High Sensitivity Carbon Dioxide Analyzer Elio Scarano and Claudlo Calcagno lnstitute of Analytical Chemistry, Faculty of Pharmacy, University of Genoa, @a/y
A C02 analyzer Is descrlbed based on the following prlnclpies. A 0.1M KCI and a 10-3M NaHC03 solution (the base solution) slowly flows from a reservoir (at room temperature) to a pH flow-cell (at 25 "C), through a stainless steel pipeline. A piece of the steel pipeline Is substituted for a Teflon tube (the tubular membrane), which Is enclosed In a sealed cell (the analysis cell) containing the sample or the standard C 0 2 solution (at 25 "C). A very small quantity of COP permeates through the Teflon membrane and dissolves in the flowing solution. The pH of the solution flowing-out of the Teflon tube Is therefore lower than that of the flowing-In base solutlon. From the pH variation, the COP content In the sample is Inferred. A very simple linear equation describes the behavior of the analyzer. Free C02 concentrations until iO-5M are measurable. The theory of the analyzer Is in good agreement with both the Debye-Huckel theory and the theory of the permeation of gases through compact membranes. Application in water analysis has been accomplished. Free COP, HC03-, C032- and OH- have been determined In synthetic samples and In tap water samples, In the concentration range 5 X 10-5-2 X 10-3M, with good precision and accuracy. The method of analysis eliminates any C 0 2 exchange between sample and surrounding atmosphere, after the sampling procedure.
Carbon dioxide is of paramount importance for geology, oceanography, climatology, life, and human activity. A number of analytical problems arise from this situation and a great effort has consequently been made to develop reliable analytical methods of determination for Cop, HC03- and C032-. Unfortunately such methods are generally troublesome and imprecise, because of the unfavorable equilibrium and kinetic conditions ( I ) , but mostly because of COz absorption from the surrounding atmosphere and COS loss from liquid samples (2).Difficulties are increased when low or high levels of COz content, samples of small size, necessity of rapid and continuous response are encountered and high accuracy is requested. Many methods of determinations have been developed, such as gravimetric, titrimetric, potentiometric, conductometric, coulometric, turbidimetric, spectrophotometric, thermometric, manometric ( 3 ) . Nondispersive infrared spectrophotometry (4, 5), ultraviolet spectrophotometry ( 6 ) , and gas chromatography have also been employed and improvements and new methods are being constantly studied (7, 8). Among the new methods, an interesting approach to COn analytical problems is the development of COz analyzers, based on the potentiometric measurement of pH changes of CaC03 saturated solutions (5, 91, or NaHC03 solutions (IO, II), when some COz is added to them. In these analyzers, the gaseous sample bubbles through the analyzer solution (5, 9); otherwise, gaseous or liquid samples contact the analyzer semipermeable membrane, through which some COz passes and dissolves in the analyzer low volume immobilized NaHC03 solution (10-12).On this basis, COZ electrode systems have been developed for continuous moni-
toring of COz in atmosphere (5); for COz partial pressure, Pco2, measurements in blood (IO, 11);for urea and amino acids determinations (12).Although these methods and analyzers have shown a number of drawbacks, the principle appears to be sound; it has been promoted by the concern NOz, over the development of gas electrodes ((202, "3, Son, etc. ( 1 3 ) ) ,of enzyme electrodes and over atmospheric pollution and its control (14).Advances in both theory and application of potentiometric gas sensing electrodes with immobilized base solution (13) and ammonia gas probe (15)have recently appeared. The COz analyzer described in this paper, although having a number of peculiarities, is based on the same principle. A 0.1M KC1 and a 10-3M NaHC03 solution (the base solution) slowly flows from a reservoir (at room temperature) to a pH flow-cell (at 25 "C), through a stainless steel pipeline. A piece of the steel pipeline is substituted for a Teflon tube (the tubular membrane), which is enclosed in a sealed cell (the analysis cell) containing the sample or the standard COz solution (at 25 OC). A very small quantity of Cop permeates through the Teflon membrane and dissolves in the flowing solution. The pH of the solution flowing-out the tubular membrane is therefore lower than that of the flowing-in base solution. From the pH variation, the COz content in the sample is inferred. In this paper, we report also on the application of the COz analyzer in water analysis for COz, HC03-, Cos2- and OH- determinations. The described method avoids any COz exchanges between sample and surrounding atmosphere, after the sampling procedure.
EXPERIMENTAL Reagents, Solutions, Materials. Reagent grade chemicals, 7.41 Beckman pH buffer solution, high purity tank nitrogen and bidistilled water were used. Dimensions of polytetrafluoroethylene tubing (PTFE, Du Pont de Nemours, Teflon Spaghetti Tubing) were: o.d., 1.45-1.68 mm; i.d., 1.14-1.37 mm; wall thickness, 0.15 f 0.05 mm; internal volume, 1.02-1.48 cm3; (calculated), 1.137-1.147 cm3, m-l (measured (16)).Dimensions of the stainless steel tubing were: o.d., 1.7 and 1 mm; and i.d., 1.2 and 0.6 mm. Teflon sheaths were used for ground glass joints everywhere in the apparatus, except in the case of the pH flow-cell, for which a neutral grease was used. Apparatus. The block diagram of the apparatus is shown in Figure 1;the analysis cell is reported in Figure 2; and tubing connections are shown in detail in Figure 3. The p H flow-cell was a Beckman Micro Blood pH Assembly. The analysis cell and the pH flow-cell were independently thermostated a t 25 i 0.1 OC; the pH flow-cell was electrically shielded. A buret (1 ml-0.01 ml) with the closure on the tip ( 1 7 ) was used for the introduction of solutions into the analysis cell. Greased ground glass stopcocks were avoided and substituted by normal and Quickfit Rotaflo Teflon-glass stopcocks. A 1019 Beckman Research pH-meter and a Hewlett-Packard HP-45 Calculator were used. Procedures. The standardization of the pH flow-cell was generally made in the evening, after a series of experiments, with static buffer solution; after standardization, the pH flow-cell was washed all night with the base solution slowly flowing (0.1-0.2 ml, min-') from the reservoir through the solution outlet L (Figure 1). This procedure was necessary because the pH flow-cell had some sites of liquid stagnation near the glass electrode bulb and the greased ground glass joint and, although only small amounts of solution were involved, they could influence pH measurements because of the low buffer index of the flowing solutions. For accurate meaANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
*
1055
N
O
-..
