An Improved Linear Plotting Method for End-Point Detection of Chelatometric Titration with Metal Indicator Hisakuni Sato and Kozo Momoki Laboratory for Industrial Analytical Chemistry, Faculty of Engineering, Yokohama National University, Ooka-2-31-1, Minami-ku, Yokohoma, Japan
ALTHOUGHTHE
PRESENT
authors proposed in our last paper
(I) a rigorous curve-fitting method using a digital computer 7
to obtain the correct end point for the photometric stepindicating titration in chelatometry, the computers are not always used at this time for such a purpose. So, in the present paper, an improved linear plotting method for the graphical end point is presented. In acid-base titrations, some types of linear plotting methods have been developed by Higuchi and his coworkers (2-4). Musha, Munemori, and Ogawa (5) have applied a modification of Higuchi’s method for chelatometric titrations with indicators. The present method is similar to the method used by Musha et al., but the corrections for the dilution effect and for the indicator concentration are newly taken into account. The present method is especially useful when the conditional formation constants are not known beforehand. Some application results are shown by using the titration data for the Mg-Calmagite-EDTA system. The notations in this paper, and reagents and apparatus used here are almost all the same as in the previous paper
F
(0.
M - EDTA (mi)
THEORETICAL EQUATION FOR IMPROVED LINEAR PLOTTING METHOD The theoretical equation for the photometric titration curve (1) can be expressed practically as the relation between the volume of titrant added ( v ) and the ratio of the free indicator concentration (a) as follows:
a =
Figure 1. Linear plot for titration of Mg-Calmagite-EDTA lent point of a titration. The second and the third terms in the braces of Equation 1 correspond to the concentrations of MI and M, respectively. Usually, C I is given as much smaller than C M ( m M / V oso) that the second term may a p proximately be neglected for the titration. Thus, for the titration curve before the equivalent point, Equation 1 can be reduced to :
(4)
gA - A m AI - AMI
in which only 1 :1 complex formations are assumed between metal ion and indicator as well as metal ion and titrant. In Equation 1, the term K M I ~ ~ / K MY ( Ia ) is ascribed to the presence of the free titrant Y* in the solution being titrated, the concentration of which is zero at the starting point of the titration. In comparison with the concentration of other species such as M or MY, the concentration of the free titrant can usually be neglected before the equiva-
If the dilution-correction coefficient, g, is eliminated in Equation 4 (also in Equation 2), we obtain the same equation as the basic relationship derived by Musha et al. (5) for their linear plotting method. Since, however, the relative concentration of MI to CM cannot be neglected for the more accurate treatment of the titration curves, the term V,CI (1 - a ) in Equation 1 cannot be neglected. Then Equation 1 can be reduced to:
where (1) H. Sato and K. Momoki, ANAL.CHEM., 42,1477 (1970). (2) T. Higuchi, C. Rehm, and C. Barnstein, ibid., 28, 1506 (1956). (3) C. Rehm and T. Higuchi, ibid., 29, 367 (1957). (4) K. A. Conners and T. Higuchi, Anal. Chim. Acta, 25, 509 (1961). (5) S. Musha, M. Munemori, and K. Ogawa, Bull. Chem. Soc. Jap., 32, 132 (1959). 938
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
x=
L:
+
CI ~
V,(1 - a )
(6)
fY
Equation 5 is of the same form as Equation 4 with a difference in the last term from L; in Equation 4 to Xin Equation 5 . As in Equation 6, X has the additional term, which can
Table I. Results for the Titrationo of Mg-Calmagite-EDTA System Mg taken, rng Mg found, mg Deviation, mg KMIX 10-6 -0.0006 7.19 0.0458 1 0 .ma $0.0004 3.49 0.0468 1’ +0.0004 3.76 0.1154 2 0.1150 $0.0001 3.12 0.2294 3 0.2293 O.oo00 2.76 0.4578 4 0.4578 2.49 1.1432 -0.0003 5 1.1435 Titration conditions; V , 50 ml, CI 1.29 X 10-6M, pH 10.0, X 520 mr. No.
a
AMI A0 A , of No. 5 A0 A0 A0 A0
Table 11. Results for the Titratiov of (Ca f Mg)-Calmagite-EDTA System Taken
Found Ca ME, Ca Mg, No. Ca,rng Mg,mg meq meq 1 0.0787 0.2104 0.01061 0.01060 2 0.3937 0.1153 0.01456 0.01454 0.0678 0.01653 0.01649 3 0.5510 0.0202 0.01851 0.01847 4 0.7087 a Titration conditions; V , 50 rnl, CI 1.12 X 10-6M, pH 10.1, X 520 mp.
