 = - 0 . 2 9 8 v 2 2 / ~ where a = activity coefficient Y = valence of ion considered Zvc2 = sum of products of individual ion concentrations (molality) multiplied by squares of their valences.
Values of a! calculated by this equation may be read from Figure 2, in which a is plotted against Bcv2 for mono-, bi-, and tri-valent ions. If the total concentration of the carbonate compounds is known, ion concentrations may be selected whose sum equals the total concentration, and which, when multiplied by the corresponding activity coefficients, lead to activities whose ratio to one another corresponds to those given in Table I1 for the particular pH. The ion concentrations of phosphoric acid are calculated in the same way as the carbonate. I n case the concentrations are so low that the activity coefficient of the ions considered are equal, the activity ratios will be equal to the concentration ratios and the concentrations may be very easily calculated. A clear under-
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0,9999 0,9999 0.9999 0.9999 0.9998 0,9998 0,9997 0.9997 0.9996 0.9994 0.9993 0 9991 0.9988 0.9986 0.9983 0.9978 0.9972 0.9965 0.9956 0.9945 0.9931 0.9913 0,9890 0.9863 0.9828 0,9784 0.9730 0.9662 0.9577 0.9475 0.9347 0,9192 0.9003 0.8777 0.8508 0,8191 0.7825 0.7408 0.6942 0.6433 0.5889 0.5321 0 4746 0.4178 0.3630 0.3116 0.2645 0.2222
UC
UC
0.0000
0.0000
0.0000 0.0001
0.0001
0.0001 0.0001 0.0002 0,0002 0.0003 0.0003 0.0004 0.0006 0.0007 0.0009 0.0011 0.0014 0.0017 0,0022 0.0028 0.0035 0.0044 0.0065 0.0069 0.0087 0.0110 0.0137 0.0172 0.0216 0.0270 0.0338 0.0423 0.0525 0.0653 0.0808 0.0997 0.1223 0.1492 0.1809 0.2175 0.2592 0.3058 0.3567 0.4111 0.4678 0,5253 0.5821 0.6368 0,6882 0.7352 0.7774
0.0000 0.0001 0.0001 0.0001 0.0002 0.00oa 0.0003 0.0004
aH+.103 100.00 79.44 63.10 50.12 39.81 31.62 25.12 19.96 15.85 12.30 10.00 7.944 6.310 5.012 3.961 3.162 2.512 1.995 1.585 1.230 1.000 0.7944 0.6310 0.5012 0.3981 0.3162 0.2512 0.1995 0.1585 0.1230 0.1000 0.0794 0.0631 0.0512 0.0398 0.0316 0.0251 0.0200 0.0159 0.0123 0.0100 0.0079 0,0063 0.0050 0.0040 0.0032 0.0025 0.0020 0.0016 0.0012 0.0010 0.0008 0.0006 0 . 0005 0,0004 0.0003 0.0003 0.0002 0.0002 0.0001 0.0001
0.0000 0,0000 0.0001 0.0001 0.0001 0.0001
standing of the method of calculation may be obtained from the examples which follow: Application of Formulas
When maximum accuracy is desired, the requirements for the calculations are complete analysis of the water, including pH value, total carbon dioxide, and total phosphate, regardless of the form of combination. For routine work, where less accuracy is necessary, the requirements are pH value, total phosphate, and amount of acid necessary to titrate the water, preferably from pH 8.5 to pH 5 . Three samples of synthetic water were prepared from 0.1 M solution of the necessary reagents. Sample 1 represents a boiler water formed by the distillation of lime-soda or zeolite-treated water; sample 2 represents a boiler water in which phosphates are used; and sample 3 represents a raw water. Table 111-Results of Test of Synthetic Water REAGENT CONCENTRATION OF REAGENT IX SOLUTION (c. P.) Sample 1 Sample 2 Sample 3 Millimols/liter Millimols/liter Millimols/liteu 1.000 0.500 (NaHCOd 1,000 NarCOa 6 000 0 8.000 NaOH 1.000 0 KHzPO4 0 3.000 0.500 7.000 NarS01 1,000 0.400 . 5 000 NaCl 0 0 300 0 HCI