a
I \
U 0L.SS
0
TIGO*
P.STIII
T.TIFLOY
Flgure 3. Tubing connections (A) Steel-steel; ( 6 )steel-glass: (C)steel-glass-Teflon
Flgure 1. General view of the apparatus (A) 6-1. glass reservoir for the base solution; ( 6 ) analysis cell: (C) tubular membrane: (D) pH flow-cell: (E) glass electrode: (F) saturated calomel electrode; (G) KCI saturated solution remote reservoir: (H) glass vessel for the waste of the flowing-out solution and for td measurement: (I) first solution outlet (steel tubing); (L)second solution outlet (steel tubing): (M) Tygon tubing: (N) glass-Teflon stopcock (position: (a) CO2 eliminaglass-Teflon stopcock: (0) tion: (b) protection from the surrounding atmosphere; (c) working as Mariotte bottle): (P) greased ground glass joint: (a)and (a’) steel-steel tubing connections: (R) Tygon-Tygon tubing connection. Vessel H was mounted on a staff, whose height was adjustable by means of a micrometric screw for A h and td accurate regulation
n
Flgure 2. Analysis cell and its fittings (A) I - m Teflon tubular membrane: (B)opening, fitted out with a Teflon sheath; (C) side tube (internal diameter 1 mm, internal volume -0.1 ml); (D) glassTeflon stopcock: (E) magnetic stirring bar: (F) upper part of the buret: (G) lower part of the buret: (H) Quickfit Rotoflo glass-Teflon stopcock: (I) ground glass joint, with a Teflon sheath: (L) device for dissolved CO2 stripping (Vied out with a soda-lime trap). The buret, with the closure on the tip, was connected, through stopcock H, with a 100-mi glass reservoir (not shown In the figure), containing the 0.2M Na2C03 solution or the 1M HCI solution
surements, the standardization procedure was repeated every day. Day-to-day variations ranged from 0 to 0.01 pH unit. T o measure the pH of the flowing-out solution, (pH)f,, the apparatus was assembled as in Figure 1. To measure (pH)b, the pH of the base solution, the pH flow-cell was directly connected to the base solution reservoir through the outlet L. (pH)b measurement was carried out in the morning, before a series of measurements. (pH)b was largely independent of the solution flow rate; (pH)f, was highly dependent, but very constant in the experimental control conditions of the base solution flow rate. Generally (pH)b and (pH)f, values were stable for a long time, with an associated noise lower than 0.001 pH. A source of trouble (increase in signal noise and variation of solution flow rate) was given by gas bubbles entrapped in the tubing. Bubbles in the pH flow-cell were eliminated with a high flow rate 1056
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
of the solution and an appropriate positioning of the cell; and they were avoided by handling tubing connection and disconnection operations with care. Formation of bubbles in the tubing past the pH flow-cell was an ordinary matter, but their removal by shaking was easy. Increased signal noise and difficulty in eliminating gas bubbles came from the presence of some grease in the p H flow-cell particularly on the bulb of the glass electrode and in stagnation sites. The excess grease was removed by means of amounts of distilled water, ethyl alcohol, ethyl ether, alcohol, and water again in that order, made to pass through the assembled cell by suction. Electromagnetic signal noises, although low, were suppressed by putting the pH flow-cell in a Faraday cage. Mechanical noises and noises from room temperature and atmospheric pressure variations were not revealed. The (pH)b value of a stock of the base solution was dependent on circumstances of preparation, ranging around 7.5. T o obtain a more alkaline value, a nitrogen stream was allowed to bubble through the solution into the reservoir. As the desired (pH)b value was reached, the gas flow was passed over the solution; the so-obtained (pH)b value remained constant within a few 0.001 pH unit. The flowing solution flow rate, F (1, sec-’), and the dropping time, t d (sec), of the waste solution were dependent on Ah, the difference in height between the liquid level in the reservoir and the orifice of the waste solution outlet (Figure 1).A high reproducibility of Fltd values was found. Thus, F was controlled by means of t d measurement and adjusted with A h microvariations. Up to 5” of room temperature variation gave no effect. F remained constant for a long time, because of its low value and the great solution reserve. A more accurate control was obtainable by making the base solution reservoir function as a Mariotte bottle. The volume of the analysis cell, V , (ml), was accurately determined gravimetrically (16).The cell (assembled as shown in Figure 2 with only the lower part of the buret, empty and with its tip closed, included) was weighed, emptied, and dried; then filled with distilled water through solution inlet B, keeping the stopcock of the side tube closed; the lower part of the buret was put in, taking care to avoid trapping any gas bubbles; the cell was carefully dried externally and weighed again. From the described procedure, it follows that the volume of the analysis cell was equal to its geometrical internal volume minus the volumes of the tip of the buret, of the magnetic stirring bar, of the tubular membrane, and of the side tube. To set up a known concentration of free CO2 in the analysis cell, the latter, completely filled with 1M HC1 solution through the opening B and assembled with the device L (Figure 2), was put in the thermostatic bath. The side tube C was joined to the nitrogen tank by means of a stainless steel tube, and a stream of pure nitrogen was allowed to bubble through the 1M HC1 solution into the cell for about one hour, thus eliminating the dissolved Con. Afterwards, the nitrogen stream was stopped, the 1M HC1 solution was allowed to fill the side tube C, the stopcock D was closed, and the device L was rapidly substituted by the buret, taking care not to leave gas bubbles inside the cell. In this way, the actual concentration of CO2 inside the analysis cell, [Con (aq)],, (Le., the C02 concentration a t the external side of the tubular membrane), was practically zero. To obtain the desired value of [Cog (aq)],,, first the stirring inside the cell was stopped and the stopcock D was opened; then a known volume of a 0.2M NagC03 solution was added to the solution inside the cell (of
Table I. (PH)ro vs. [C02(aq)lex [ c o ~ ( ~ ~ ) I , , / I o - ~ .=v 52.13 Ex. No.
Tirna/rnin
104.12
155.97
207.69
(PH)fo
(PH)~
AP#
7.284 7.152 1 7.440 7.766 7.469 2 8.220 7.804 7.498 3 8.280 4 8.700 8.360 7.886 5 8.814 8.546 8.150 8.662 8.302 6 8.900 7 8.980 8.762 8.440 8.832 8.598 8 9.024 9.320 9.200 9 9.420 a ApH = (pH)b - (pH)f, last value.
7.052 7.292 7.304 7.548 7.694 7.852 8.024 8.200 9.066
6.975 7.162 7.170 7.334 7.444 7.516 7.622 7.742 8.896
207.69
0.465 1.058 1.110 1.336 1.370 1.384 1.358 1.282 0.524
-
Flgure 4. pH of the flowing-out solution vs. time, following a
[co2(aq)lexvariation
Table 11. (Cco,)fovs. [C02(aq)lex
(PH)~ = 7.810: [COl(aq)]., = 52.13 X 10+M
CC02(aq)l ex/10-5.v =
1 2 3 4
5 6 7 8 9
105.93 99.19 98.80 95.15 93.69 92.39 91.02 90.16 80.02
52.13
104.12
155.97
108.74 102.29 101.97 98.25 96.74 95.58 94.39 93.43 83.04
111.98 105.54 105.11 101.35 99.63 98.65 97.64 96.24 86.27
115.21 108.57 108.33 104.46 102.91 101.60 100.43 99.32 89.34
A(Cco2) = (Cco,)fo last value
- (CC&.