+
+
Table 111. Results for the Titration” of Mg-Calmagite-EDTA System in the Presence of 1M KCl Mg Mg taken, mg found, rng Deviation, mg &I 0.2306 0.2354 0.0048 0.0044 0.4636 2 0,4592 3 0.6877 0.6926 0.0049 a Titration conditions; V,, 50 ml, CI 1.21 X 10-6M, X 520 mp. No. 1
X 10-6 1.05 1.03 1.01 pH 10.3,
0.I
0.0 now be named as “indicator correction term,” to u. The plot, g(l - .)/a us. X , should be linear within the experimental errors in a region where the assumption of neglecting the concentration of Y* holds. The intercept of the plot with the X-axis indicates the equivalent volume of the titrant solution to the metal ion present. The slope of the plot is to be proportional to KYI. Although the determination of A M I , which is necessary for the calculation of a , is a remaining problem as in the curve fitting method ( I ) , the absorbance A, of the solution to be titrated at I; = 0 can be used instead as the first approximation when AMIhas not been measured. The effect of this approximation in the improved linear plotting method will be discussed later.
I
O
-
2
0.2 ~ (m - l )~
Figure 2. Linear plot for titration of Mg-CalmagiteEDTA I1 of these plots are shown in Table I with some other results. Accurate end points are obtained for such small amounts of metal ion. Theoretically speaking, the slope of the linear plot increases apparently and the plot becomes a curved line when the difference between A, and A M Iincreases in a titration system. That A, is used in the place of AMI means that a is substituted with the fractional color change cp.
(7)
RESULTS AND DISCUSSION In Figures 1 and 2, the linear plots for the two titrations of different concentrations of Mg(I1) are shown. The plots marked with a are made by the method of Musha et al. When the concentration of Mg is relatively large, the dilution effect appears large as shown with the plot b, which is based upon Equation 4, in Figure 1. The plots c in Figure 1 and b in Figure 2 are made by the present method using A , for Ann. The latter plot is seen to be slightly curved, because A, is considerably smaller than A M Iin the titration condition. On the other hand, in Figure 1, A, is nearly equal to A M I , and the linearity of the plot c is excellent. When the value of A M Iwhich , was estimated from the titration data of Figure 1, was used instead of A, in Figure 2, the linearity was better as shown with the plot c in the figure. This approximation method for A M Iis practically useful. The numerical results
~
The relationship between a and cp can be represented as a =
a 0
+ (1 - a&
(8)
where a. represents a at u = 0. Therefore, if a,,, which is the function of CM,CI, and KXI, is small in some extent, cp does not differ so much from a. In the titration condition of No. 1 in Table I (Figure 2), a. was about 0.11, resulting in a slightly curved plot b in Figure 2. In Table I1 and 111, other application results of the improved linear plotting method are shown. When calcium ions coexist with magnesium ions, the sum of these can generally be titrated by the same titration conditions as that for magnesium only. As shown in Table 11, the present method is also useful for such a case to obtain the end point for the total amounts directly. ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
0
939
~
~
The coexistence of considerable amounts of potassium chloride in Mg-Calmagite-EDTA system was found to reduce the conditional formation constants, K M I and K M Y (1). Even if such reduced values of these constants are not known, the present method can give appropriate end points as shown in Table 111. The deviations shown between Mg taken and Mg found are considered to be ascribed to the alkaline earth impurities in potassium chloride.
Thus, precise and accurate end points for the chelatometric titration with indicator can be obtained. Although the calculation necessary for the plot is somewhat troublesome, the present method can widely be applied to practical problems. RECEIVED for review December 7, 1970. Accepted February 16, 1971.