--
Table 11-Activity
Fractions-HaPO4, aHPOl--
aHaPOk
PH
UP
UP
0.2895 0.2445 0.2045 0.1696 0.1395 0.1141 0.0928 0.0752 0.0607 0.0488 0.0391 0.0313 0.0251 0.0200 0.0160 0.0127 0.0101 0.0081 0.0064 0.0051 0.0041 0.0032 0.0026 0.0020 0.0016 0.0013 0,0010 0,0008 0,0006 0.0005 0.0004 0.0003 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0000
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0
8.1
8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
10.0
10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13.0
--
0.0000
0.0000
HnCOa, a n d HzO for Phosphoric a n d Carbonic Acids and Water (Contznued)
--
a~04-
“P 0.7105 0.7555 0.7955 0.8304 0.8605 0.8859 0.9072 0.9248 0.9393 0.9512 0.9609 0.9686 0.9748 0.9799 0.9839 0.9872 0.9897 0.9917 0.9933 0.9945 0,9954 0.9962 0,9967 0.9971 0.9973 0.9973 0.9972 0.9969 0,0966 0.9959 0.9951 0.9940 0.9926 0.9908 0.9886 0.9858 0.9822 0.9777 0.9721 0.9653 0.9567 0.9461 0.9330 0.9171 0.8979 0.8747 0.8472 0.8150 0.7777 0.7360 0.6882 0.6368 0.5821 0.5262 0.4679 0.4111 0.3568 0.3058 0.2592 0.2175
e
l
ar! 0.1849 0.1627 0.1252 0.1020 0.0827
UP
0.0000 0.0001 0.0001
0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0009 0.0011 0.0014 0.0018 0.0023 0.0028 0.0036 0.0045 0.0057 0.0071 0.0090 0.0112 0.0141’ 0.0177 0,0222 0.0278 0.0347 0.0433 0,0539 0,0670 0.0829 0.1021 0.1253 0.1528 0.1850 0.2223 0.2640 0.3118 0.3632 0.4179 0.4748 0.5321 0.5889 0.6432 0.6942 0.7408 0.7825
(a) Because of the difficulty in preparing distilled water free from carbon dioxide, the total carbon dioxide contained in each sample was determined by evolution in Knorr’s apparatus, absorption in ascarite, and weighing. The pH values were determined electrometrically, using the hydrogen electrode. Inserting the determined values we obtain: ’
after Correction for Carbon Dioxide CONCENTRATION OF ION IN SOLUTION Sample 1 Sample 2 Sample 3
0.0668 0.0538 0,0432 0.0346 0.0276 0,0220 0.0176 0.0140 0.0111 0.0088 0,0070 0.0055 0.0044 0.0034 0,0027 0.0021 0.0017 0.0013 0.0010 0.0008 0.0006 0.0004 0.0003 0.0003 0.0002 0.0001 0.0001 0.0001
0.~000
0.0000
a0
0.8146 0.8466 0.8739 0.8988 0.9157 0.9312 0.9436 0.9535 0.9613 0,9672 0.9714 0.9741 0.9755 0.9757 0.9746 0.9721 0,9683 0.9628 0.9557 0.9462 0.9344 0.9197 0.9016 0,8798 0.8536 0.8227 0.7869 0.7458 0.7006 0,6494 0.5955 0.5390 0.4816 0.4246 0.3696 0.3177 0,2700 0.2271 0.1892 0.1546 0.1284 0.1047 0.0850 0.0687 0.0554 0.044Fj 0.0357 0.0285 0,0228 0.0182 0.0145 0.0116 0.0092 0.0073 0.0058 0.0046 0.0037 0.0029 0.0023 0.0018
Milli-
mols/liter 29.000 0 so4 7.000 5.000 Cl Total Po4 0 Total COz 1.150 11.95 PH
Na K
MilliMilliMi& MilliMil& equio./litev mols/titev equiu./liter mols/liter epuiv./liter 29.000 15.000 15.000 1.900 1.900 0 1.000 1.000 0 0 14.000 3.000 6.000 0.500 1.000 5.000 1.000 1.000 0.700 0.700 .. 1.000 ... 0 ... ,, 1.177 .. . 0.441 .. .,. 11.75 ... 6.3 ...
. .
.