% '
12.25 12.52 12.60 12.58 12.17 12.47 12.61 12.34 12.44 Mean 12.44 Std dev 0.16 Re1 std dev 1.27 118.18 111.71 111.40 107.73 105.86 104.86 103.63 102.50 92.46
-
With [COz(aq)],, > 10-3M, daily small increases of (pH)f, were observed, corresponding to a CO2 loss from the analysis cell.
RESULTS
course, a t the same time, an equal volume of the last solution flowed out the cell through the side tube C). Finally, stopcock D was closed and the magnetic stirring started and maintained throughout the time of measurement. After each addition of 0.2M Na2C03 solution, the value of [Con (aq)],, was calculated by means of the following formula:
where ([COz (aq)],,), = concentration after the ith addition; ([COz (aq)]ex)r-i= concentration before the ith addition; Vi = volume of 0.2M N a ~ C 0 3solution of the ith addition. The reliability of the apparatus was mainly based on its tightness to gases and liquids. For this purpose, tubing connections, stopcocks, and joints were carefully checked. Perhaps a weak point was the Teflon sheath of the ground glass joint (Figure 2, B) of the analysis cell: grease could have been more suitable, but we feared that the external surface of the tubular membrane might become covered with grease and, consequently, there would be a variation of its CO2 permeability. Experimentally, the apparatus proved to be very reliable in this regard for a very long period of time and for [C02(aq)Iexvalues up to 10-3M. For example, in one case with [COz(aq)],, = 8.73 X 10-4M and (pH)b = 7.788, the experimental values of (pH)fo ranged from 7.407 to 7.410, a t 25 "C, a t the beginning and after 10, 50, 90, 144 hours (between one set of measurements and the next, the apparatus remained a t room temperature and F was zero).
The experimental results reported in Figures 4 and 5, in Tables 1-111, and in the text are relative to a single value of F (5.25 X 1. sec-l), to the temperature of 25 f 0.1 OC, to the same analysis cell ( V , = 766.92 ml), and to an eightmonth period of time, before, during, and after which the cell was also used for water analysis (see later) and other types of experiments. Another analysis cell was also used and showed analogous behavior. In Figure 4, the variation of the pH of the flowing-out solution is reported as function of the time, following a [C02(aq)],, variation. Figure 5 shows calibration curves. The influence on (pH)fo of stirring interruption inside the analysis cell was as follows: after the interruption, (pH)foremained unaffected for ten minutes, then its value increased slowly by about 0.01 pH in approximately an hour. Ten minutes after the re-establishment of agitation, (pH)f, began to decrease and in an hour attained its first starting value. The influence of temperature variation of the analysis cell on (pH)f, is shown roughly by these data: 16.3-25 OC and 7.464-7.362 (pH)f,; 17.8-25 OC and 7.430-7.330 (pH)fo: i.e., 0.001 pH variation for every 0.1 "C variation of temperature about. DISCUSSION The experimental relation between the pH of the flowing-out solution and the external carbon dioxide concentration (i.e., the calibration curve (pH)f, vs. [C02(aq)],, can be interpreted by means of (a) the relation between pH and ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1057
Table 111.Calculated Constants and Values from Experimental D a t a Ex. h o .
(cCO,)h 10-511
1 2 3 4 5 6 7 8 9
105.93 99.19 98.80 95.15 93.69 92.39 91.02 90.16 80.02
C C O ~ ( ~ S ) [IC~0/2 ( a q ) l f g 10-5u 10-5 M
6.23 1.01 0.87 0.31 0.23 0.19 0.15 0.13 0.04
cCOz
b
0 ,
18.27 11.86 11.65 7.97 6.18 5.23 4.09 3.09 0.19
X
[cNaOH
2
10
5.96 6.01 6.07 6.04 5.86 5.96 6.01 5.89 6.01 Mean 5.98 Std dev 0.07 % Re1 std dev 1.15 a Calculated values corresponding to [COa(aq)],, = 207.69 X 10-JM.
105.82 99.21 98.82 95.11 93.67 92.42 91.18 90.21 79.98
composition of NaOH-C02-KCl aqueous solutions, and (b) the law describing the passage of CO2 through a compact semipermeable membrane. p H of NaOH-CO2-KCl Aqueous Solutions. The pH of such solutions is expressible in terms o f a) Analytical concentration (mol, of its components: CNaOH, Cco2, and CKc1. For Cco2 (total amount of c02), the following relation holds for: Cco2 = [C02(aq)] + [HCO,']
=
+ [C032-] (2)
where the terms in brackets are actual concentrations and [COz(aq)] is the sum of the actual concentrations of the CO:! dissolved in the solution, CO2(sol), and H2CO3 ( I ) ; b) The proton (oxydril ion) condition:
giving C C O ~ and ( ~ ~[COz(aq)] ) as functions of aH+, Le., of measured pH. In our experimental conditions, C N ~ O H and C K C ~ are known and constant ( 10M3Mand 10-lM respectively) and only Cco2 is variable about the value 10-3M, both in the base and in the flowing-out solutions. Also, because in the Cco2range from 5 X lO-*M (carbonate solution), to 10-3M (bicarbonate solution) and to 2 x 10-3M (half and half CO2-bicarbonate solution), the ionic strength is practically constant at the value 0.1001, the f values are constant and easily calculable. K and f values at 25 "C are: K1 = 10-6.352; K2 = 10-10.33; K , = 10-13.996( 3 ) ;fH+ = 0.8248; foH- = 0.7605; fHC03- = 0.7682; fCO3z- = 0.3616 (calculated values from (3)); and fC02(aq) = 1 (18). K , and f values in Equations 9 and Substituting C N ~ O H 10, operational Equations are obtained. In Figure 6, pH vs. Cco2is reported. Handling of Equations 9 and 10 is difficult without a computer. For convenience, calculated values of Cco2 and [COz(aq)]are reported in Table IV as a function of pH. InTable IV. Theoretical Calculated Values of Cco2 a n d [COz(aq)] at 2.5 "C ICOZ(aq)l:
c) The protonation equilibrium constants: K 1 -
PH
~H+~HCOR~ C 2O (as)
d) The ionic strength of the solution, F, and the activity coefficients of the chemical species involved: fH+, fOH-, fCOz(aq), fHco3-, and fco32-. From the fundamental activity-conceMration relation: a = fc, and Equations 2,4, and 5, both [HC03-] and [C032-] are obtained:
[HCO:]
=
K1 K2 f C 0
( a.q) f H
C O 3-
[co,"-] = KiK cco u2H'fHC03-fC032-
~ f ~ 0 ( 2a p ) f H C 0 3 -
+
aH+KifC02(aq)fC032-
-k
(8 )
K1 K2 f C 0 2 ( aq) f H C O 3-
Combining Equations 3, 6, 7, and 8, final expressions are obtained: 1058
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
6.800 6.900 7.000 7.100 7.203 7.300 7.400 7.500 7.600
