THERMODYNAMICS OF LEAD BROMIDE‘ BY JESSIE Y. CANN AND RUTH A. SUMNER
The purpose of this investigation is to determine, by means of electromotive force measurements, the free energy of formation, AF, the change of entropy, AS, the change in heat content, AH, and the activity coefficieqt, y, of lead bromide. Free Energy of Lead Bromide The published measurements of the potential of the cell corresponding to the reaction Pbw 2 AgBr(,) = PbBrzc., 2 Age)
+
+
are not concordant. We therefore have measured the cell P b (in Sat. Amalg.), KBr(,q), AgBq,,, Agr.) in which the electrolyte was a PbBrz(,), PbBrz(,,,) saturated solution of lead bromide in 0.01,0.025, and 0.1M KBr to which a small amount of hydrobromic acid had been added. The lead bromide used by J. Y. Cann was a portion of the same material which was used by Randall and Vietti,2 and which had been re-crystallized four times from conductivity water. The potassium bromide solution was prepared from high-grade “analyzed” material, and the hydrobromic acid was a dilute solution of a pure acid through which hydrogen had been bubbled to remove traces of bromine. The lead amalgam was of the same supply as that used for the determination of the potential of the lead electrode.a The silver bromide spirals were prepared by electrolyzing silver oxidesilver spirals prepared as previously described: in a O.IM solution of potassium bromide. The lead amalgam and spirals were freed from absorbed film or gases, and the solutions introduced as described previously.8 The cells were the ordinary H-cells of Pyrex, and the thermostat was either the ordinary oil thermostat regulated for 25O, or the one used by Gerke, fitted with an easily adjustable thermo-regulator. The thermometer was a mercury thermometer which was checked against a standard resistance thermometer that had been calibrated by the U. S. Bureau of Standards. Nine cells were made up. Cells I , 2, 3, and 4 contained 0.01M KBr. The first cell, which had lead bromide only over the lead amalgam, gave un-
+
This problem was suggested by Merle Randall, and the experimental part of the work was started at the Universit of California by J. Y. Cann on sabbatical leave from Smith College, and continued b A. Sumner a t Smith College as artial fulfillment of the reqwements for Special Honors in Chemistr Charlotte Klingkr, Graduate Student a t Smith College, has repeated the results of t t e authors, havlng made four cells, each of which gave a steady constant value of E O 2 9 8 1 = 0.3465,agreeing precisely with the results obtained previously. 2 Randall and Vietti: J. Am. Chem. SOC.,50, 1526 (1928). a Randall and Cann: J. Am. Chem. Soc., 52, 589 (1930).
&.
2616
JESSIE T. CANN AND RUTH A . SUMNER
"
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64:::
+ 0
0
0
0
0
0
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-
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THERMODYNAMICS OF LEAD BROMIDE
2617
satisfactory results and was discarded. No. 2, a large cell, gave E2g8.1 = 0.3 53 I V which gradually decreased to 0.3519 V. This contained only 0.5 cm. layer of solid lead bromide in each side of the H-cell. No. 3, a very small cell, with a larger quantity of solid lead bromide, gave 0.3482 V a t 25' after about seven days; but after standing in the thermostat for over thirty days the potential became constant a t E2981 = 0.3469 V which agrees with the potential of three other cells. No. 4, the same type of cell as No. 2, gave a very constant potential of 0.3498 V during about two weeks; but we feel, in view of later developments, that the amount of solid lead bromide ( I cm layer) was not sufficient. Cell No. 5 contained 0.1 M potassium bromide and enough solid lead bromide to completely cover the silver-silver bromide spiral. The cell was taken through the temperature range from 15' to 42' and back again four times, and about seventy-five values, taken after the initial erratic period of three days, during which time the value of the potential rapidly decreased at the constant, initial temperature of 25O, were plotted, a few of which (taken at random) are shown in Table I. Cell No. 6 contained 0.025 M potassium bromide, was erratic and discarded. Cells No. 7 and 8 contained 0.025 M potassium bromide with enough solid lead bromide to fill the cell to the middle of the cross of the H. No. 7 was taken through the temperature cycle twice and agreed with Cell No. 5. Cell No. 8 was high a t the beginning, but after the traverse of a temperature cycle of fourteen days, agreed with the previous cells. Cell No. 9 contained 0.1 M potassium bromide with a very large amount of solid lead bromide and gave results in agreement with Cells 3, 5 , 7 and 8. Random potentials of these cells are given in Table I. Nine cells were prepared by R. A. Sumner. Numbers I and 2 contained 0.1 M KBr, 3 and 4 contained 0.01 M KBr, 5 and 6 contained 0.05 M KBr, and 7 and 8 contained 0 . 0 2 5 M KBr. These cells were made up in exactly the same manner as the last and best ones prepared by J. Y. Cann. Numbers 5 and 7 gave erratic values and were discarded. Numerous readings, over a period of a year, were taken on cells I , 2, 3, 4, 6 and 8, and Table I1 gives a list of representative values at various temperatures.