To illustrate the method, ions of carbonic and phosphoric acids in sample 2 are calculated below. (b) Assuming the activity coefficient (a)equals 1, for an initial approximation, we obtain from Figure 1, when pH is 11.75: 0.97 0.03 0.17 0.83
X X X X
1.177 1.177 1,000 1.000
Mitlimols/litev = 1.142 = 0.035 = 0.170 = 0.830
Milliequiv./liter 2.284 0 035 0.510 1.660
IONS Monovalent Bivalent Trivalent
HCOa PO4
HPOl
(c) Then subtracting the sum of the milliequivalents per liter of sulfate, chloride, carbonate, bicarbonate, phosphate,
1.000
0.0000
MilZimols/ titev 21.546 4.972 0.170
1.230 1,585 1.995 2.512 3.162 3.981 5.012 6.310 7.944 10.00 12.30 15.85 19.95 25.12 31.62 39.81 50.12 63.10 79.44 100.00
Mols/ hie?
0 021846 0 004972 0 000170
Y*
1 4 9 Zcv* =
CY2
a
0.021546 0.019888 0 001630 0 042964
0.87 0.57 0.28
( e ) From Table I at pH of 11.75, aoH-.103 = 5.661
u, H - . ~ O ~ = 5.661 - = 6 507 millimols OH/liter a 0.87 “”-- = ac
Then
cos
0.0001 0.0002 0.0002 0.0003 0.0003 0.0004 0.0005 0.0006 0.0008 0.0010 0.0012 0.0016 0.0020 0.0025 0.0032 0.0040 0.0050 0.0063 0.0079 0.0100 0.0123 0 0159 0.0200 0.0251 0.0316 0.0398 0.0512 0.0631 0.0794 0.1000 0.1230 0.1585 0.1995 0.2512 0.3162 0.3981 0.5012 0.6310 0.7944
0.0005 0.0007 0.0009 0.0012 0.0016 0.0020 0.0026 0.0032 0.0041 0.0052 0.0066 0.0083 0.0105 0.0132 0.0166 0.0209 0.0262 0.0328 0.0409 0..0511 0.0635 0.0786 0.0971 0.1192 0.1456 0.1767 0.2127 0,2539 0.2991 0.3504 0.4044 0.4609 0.5183 0.5754 0.6304 0.6823 0.7300 0.7729 0.8108 0,8454 0.8716 0,8953 0.9150 0.9313 0.9446 0.9555 0.9643 0.9715 0.9772 0,9818 0.9855 0.9884 0.9908 0.9927 0,9942 0,9964 0.9963 0.9971 0.9977 0,9982
and monohydrogen phosphate from the sum of the milliequivalents per liter of sodium and potassium, we obtain 4.511 milliequivalents per liter or 4.511 millimols per liter of hydroxyl ion. (d) Using the values from sample 2 of Table I V and paragraph (b) to calculate XcvZ and reading the corresponding activity coefficients from Figure 2 ,
Table IV-Results ION
195
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
April 15, 1931
= 0.0321 ac
0,9679, aHc03-
1’177
0.9679/0.57 0.9679/0.57 0.0321/0.87 1.152 millimols/liter
+
and HCOa = 1.177 - 1.152 = 0.025 millimol/liter
196
ANALYTICAL EDITION
Then HPOl = 1.000 X
and PO, = 1.000
0.8633/0.57 0.8633/0.57 0.1367/0.28 0.756 millimol/liter
+
- 0.756
= 0.244 millimol/liter
(f) Recalculating the hydroxyl ion as in paragraph (c) we obtain OH by difference = 4.427 millimols/liter
a difference of 1.9 per cent from the value obtained in paragraph (c). The ion concentrations obtained in paragraph (e) may differ considerably from those obtained in paragraph (6). The calculation should then be repeated until two consecutive calculations agree within the limits desired (approximately 10 per cent). .