7.700 7.800 7.900 8.000 8.100 8.200 8.300 8.400 8.500 8.600 8.700 8.800 8.900 9.000 9.100 9.200 9.300 9.400
CC02, 10-311
1.2730 1.2164 1.1714 1.1356 1.1070 1.0841 1.0657 1.0508 1.0386 1.0285 1.0200 0.0126 1.0059 0.9995 0.9932 0.9867 0.9795 0.9715 0.9623 0.9515 0.9388 0.9239 0.9064 0.8860 0.8626 0.8360 0.8062
: c o ~ ( j~i 0~- j). I~
27.35 21.72 17.24 13.69 10.87 8.62 6.84 5.43 4.30 3.41 2.70 2.14 1.69 1.34 1.05 0.83 0.65 0.51 0.40 0.31 0.24 0.19 0.14 0.11 0.08 0.06 0.04
cCOzx
102
21.48 . 17.85 14.72 12.05 9.81 7.95 6.42 5.16 4.14 3.32 2.65 2.11 1.68 1.34 1.06 0.84 0.67 0.53 0.41 0.33 0.26 0.20 0.16 0.12 0.09 0.07 0.05
termediate values are obtainable by linear interpolation with a maximum deviation of up to 0.1%, for Cco2 values, and up to about 1% for [COz(aq)] values. Passage of COz t h r o u g h t h e Membrane. The passage of COz through a planar compact semipermeable membrane can be represented (19) by:
where qco2 (mol) = the amount of C02 passing in the time t (sec), under the concentration gradient ([CO2(aq)Iex [C02(aq)]in)M;K (1. sec-l) = a constant dependent on nature, geometry, and temperature of the membrane and on hydrodynamic conditions of solutions a t both sides of the membrane; [C02(aq)],, and [COz(aq)]i, ( M ) = actual concentrations of bulk solutions a t external and internal sides of the membrane ([COn(aq)],, > [C02(aq)]in). If [COz(aq)Iexis maintained constant; if, with a suitable stirring of the solution, the hydrodynamic conditions a t the external side of the membrane are also maintained constant; and if an internal flowing base solution with constant composition impacts the membrane under well defined and constant hydrodynamic conditions and constant flow rate F (1. sec-l): V F = (12) t both K and the concentration gradient are constant in Equation 11. In these conditions, from Equations 11 and 12, the following ones result:
where (Cco2)foand (CC02)b(defined by Equation 2) are obtainable by means of Equation 9 from the pH values of the internal base solution flowing-out, (pH)fo,and flowing-in, (pH)b, respectively (Le., after and before the impact with the membrane). Finally Equation 14 can be put in the form:
= K/F). In the case of a planar membrane, of course, [COz(aq)]in = [COz(aq)]b. In the case of a tubular membrane and a flowing internal solution, i.e., in our case, the matter is complicated because the composition of the internal flowing solution continuously changes along the entire length of tube, because of the contribution of the preceding tube sections, from the value corresponding to (pH)b to that corresponding to (pH)fo(both CcoZand [COz(aq)] increase). Nevertheless we can suppose, at a first approach, that a tubular membrane behaves as an hypothetical planar membrane with [COz(aq)]i, = [COz(aq)]b;or with [COz(aq)]f,, > [COz(aq)]i, > [C02(aq)]b. From a practical point of view and for the described experimental conditions, both the hypotheses are equivalent and valid (see below). Calibration Curves: (CCoJf,, vs. [COz(aq)leX.Graphic plots of all experimental results showed a strictly linear relation between (Ccop)foand [COe(aq)],, (Figures 5 and 7). This means that Equation 15 was valid for the tubular membrane, under the described experimental conditions. By means of the least squares method, from the data of Table I1 (obtained from the experimental data of Table I by means of Equation 9) the data of Table I11 were obtained, which showed that the additive constant, a, was, within experimental errors, equal to (CC02)b;Le., that the term K/F[COz(aq)]i, was numerically negligible compared with (CC02)b.This fact is not surprising, if we take into account the absolute low values of K I F and of [C02(aq)]in (the latter can be estimated from (pH)b and (pH)fovalues by means of Table IV or Equation 10; see Table 111). The 1. sec-l. average value for K resulted 3.14 X Therefore, the final equation describing the behaviour of the COPanalyzer resulted as a very simple one:
( c ~= ~(cCOJb ~ )+ ~K / F~[ C ~ ~ ( ~ . ~ ) I , (16) , The value of the multiplicative constant, b ( = KIF), for the given analysis cell and experimental conditions, can be obtained from experimental data by means of Equation 16 in the form:
b =
(‘C02)fO
-
(‘CO2)b
(17)
[co,(as)I,,
which correlates in a linear form ( y = a + b x ) : (Cco2)fo(= y ) and [CO2(aq)Iex( = x ) , by means of an additive constant (a = (Ccoz)b- K/F[COz(aq)]i,) and a multiplicative one ( b
From the data of Table I1 the values of b, reported in Table V, were obtained, from which we can see that precision increases with [COz(aq)Iex,and ranged from 0.4 to 4.4% with experiments. As regards accuracy, from the recalculated values of [COz(aq)],,, making use of Equation 17 and the average
Table V. Values of b Calculated by Means of Equation 17 c C 0 2 ( a q ) l , x l l o - ~ M = 52.13
155.97
104.12
207.69
b x lo2
Ex. S o .
1 2 3 4 5 6 7 8 9
5.39 5.95 6.08 5.95 5.85 6.12 6.47 6.27 5.79 Mean 5.99 Std dev 0.31 % Re1 s t d dev 5.14
5.81 6.10 6.06 5.96 5.70 6.01 6.36 5.84 6 .OO 5.98 0.19 3.20
5.95 6.01 6.11 5.97 5.91 5.91 6.03 5.87 5.98 5.97 0.07 1.22
5.90 6 -03 6.07 6.06 5.86 6.00 6.07 5.94 5.99 5.99 0.08 1.28
Mean
Std dev
% Re1 std dev
5.76 6.02 6.08 5.99 5.83 6.01 6.23 5.98 5.94
0.26 0.06 0.02 0.05 0.09 0.09 0.22 0.20 0.10
4.4 1.o 0.4 0.8 1.6 1.4
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
3.5 3.3 1.7
1059
Table VII. Calculated Values of RDS Ex. KO.
(PW'
1
7.440 8.900 8.302
6 6 Cco, /
I2
6.975 7.516 7.852
RDS
X
0.001 pH/,+{
4.47 x 10-6 1.50 X 1V6 1.15 x
Y
Table VIII. Influence of the pH Standardization E r r o P on the Calculation of the Constant b
Figure 6. pH vs. Cco2 Theoretical curve, calculated by means of Equation 9 for 0.1M KCI. NaOH, and Cco,M COP aqueous solution
RDS
lo-%
value of b (5.98 X it can be seen that it ranges from 0 to 10% of the error, with a higher frequency for better values (the error for every experimental point immediately results from comparison between the average value and the reported (in Table V) values of b ) . Sensitivity of the Analyzer a n d C02 Losses. From Equation 16, it follows that, a t the steady state, the rate of the passage of COz through the wall of the tubular membrane, uco2(mol, sec-I), is given by:
Ex. ho.