Determination of Mercury by Using a Gold Trap in Samples Containing Considerable SuIfide Minerals P. C. Leong and H. P. Ong Geological Survey, Ipoh, West Malaysia
WARD AND BAILEY(1) describe a method whereby trace quantities of mercury are separated by volatilizing it with ammonium iodide and colorimetrically determining the mercury-dithizonate formed by extracting it into a dithizone solution in organic solvent. This method has been found to be unsuccessful in our laboratories because little mercury-dithizonate was found to go into the organic phase presumably because of the stability of the [HgI4I2- ion. The findings of Milton and Hoskins ( 2 ) and Irving et al. (3) appear to bear this out. The present note offers a suitable method for determining microamounts of mercury in soil and rock samples which may contain considerable amounts of sulfide minerals.
ASBEST03
WOOL PLUQS
/
SAMPLE\
QOLD 'FOIL
11
/'
T O SUCTION PUMP
SILVER FOIL
%AND
/ %WAY
TAP
MICROID PIPET FILLER
ABSORPTION MIXTURE
Figure 1. Apparatus for mercury determination EXPERIMENTAL
Apparatus. The equipment required consists of a borosilicate test tube 19 mm 0.d. x 150 mm joined to an L-shaped borosilicate glass tubing of 9 mm (0.d.) as shown in Figure 1. The horizontal part of the tubing holds a column of cut-up gold foil secured in position by 2 plugs of asbestos wool. A piece of silver foil (30 X 75 mm) is placed inside the test tube to promote even heating and prolong the life of the tube. Reagents. For the absorption mixture, dilute 0.2M potassium permanganate solution with an equal volume of 10 sulfuric acid prepared from AR grade acid. Potassium permanganate (0.2M) was prepared by dissolving 0.632 gram of AR potassium permanganate in 100 ml water; boil, cool, leave overnight, and filter through sintered glass filter or through glass filter paper under suction. Lime used was calcium hydroxide AnalaR grade (BDH). Dithizone, 0.01 x , was 0.01 gram in 100 ml chloroform, stored in refrigerator when not in use. Dithizone, 0.0015 %, was prepared fresh daily by diluting 15 ml of 0.01% solution to 100 ml with chloroform. The mercury standard 0.1 %, consisted of 0.1354 gram of mercuric chloride in 0.5M sulfuric acid. Ten pg/ml mercury standard was obtained by diluting 1 ml of the above solution to 100 ml with 0.5M sulfuric acid. Procedure. Mix a 0.25-gram sample with about 0.5 gram of lime in a small porcelain combustion boat and cover the mixture with a thin layer of lime. If the sample contains little sulfide, the lime would be sufficient to prevent inter-
x
(1) F. N. Ward and E. H. Bailey, Trans. Amer. Znst. Mining Eng., - 217,343 (1960). (2) R. F. Milton and J. L.Hoskins, Analyst, 72,6 (1947). ( 3 ) H. Irving et al.,J . Chem. Soc., 1949,541. 940
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
ference by sulfur. Adjust suction pressure so that air flows through the absorption mixture at a rate of 2-3 bubbles per second. Heat the sample gently at first, then strongly with a Bunsen burner for 10 min. If it is rich in sulfide, much sulfur dioxide will be liberated and flow past the gold-foil trap, causing decolorizing of the absorption mixture (10 ml). Mercury would be retained in the gold trap. If the absorption mixture is decolorized, discard and replace with a fresh absorption mixture. Continue the determination by heating along the tube toward the rubber bung and the gold-foil trap so as to drive all condensed mercury into the absorption mixture. Allow the apparatus to cool and turn the 3-way tap to connect the filter flask to the rubber bulb. By applying pressure to the bulb, force the absorption mixture up the tube to a level above the rubber bung. Repeat this procedure a few times to ensure that any mercury condensed on the tube is absorbed. Transfer the absorption mixture to a test tube and decolorize it with a slight excess of sulfurous acid. Add 1 ml of 0.0015 % dithizone solution in chloroform, stopper the tube, and shake. Compare the color of the organic layer with the set of standards prepared as described below. Preparation of Standards. To test tubes each containing 10 ml of absorption mixture, add 0.1, 0.2, 0.3, 0.4, and 0.5 ml of 10 pg/ml mercury standard. Decolorize with a slight excess of sulfurous acid and extract with 1 ml of 0.0015% dithizone. RESULTS AND DISCUSSION
To evaluate the applicability of the method, synthetic samples prepared by thoroughly mixing pure mercuric