VOl. 3, No. 2
-
ML. 0.02 N H2SO4 24.82
PH 4.6 7.05
Methyl orange Phenolphthalein
33.58
1.24
1000 1 1.24 X X 25 50 pH 4.6
- = 0.992 millimol/liter
H + to change from pH 7.05 to
From Table I, if we assume that activity coefficients are equal, and Let C = millimols of COz/liter,
MillimoZs/liter
C 0.2036 0.7960 0.0004 0,9863 = 0.0137 = 0.0251 = = = =
QUANTITY
ION
COa 0 0004 C HCOa (0.7960
+ 0 0004 -
REQUIRES FORMS (Millimols H 9 0 0004 C 0 0004 C HCOa 0 0137) C 0 7827 C 0.7827 &Cos
-
Millimol/liter H + = 0.992 = 0 7831 C f 0.0251, to change pH from 7 05 to 4.6, from which C = 1.234 miIlimols/liter
This compares quite well with the value 1.15 determined by evolution and weighing the carbon dioxide. Inspection of Table I shows that best results from the titrations will be obtained if pH values of 8.5 and 5.0 are taken as data, under which conditions the formula becomes H + = 0.0132 Figure 2-Ion-Activity
C o e f i c i e n t from H w e l and Debye Equation
Log a = -0.298
Y 1,mc~r
ZC9
Ion Valence-1
2
3
a
1.00 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.90 0.85 0.80 0 7h 0.70 0.65 0.60
0
0.000214 0.000865 0.00197 0.00354 0.00559 0.00812 0.0112 0.0148 0.0189 0.0236
where H+, C, and P are millimols of H+ ion required to change the pH of one liter of water containing C millimols of carbonate compounds and P millimols of orthophosphate compounds from pH of 8.5 to pH of 5.0. If P is known, C may be calculated from this formula and the results used in conjunction with the original pH of the water, in the same manner as the example (sample 2) calculated above. I n case the water is not completely analyzed, Zcu2 cannot be calculated and we must assume that the ion concentrations equal their activities. Table V-Summary DETERMINATIONA.P.H.A.(f)
0,00334 0.00487 0.00684
Millimols .1 .152 ... 0.025 0.244 0.756 6.507 4.427
Valence
.X. . . 2.
x
X X X X
1 3 2 1 1
X
x X X X X
f2
P. 0. m.
30 0 Si.01 31.68 48.02 17.008 17.008
= 6.~ 9 . 1 CO. = i.5HcOs = 23.2POa = 72.6HP04 = 110.6 OH (calcd. from pH value) = 7 5 . 3 OH (calcd. by difference)
The activities of the various ions may be calculated by multiplying the ion concentration by the activity coefficient, a,as obtained in paragraph (d). The activities so obtained (not the concentrations) should be used in solubility calculations to determine the character of precipitate or scale that would deposit from the water. A summary of the results for the three samples and a comparison with various standard methods is given in Table V. The total carbon dioxide (regardless of its form of combination) may be calculated from the titrations with fair accuracy if the pH at the end points is determined. For example, 25 ml. of sample 1 were titrated with 0.02 N sulfuric acid and electrometric pH run a t the phenolphthalein and methyl orange end points. The calculations were as follows:
of Results for Three Samples EXCESS EQUILIBWINKLER(6) ACID(^) RIUM DATA
SAMPLE 1: P H , 11.96
HCOa Cos OH by method OH by difference
(8) Converting the values obtained in paragraph (d)
and paragraph (e) to parts per million by means of the factors given in Table I:
+ 0.974 C + 0.966P
0 107.6 290.2
0 99.0 293.6
...
...
SAMPLE
HCOa COa HPOi PO4 OH by method OH by difference
Za:
0 154.7
182: s
184:6
0
.
I
.
1.2 67.8 184.5 131.3
0 30.7
1.5 69.1 72.6 23.2 110.6 75.3
...
P H , 11.76
158.6
...
0 46.1 307.6
...
...
... zii:i ...
SAMPLE 8: PH, 6.3
4.0 ... 4.0 11.2 Free COa 20 8 26.0 ... 11.4 HCOa by method ... 12.2 HCOa by difference ... o Alkalinities by first three methods were not corrected for phosphate.
...