1 1 2 6
9 3.14 x 10'TICOz(aq)],, (18)
$1
(PH)~
(P~)fo
(Qor)b/ 10-511
(CC02)foI io-31
io-6v
7.440 7.450 7.440 7.430 8.220 8.230 8.900 8.890 9.420 9.410 9.420 9.430
6.975 6.985 7.284 7.274 7.766 7.776 7.516 7.506 8.896 8.886 9.320 9.330
105.93 105.78 105.93 106.09 99.19 99.13 92.39 92.55 79.99 80.31 79.99 79.67
118.17 117.75 108.74 108.95 102.28 102.19 104.87 105.00 92.45 92.61 83.03 82.74
4.47 5.89 5.76 3.34 5.39 5.49 1.15 5.93 5.87 1.50 6.01 5.99 3.96 6.00 5.92 5.21 5.83 5.89
b
X
lo2
E~~~~ %
-2.2 +1.8 -1.0
-0.3 -1.3 +1.0
Standardization error = 0.01.O pH.
and the per cent relative loss of COz with time by;
where Qco2 (mol) = VC[CO2(aq)],, = total amount of free COz in the analysis cell. From Equation 18, representative uco2 values are obtained, reported in Table VI, from which an estimate can be made about the quantity of C02 necessary for a measurement or determination (15). From Equation 19, it results that the loss of CO:! of the sample in the analysis cell is about 0.15%, h-l, with the base solution flowing into the tubular membrane. In noflow condition, the loss of COP is given by 1.14 X [C02(aq)],, (mol), where 1.14 X (1.) is the internal volume of the tubular membrane. This is, of course, the maximum loss, which is attained slowly. The corresponding per cent loss, qco2X IOO/Qco,, is about 0.15. As for sensitivity, there are other criteria of estimate, besides the low values of uco2.The reciprocal differential sensitivity is given by:
(20) where ApH can be expressed in 0.001 pH unit, due to the fact that the signal noise is lower than 0.001 pH unit. The RDS is not a constant quantity, being dependent on pH range, the minimum value being reached near pH 8.092 (Cco2 in the flowing solution = 10-3M; see Figure 6). Calculated values of RDS, from data of Table I, are reported in Table VII. The differential sensitivity is calculated from: ANALYTICAL CHEMISTRY, VOL. 47,
X
0.001
9
1060
(pH)''
NO. 7, JUNE 1975
The DS is independent of p H and only related to the analysis cell characteristics and to the experimental conditions. About the reciprocal absolute sensitivity, RAS, i.e., the minimum detectable value of [CO2(aq)],,, the experiments reported in this paper are not well suited for giving the magnitude of this quantity, the lower value of [COz(aq)],, reported being 5.21 X 10-4M. Nevertheless, it has repeatedly seen that the 1M HC1 solution, not treated for the elimination of the dissolved CO2, gave a sharp signal of some 0.001 pH unit, in accordance both with the RDS values and the free-COZ content of a 1M HCl solution exposed to the air (which can be estimated about 10-5M (20)).
Besides, preliminary experiments have shown that the sensitivity can be increased a t least of one order of magnitude by means of a) Higher values of b (Le., optimization of the rate K / F ) . b) Higher values of K (Le., increased length of the tubular membrane; decreased thickness of the wall of the membrane (the use of thin membranes should also make possible to diminish the time of analysis)). c) Lower buffer capacity of the base solution (0.1M KC1 solution and distilled water, deprived of the dissolved COz, have shown a promising behavior; in case of water, the p H variation signal was influenced by liquid junction potential variation, and was associated with a signal due to the variation of the streaming potential (21)). d ) Diminution of the signal noise and amplification of the signal, through the increase in the overall experimental conditions control. e) An enrichment methodology, based on stopping the flow of the
2P>l. 2P.T
2P I
2pty
1T-m
Zp_
.
P-0
1
p=o 1 -
___..
-.
p=r
0
Y
I
14
0
100
1yI
MO
[CO, ~ ] e x / 8 6 ~M
Figure 8. Distribution diagram
Figure 7. Calibration curves, (Cco2)f0vs. [CO2(aq)lex values calculated from experimental (pH),, values by means of: (a) f values calculated on the basis of the Debye-Huckel theory; (b) unitary values for all activity coefficients involved (&o,)fo
base solution for given periods of time, followed by the rapid passage of the solution in the p H flow-cell, and the registration of the p H variation: peak shaped curves were obtained with peak height linearly increasing both with the time of interruption of the flow and with [CO2(aq)],,. Precision, Accuracy, and Reliability. Data about precision and accuracy of measurements are reported in the text as well as in Tables 11,111, and V. From a general point of view, precision and accuracy of the methodology of direct potentiometry for p H measurements with the glass-saturated calomel electrodes system suffer from a number of factors, particularly: the asymmetry potential of the glass electrode and its variation; the lack of accuracy in defining and preparing standard solutions; the uncertainty in standardization procedure; the irreproducibility and the drift of the reference electrode potential, due particularly to the poor control of the junction potential. This matter is being seriously considered today ( 1 4 , 22, and 2 3 ) , emphasizing the possibility, on one hand, of measurements up to 0.001 p H and the meaninglessness of measurements a t this level, on the other hand. Even if all precautions suggested by modern literature were taken, uncertainties remain, whose entity is debated and valued 0.01-0.03 p H unit (14). In our case, variations in repeated standardization never exceeded 0.01 pH unit. Assuming this value as the maximum error in pH measurements, the error of the constant b has been calculated for some cases (Table VIII). Because experimental errors of the constant b generally do not exceed those reported in Table VIII, it may be inferred that other sources of errors in apparatus and procedures are minor sources and, consequently, that the reliability of the analyzer is high.
(a) COAaq); (b) HC03-; (c) C03*-. Analytical cases of the system H20-COs. following the classical classification based on bicarbonate (0and carbonic acid (7) equivalence points
Besides precision and accuracy, three factors are to be stressed about the reliability of the C02 analyzer: the high stability of the analysis cell both in the time and in respect to tightness (a useful quality for water analysis); the simple linear equation describing the analyzer behavior and the very good agreement with both the Debye-Huckel theory and the theory of the permeation of gases through compact membranes (Figure 7 ) ; the relative inexpensiveness of the apparatus and the simplicity of procedure. The error due to the free C02 loss in the time can be easily corrected by calculation (Equation 19). Finally, it is quite evident that the time required for determinations will be largely diminished by the use of thinner or more permeable membranes.