Conclusions
(1) Ion concentrations derived by this method are in apeement with physico-chemical theory. (2) The method may be applied to any weak, acid whose dissociation constant is known. (3) The application of the method leads to a practical and theoretically correct solution of the problem of corrosion inhibition and scale prevention in industrial waters. (4) It must be remembered that the calculations have been made from data determined a t 25" C. and do not apply at higher temperatures. This points to the need for the following data so that the problems of corrosion and scale formation a t higher temperatures may be logically attacked:
INDUSTRIAL A N D ENGINEERING CHEMISTRY
April 15, 1931
( a ) Accurate dissociation constants for the weak acids and
water throughout the temperature range in which water is used. ( b ) Means for determining or calculating pH values at high temperatures. (c) Determination of the activity coefficient of the ions involved at high temperatures or modification of the Debye and Hiickel equation for use at these temperatures. *
Acknowledgment
The author is indebted to J. C. Warner and 13. Seltz, Carnegie Institute of Technology, for their cooperation in
197
the derivation of the formulas, and to the laboratory staff of the Duquesne Light Company for their assistance in making the analyses. Literature Cited (1) American Public Health Assocn., “Standard Methods of Water Analysis,” 6th Ed., p. 32 (1925). (2) Hall e t al., Carnegie Inst. Tech., Bsll. 84. 162 ( l Q l l ) . (8) Lewis and Randall, “Thermodynamics,” p. 811, McGraw-Hill, 1928. (4) Lewis and Randall, Zbid., p. 327. (6) Noyes, J . Am. Chem. SOC.,26, 1090 (1924). (6) Treadwell and Hall, “Analytical Chemistry,” Vol. 2, p. 48.5,Wiley, 1927.
Simple Laboratory Autoclave’ Harold A. Cassar2 TECHNICAL SERVICE DIVISION,
STANDARD OIL COMPANY OF N E W JERSEY. ELIZABETH, N . J
HE difficulty of obtaining small autoclaves (200 to 500 cc.) and the expense of the larger ones induced the author to design the simple type described below. ‘The cost of this type was in the neighborhood of twenty doflars.
T
Description of Autoclave
The autoclave consists of four main parts: bolt, outer head, inner head, and shell; and the following fittings: 2 short high-pressure nipples, one high-pressure tee piece, one pressure gage, and one needle valve. The construction is readily understood from Figure 1. The shell is made from mild steel tubing which is available in all diameters and thicknesses at large hardware stores. The bottom is closed by means of a well-fitting plug of the same material, which is then welded. The gasket for the inner head is made by pouring molten lead into the recess provided for it for low-temperature work, or by hammering a well-fitted disk of copper into the recess for temperatures above 180” C. No trouble was ever experienced in making the joint tight, and one of the advantages of this type of head is that it can be closed down in a few seconds, a very important consideration when one is dealing with liquefied gases such as ammonia or propylene, which can be put in the autoclave in the liquid state in large test tubes only so long as the operation of closing the autoclave is rapid. The operation of closing the autoclave consists of pressing the inner head down firmly onto the lips of the shell, screwing the outer head loosely onto the shell, and tightening the bolt by applying one wrench to the hexagon cut on the top of the outer head, and the other wrench to the square head of the bolt. As an added convenience, the bolt can be cut in the form of a differential screw, the left-handed portion of the thread screwing into a knob left on top of the inner head, a device which enables one to use much smaller wrenches, but naturally raises the expense of producing the article.
ficulty of sealing glass tubes containing volatile liquids, or worse still, chemicals that attack the glass when hot and ruin the seal by frosting the glass, or that evolve poisonous vapors when heated, is entirely done away with. On removing the outer head after an experiment, the inner head will usually be found to stick to the lips of the shell. However, it is easily pried loose with a screw driver applied between the lower edge of the inner head and the ledge on top of the shell. It is for this operation that the lips of the shell have been made higher than was otherwise necessary. The autoclave is best heated in a steam oven for low temperatures, or in an oil bath with simple thermostat for higher temperatures. A safety valve is not included, since it is
Use of Autoclave
The charge is best put into a large test tube which fits snugly into the shell of the autoclave. The reactions usually carried out in sealed glass tubes can be run very advantageously in the smaller sizes of autoclaves. The pressure gage enables one to follow the course of the reaction. The valve is opened at the end of the experiment so that there is no danger in opening the autoclave, an operation which has caused many unpleasant accidents when using glass tubes. Time is saved both in closing and in opening the autoclave, and the difReceived February 4, 1931. Present address, the Massachusetts Institute of Technology, Cambridge, Mass. 1 2
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Figure 1-Simple Autoclave for Research Use A-Bolt F-High-pressure nipple B-Inner head G-High-pressure tee piece C-Copper or lead gasket H-Needle valve D-Outer head I-Shell E-Pressure gage J-Weld