WATER ANALYSIS The system HzO-CO~can be represented in two ways (Figures 8 and 9). Usual determinations involving COz in water analysis are reported in Table IX and the possible analytical cases of the system HzO-COz in Table X. In actual facts, cases 1 and 9 are uncommon because of the improbability of aqueous solutions of an acid and of a base without some Cop dissolved in them. The nine cases are represented in Figures 8 and 9. In Figure 8, connection is made with classical titrimetric determinations of acidity and alkalinity based on bicarbonate (P, phenolphthalein) and carbonic acid ( T , total) equivalence points (corresponding approximately to pH values 8.3 and 4.5). In Figure 9, the nine cases are represented from the point of view of the proposed method. Principles of the Method. The fundamental equation for any water sample, relating to its CO2 content, is:
Table IX. Determinations Involving C 0 2 in Water Analysis C h c m l c a l specles
HSO'
CO, (as) HCOj-
c0,zOH-
haturc
Type of deterrnmat?on
Acid Acid Ampholyte Base Base
Mineral acidity Free CO, Bicarbonate Carbonate Miner a1 alkalinity
Total {acidity Phenolphthalein alkalinity ANALYTICAL CHEMISTRY, VOL. 47, NO. 7 , JUNE 1975
*
1061
Table X. Analytical Cases of the System HzO-COz Analytical case
Chemical species determined
H,O+ H,O+ and COz(aq) COz(as) COz(aq)and HCO,' HCO,' HCO,- and C0,'CO,*C03'- and OHOH-
where Cco2 is the unknown total concentration of COz and the terms on the right side of the Equation are the unknown analytical concentrations in the original sample. After adding some HC1 to the sample, Equation 22 becomes Equation 2, where the terms in brackets are actual concentrations. Of course, one, two, or three terms also on the right side of Equations 22 and 2 may be absent; only in one circumstance, very close to pH 8.3, all three terms are present. When HC1 is progressively added to the sample solution containing the bases OH-, C032-, and HC03-, it reacts giving respectively H20, HC03-, and COz(aq). When COz(aq) is produced, the solution develops a Pco2 (and a [COz(aq)],,, which is, with the proposed method, measurable). In this occurrence, the following relation holds, rising from the proton condition: [H'] =
CHCl
- CoH- -
CCo32-
"+ CO#'
Flgure 9. C02
partial pressure vs. pH
Analytical cases from the point of view of the proposed methodology
- [COz(aq)] + [OH-] (23)
where C H C ~is the stoichiometric concentration of the added HCl and COH- is the unknown concentration of the strong base in the original sample. At pH 7, Equation 23 simplifies: 'HCl
=
cOH-
+
cC032-
+ [co,(aq)]
Figure 10. Analysis of
If COH- = 0, Equation 24 becomes: cHCl
=
cco32-
+ Cco,(aq)]
Cnc,/!8
(24)
M
a NaOH-Na2C03 solution
[C02(aq)lexvs. CHC~ (see Table XII)
(25)
and if carbonates also are absent in the original sample: CHcl = Cco,(aq)I
(26)
When the original sample contains free COS and HC03-, after the HCl addition, at pH 7 :
(27)
Case 3: Cco2 = C C ~ ~ Identification: ( ~ ~ ) . CCOz(aq) I [COp(aq)] I Cco2.No mineral acidity is present. C C O ~ is( ~ ~ J directly determined. Case 4: Cco2 = C ~ O ~ ( CHCO~-. ~ ~ ) Identification: C C O ~ ( CCo2. Results: Case 2: CcoZ = C C O ~ ( Identification: ~~). C C O ~ (=~ ~ J Cco32- = Cco2;C O H - = C H C-~ Cco32- - [COz(aq)]. Analytical Procedures. Synthetic samples were stored [COn(aq)] = Cco2.Mineral acidity is determinable, e.g., tiin a glass vessel closed with a rubber stopper through which trimetrically. CCOz(aqjis determined with a direct measurepassed two glass tubes, the first connected to a hand air ment on the pure sample.
+
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
rl
250
,/-
i
i
i
1
200
0
2
1
3
5
4
CHCl/'@
Figure 12. Analysis of tap water [CO?(aq)lsxvs. CHCI(see Table XVI)
Figure 11. Analysis of a Na2COs solution [CO2(aq)]., vs. CHCI(see Table XW)
Table XI. NaOH-NaZC03 Solutions Age of
pump, through a soda-lime trap, and the second for the delivery of the sample solution. For sampling, the analysis cell was carefully washed with water and dried with a nitrogen stream. Then the cell and the side tube were thoroughly filled with the sample solution, the cell was immediately plugged with the buret, and the stopcock of the side tube closed, so that the cell content remained well confined from the surrounding atmosphere. Alternative procedure, preferred for the tap water sampling, was thorough washing of the cell with the sample before filling. After filling, the analysis cell was thermostated, leaving the excess solution to escape through the side tube. The addition of the HCl solution about 1M was made with the procedure described for the 0.2M NaZC03 solution. (pH)b was measured before and/or after determinations. (pH)fo values were read 30-45 minutes after each HC1 addition, in well defined experimental conditions. Calculations. The free COz concentration in the analysis cell resulted from Equation 16:
Total
sample1 COH-/
day
Stock I Titrimetric method Proposed method
2 0 1 12
10.311
0
10-3.w
cHco3-/ alkalinity/ l0-L
lO-?rP
1.72
2.18
6.08
1.738 1.776 1.541
2.138 2.105 2.059 2.408
6.014 5.986 5.659 5.604'
13* Stock I1 Titrimetric method Proposed method
Cc0~2-l
1.88
0.788
2.17
6.22
0 1.955 2.020 5.995 Total alkalinity = CoHPCCO z - . * Sample exposed to the air under agitation. Calculated value = ~ ( C C O , ~+- 0.6C~c0,-
+
a
(30) (28)
(CC02)b and (cCop)fowere obtained from experimental (pH)b and (pH)fovalues by means of Equation 9 or Table IV. CCOn(aq), [COdaq)], and Cco2 resulted from [COz(aq)Iex: C C O A ~=~ )[COz(aq)l,,, when CHCl = 0; [ C W a q ) ] = [COz(aq)],,, for every intermediate C H C value; ~ Cco2 = [COz(aq)],,, when [COz(aq)],, reached its maximum value and was independent of CHCI. [C02(aq)Iexvalues were corrected for the free COz loss during the time of analysis by means of A C = 0.15 X C , x ( A t ) , / r o o
where [COz(aq)]i = the true value after the ith HC1 addition; [COz(aq)]i* = the experimental value; [COz(aq)]i-~= the true value before the ith addition; and cco, =
(v,,'(CCO2 ) * v,.. . ( V ,
( V C - V*,(V,
-
- V,)
v,(C co 2 ) * = vc - vr (31)
where (Cco2)* = the experimental value of Cco2,and V , = total volume of the HC1 solution added. C H Cwas ~ given by the following formula:
(29)
where AC = the term to be added to the experimental ,~ to the i t h value of [C02(aq)Iex;C, = [ C 0 ~ ( a q ) ] relative HC1 addition; ( A t ) ( h ) = time elapsed between ith and (i 1)th HC1 additions; 0.15 (%, hr-l) = per cent loss of [COz(aq)],, per hour for the analysis cell employed (see above). Remembering that for every given HC1 standard solution volume added, V,, to the analysis cell, an equal volume of the solution filling the cell was driven out, whose composition was that preceding the addition, small corrections were needed for accurate values of [COz(aq)] and Cco2:
+
where ( C H C ~ = ) ~ concentration after the ith addition; ( C ~ ~ 1 ) i -=l concentration preceding the ith addition; ( C H C ~=) ~concentration of the HC1 standard solution (reagent). The condition for the validity of Equations 24-27 (i.e., pH of the solution in the analysis cell = 7) was regarded ~ to CHCO~-/ fulfilled for that value of C H Ccorresponding C C O ~ (=~4.446 ~ ) (as resulted from Equilibrium 4); i.e., to the 20% COz(aq) and 80% HC03- about composition; Le., to the initial part of the rising portion of the curve Pco2 vs. pH (i.e., to the curves [C02(aq)lexvs. C H C (see ~ Figures 8ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1063
Table XII. Analysis of a NaOH-Na2C03 Solution with the Proposed Method" cHCIJ 10-!~
Y,/~I
1.00 2.00 3.00 3.20 3.50 4.00 6.00 7.00 cco 2
c,
€I-
(PH)~~
(CCC2)fOI 10-3~
[C02(aq)lex/ 10-?U
1.3017 8.757 0.9445 2.6017 8.757 3.9000 8.755 0.9448 4.1593 8.666 0.9554 4.5482 8.432 0.9771 5.1961 7.866 1.0150 7.7859 7.410 1.0640 9.0774 7.410 Experimentalvalue = Corrected value with Equation 31 = Corrected value with Equation 29 = Calculated value at V, = 3.20 ml =
Total alkalinitv Calculated value
0.0067 0.1839 0.5468 1.1806 2.0000
Table XIV. Analysis of a N a ~ C 0 3Solution with the Proposed Method" CCH4 10-3,~
1.8733 1.9550 1.9806 1.9933
2.0000
X
lW3M
2.0158
X
10m3M
2.0200 x 10-3'11 1.9550 x 10'3M
= 5.9950 X
lW311il
8.992 0.2608 0.5215 8.994 0.7821 8.994 1.3033 8.994 1.5637 8.994 1.8241 8.993 2.0844 8.994 2.2145 8.935 2.3446 8.890 2.6048 8.788 3.9053 7.858 4.1651 7.670 4.2949 7.620 4.4247 7.614 4.6873 7.616 4.9438 7.615 Ccoz Correctedvalue = Cco32- At V , = 2.00 ml = CHC03. Calculatedvalue = CNpco3Calculatedvalue =
0.20 0.40 0.60 1 .oo 1.20 1.40 1.60 1.70 1.80 2 .oo 3 .OO 3.20 3.30 3.40 3.60 3.80
0.9079
0.9077 0.9181 0.9255 0.9404 1.0156 1.0314 1.0365 1.0371 1.0369 1.0370 2.186 x lW3M 2.054 X 10m3M 0.132 x 10'3izI 2.120 x lW3M
0.0177 0.3010 0.5502 1.8077 2.0719 2.1572 2.1672 2.1639 2.1656
Sample = 2.120 X 10-3M N a ~ C 0 3 reagent ; = 1M HCI; (pH)b ( C C O 2 ) b = 0.9075 x m 3 M .
Table XIII. NazC03 Solutions
= 8.994;
CNa2Cc3/'o-!u Given
Founds
Ccc,/10~3~
2.120 1.674 1.916 1.729 1.729
2.120 1.627 1.834
2.186 1.678 2.025 1.746 1.755
a
~ , , ~ 2 - / 1 0 ' ~ CHCO~-/~O-~.V
2.054 1.575 1.643
0.132 0.103 0.382
Calculated value = Cco32- + O.5CHCo,- .
12)). As can be seen from Equation 23, points after the selected one are biased by an error 10-pHM, and points before by an error 10-poHM. Analytical Results. The analytical results reported in this paper are relative to 25 "C, to a single analysis cell (V, 766.92 ml; F = 5.25 X 10-6 1. sec-l; b = 5.98 X to a wide range of (pH)b values, to one-year period of time, before, during, and after which the analysis cell was also used for other types of experiments. Determinations were made on NaOH-NazC03 and on NazC03 aqueous solutions synthetic samples, and on tap water samples. NaOH-Na2C03 Solutions. Two stocks of NaOHNazC03 solutions were prepared and stored in glass vessels, protected from atmospheric COz. COH-and Cco32- of these solutions were determined, at room temperature and in open vessels, by means of a titration procedure, with 2.006 X 10T2MHCl and phenolphthalein and mixed bromocresol green-methyl red indicators, on 50-ml samples (24). The following results were obtained. Stock I . Number of titrations 10; Vp (volume of HCl standard solution at the phenolphthalein equivalence point) = 9.72 ml (std dev = 0.03 ml; % re1 std dev = 0.34); VT (total volume of the HCl standard solution at the mixed indicators equivalence point) = 15.16 ml (std dev = 0.08 ml; % re1 std dev = 0.56). Stock 2. Number of titrations 4; Vp = 10.08 ml (std dev = 0.03 ml; % re1 std dev = 0.28); VT = 15.48 ml (std dev = 0.04 ml; % re1 std dev = 0.24). Final results with both titrimetric and proposed method are reported in Table XI. In Table XII, a determination with the proposed method is reported in detail. From Table
-
1064
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
Table XV. T a p Water Cco2(aq)'
~ ~ 0 3 2 - J
CHCO~-J
Sam- c c 0 2 / ple
10-3~
Total
alkalinity/ 10-3~
%
10-3~
Y
IO-%
%
10-3~
1 2.490 2 2.517 0.047 1.9 0.106 4.1 2.365 94.0 2.576 3 2.616 0.068 2.6 0.087 3.3 2.461 94.1 2.635 XI can be seen: the decrease of the OH- content with time, in accordance with the instability of alkaline solutions stored in glass vessels ( 2 4 ) ;the take up of C02 of the alkaline sample from the surrounding atmosphere. The value 5.604 X 10-3M in Table XI was calculated by means of the relation 2(Cco3z- o.5cHC03-) = total alkalinity, on the base of the following considerations. If some COz(g) reacts with a NaOH-NazC03 solution, first all NaOH is turned into N a ~ C 0 3(but the total alkalinity is unchanged); then the reaction C032- + COdaq) = 2HC03determines, from which it can be deduced that for every COz(aq), two HC03- appear and one c03'- disappears. Then:
+
where, in this case, ~ ( C C O ~ Z was - ) ~the ~ ~total ~ , , alkalinity. Na2C03 Solutions. Four NazC03 solutions were prepared with distilled water not deprived from Con. Results are reported in Tables XI11 and XIV, from which absorption of atmospheric COSis evident. T a p Water. Three determinations were made on independent samples; the second and the third were made at one-day distance; the first, several months before. The second and the third samples were checked by means of titrations with 2.006 X 10-2M HCl standard solution and mixed indicator, at room temperature, at open air, on 50-ml samples ( 2 4 ) .Results were: P alkalinity = 0; T alkalinity = 2.72 X 10-3M and 2.73 X 10-3M, respectively. The pH of the water at 25 "C resulted -7.80. Results are reported in Table XV and XVI. From Table XV, the coexistence of
water). The other cases are comprised in the preceding ones.
Table XVI. Analysis of T a p Water with the Proposed Method" HC 1/ ~o-~,M
V,/ml
0.00 0.30 0.60 0.90 1.30 2.30 2.60 2.90
(PH)~~
(Ccoz)fo/ IC O ~ ( a q h,.J cco3*-/ 10% io-3~ io-%
LITERATURE CITED
8.734 0.9474 0.0468 0.3905 8.576 0.9646 0.3344 0.1025 0.7809 8.284 0.9877 0.7207 0.1058 1.1711 7.936 1.0101 1.0953 0.1201 1.6911 7.586 1.0402 1.5987 0.1349 2.9905 7.254 1.0940 2.4983 3.3799 7.252 1.0944 2.5050 3.7691 7.252 2.517 X lW3M 0.047 x lW3M 0.106 x lW3M (calculated value at V, = 0.60 ml;Cco3z- = CHcl- [COz(aq)] + \
-
cHC03-
Total alkalinity = 2.576 x lV3M uReagent = 0.9983M HCI; ( P H ) = ~ 8.756; ( C C O ~=) 0.9446 ~
X
10-3M.
CO2(aq), HC03-, and C032- appears, but their relative amounts are not in accordance with the percentage values calculated a t = 0 (1.1,98.0, 0.9%, respectively) and a t = 0.1 (1.4, 97.4, 1.2%). A possible explanation is that the analyzed samples were not in equilibrium, because of the lower temperature and the higher Pco2 values in the pipe-line, and of the slowness of steps 3 and 4 in the following path:
co3'-
--+
1
H C O ~ - - - + H,CO,
-;+
2
CO,(aq)
-;-+
(1) S. Bruckenstein and I. M. Kolthoff in "Treatise on Analytical Chemistry", Part I, VoI. 1, I. M. Kolthoff, P. J. Elving, and E. B. Sandell, Ed., Interscience Publishers, New York, NY, 1959, pp 426-427. (2) T. B. Taylor in "Treatise on Analytical Chemistry", Part 111, Vol. 2, I. M. Kolthoff. P. J. Elvina. and F. H. Stross, Ed., lnterscience Publishers, New York, NY, 1971, p.-301. (3) "Handbook of Analytical Chemistry", L. Meites, Ed., McGraw-Hill. New York, NY, 1963. (4) H. B. Elkins and L. D. Pagnotto in "Treatise on Analytical Chemistry', Part Ill, Vol. 2, I. M. Kolthoff, P. J. Elving, and F. H. Stross. Ed.. Interscience Publishers, New York. NY, p 21. (5) J. P. Lodge, Jr.. E. R. Frank, and J. Ferguson, Anal. Chem.. 34, 702 (1962). (6) A. L. Underwood and L. H. Howe 111, Anal. Chem., 34, 692 (1962). (7) M. J. Fishman and D.E. Erdmann. Anal. Chem., 43, 356R (1971). (6)M. J. Fishman and D.E. Erdmann, Anal. Chem., 45,361R (1973). (9) P. E. Toren and B. J. Heinrich. Anal. Chem., 29, 185 (1957). (10) S. R. Gambino, Clin. Chem., 7, 236 (1961). (11) J. Severinghaus and A. F. Bradley, J. Appl. Phys., 13, 515 (1958). (12) G. G. Guilbault and F. R. Shu, Anal. Chem., 44, 2161 (1972). (13) J. W. Ross, J. H. Riseman, and J. A. Krueger, Pure Appl. Chem., 36, 473 (19731. (14) A. K. Covington. CRC Crit. Rev. Anal. Chem., 3 , 367 (1974). (15) D.Midgley and K. Torrance, Analyst(London),98, 217 (1973). (16) L. B. Macurdy in "Treatise on Analytical Chemistry", I. M. Kolthoff. P. J. Elving, and E. B. Sandell, Ed., lnterscience Publishers, New York. NY, Part I, Vol. 7, pp 4309-4313. (17) E. Scarano, M. Forina, and C. Calcagno, Anal. Chem., 45, 557 (1973). (18) T. S. Lee in "Treatise on Analytical Chemistry", Part I, Vol. 1, I. M. Kolthoff. P. J. Elving. and E. B. Sandell, Ed., lnterscience Publishers, New York, NY, 1959, p 234. (19) D P. Lucero and F. C. Haley, J. Gas Chromatogr., 6, 477 (1968). (20) "Handbook of Chemistry and Physics", 49th ed.. Chemical Rubber Company, Cleveland, Ohio, 1969, p B-189. (21) M. Forina and E. Scarano, h g . Chim. /tal., 7 , 77 (1971). (22) R. D.Caton, Jr., J. Chem. Educ., 50, A571 (1973). (23) R. D.Caton, Jr., J. Chem. Educ., 51, A7 (1974). (24) "Standard Methods for the Examination of Water and Waste Water", 1l t h ed., 1960, APHA, WPCF, pp 44-47.
COk)
+
Cases examined have been 8 (NaOH NaZCOs), 7 ( N a ~ C 0 3 )6, (Na2C03 NaHCOs), and an analytical case with characteristics of cases 6, 5 , 4 a t the same time (tap
+
RECEIVEDfor review September 30, 1974. Accepted February 5 , 1975. Work supported in part by a grant from the Consiglio Nazionale delle Ricerche, Rome, Italy.
General Computer Program for the Computation of Stability Constants from Absorbance Data D. J. Leggett and W. A. E. McBryde Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
A new computer program, SQUAD, has been developed enabling the evaluation of the best set of stability constants from absorbance measurements. The method can be used to determine pKa's, metal Ion hydrolysis constants and study multicomponent equilibria. A rigorous testing procedure has been used to investigate the limitations of the method. SQUAD has been applied to the nickel ethylenediamine system to yield log plol = 7.36, log @,02 = 13.74, log @ l o 3 = 18.06.
The application of machine computation to the elucidation of solution equilibria has been reviewed up to 1971 ( I , 2 ) . Since then, several authors have published programs which enable the calculation of stability constants from various types of data. These programs may be classified
into two groups, i.e., general and specific (usually with some approximations). Kankare (3) has developed a general approach, employing absorbance data, of the direct search type ( 4 ) designed for small core computers (16K bytes). This set of programs has a built-in safeguard against the calculation of negative molar absorbtivities during any stage of the calculation, a strategy also adopted by Nagano and Metzler ( 5 ) .Another general method, utilizing potentiometric data, by Sabatini and Gans (6, 7) employs the Davidon-Fletcher-Powell (8, 9) modification of the Gauss-Newton iterative method. These authors have commented on the unreliability of SCOGS ( 1 0 ) and we will discuss our experiences with this program later in this paper. Feldberg et al. ( 1 1 ) have used a simplified version of SillBn's twist matrix method ( 1 2 ) . ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
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