FIQ.I
2618
JESSIE Y. CANN AND RUTH A. SUMNER
In addition, four cells were prepared by C. Klingler. These all contained M KBr. These last cells came to equilibrium within a day or two and gave steady, constant values of E"Zg8,l = 0.346 j at 2 j°C. This checking of results by three independent workers convinces us that our method of preparing the cells and the values obtained, are correct. Curve I shows the measured potentials of the best cells. 0.1
All the measured potentials were plotted against the temperature and from the best average curve we find = 0.346jV; dE/dt(tg8.1) = -0.000289 V/o. Whence Pb (in sat. amalg.) 2 AgBr(,, = PbBrsc,, z Ag(,); AFtya.1 = - I 5995 cal., ASm.1 = - 13.34 Cal./o; aH298.1 = -19972 cal. (1) Combining with the data of Gerke4 for the formation of saturated lead amalgam, we find
E298.1
+
+
+
+
2 AgBrc,) = PbBrz(,) z Age,); AF0289,1 = -162j8 cal; Pb(,) AS0298.1 = -12.599 cal./o; AH'298.1 = -20014 cal.
(2)
Then combining with Randall and Halford'sj value for 2
Ago
Pb"
+ Brz" =
2
AgBr;
AF"298.1 = 2
(-22917)
+ Brz0 = PbBr2; AF02y8.1= -62092
cal.
we find
(3)
(4)
This value is in good agreement with the value of Latimer6 Le. AF"t89.l = -62,065 Cal. It alsoagrees with that of Krahmer7i.e.AF"zg8.l = -62057 cal. Combining our value L L S $ ~=~ , ~12.599 for Pb(,, 2 AgBr(,, = PbBrz(s) 2 Ag(s) with aS"2Y8.l = -0.96 for AgBr usingthe values SA^ = 10.2 j, obtained from the reaction S A ~ O SW -+ SA,B,O, SBrO= 16.3 and SAgBr= z j . S y 8 we find for t,he reaction, Elements
+
+
+
PbBr2;
(5)
= -14.519,
S O Z ~ ~ . ~
whereas Latimer6 obtains - 12.63; thus showing a difference of 1.889 entropy units. It was because of this difference, dependent upon the temperature coefficient of the cell, dE/dT, that the experimental work has been checked by three individuals. Combining AW"2ya.l = - 20014 for t'he reaction Pb 2 AgBr = PbBr2 2 Ag with Bichowsky'sg value of AH0298.1= -23840 for AgBr, we obtain AHo2y8.1 = -67694 for P b Brz = PbBrt (6)
+
+
+
Gerke: J. iim. Chem. Soc., 44, 1684 (1922). Randall and Halford: J. Am. Chem. Soc., 52, 192 (1930). Latimer and Iloenshel: J. Am. Chem. Soc., 48, 19 (1926). ' Krahmer: Z. Elektrochemie, 26, 97 (1920). 8 The value 25.j9 is an average of 2 6 2 , obtained by Eastman and Milner (personal communication) and 25.j 6 obtained by sucken, Clusius and Woitinek: Z. anorg. Chem., 203, 39 (1931). 9 Intern. Crit. Tables, Vol. V. 4
-
2619
THERMODYNAMICS OF LEAD BROMIDE
For this value Gerke'o obtained - 67480. Using the third law and our values of AF0298.1 = - 62092 and of ASoa8.1= - 14.519, we find AH02981 = - 66420. Braune and Koref" found AH"zQ8 1 = -66350. If now we use LatimerW value of ASozQ81= -12.63 for PbBrz, Krahmer' found = -65857. and employ the third law, we find AH0288.1 AH"2~8.1= -65580 and Thomsen12 found -64456. We take the value of AH0298 = - 67694 as correct.
Activity Coefficient of Lead Bromide Randall and Vietti2 have determined the solubility of PbBrz in KBr solutions. They state that by graphical methods they have been unable to determine the activity coefficient of PbBrz in KBr consistent with other data. Using their data and plotting log r/m* against 113, and extrapolating to zero concentration, we found the proportionality factor 46.82. Then by dividing any value of I/m* by this value,'* we found the corresponding value of the activity coefficient, y.t, Table I11 gives a tabulation of these values. TABLE I11 M KBr
M PbBrl 0.02645 0.002 0.02611 0.02500 0.005 0.02345 0.01 0.02043 0.02 o . o 2 5 * o.o1845* 0.05 0.01380 0.1 0.00859 0.00694 0.2 0.00687 0.374 * Interpolated value.
0.001
m f 0.0425 0.0425 0.0423 0.0423 0.0423 0.0413 0.0436 0.0490 0.0682 0.1011
log I / m f 1.3715 1.3716 1.3738 1.3732 1.3737 1.3835 1.3601 1.3094 1.1661 0.9953
I/mf
23.5215 23.5302 23.6471 23.6162 23.6423 24.1847 22.9157 20.3008 14.6589 9.9893
Ma
-f*
0.2835 0.2834 0.2828 0.2835 0.2851 0,2835 0.3023 0.3546 0.4684 0.6282
0.5024 0.5025 0.5050
0.5044 0,5049 0,5165 0.4894 0.4355 0.3131 0.2113
In order to determine the activity coefficient from electromotive force measurements, use is made of the following equation: E = -3RT/2F In (k'y m &, in which14the constant k', which includes E", may be found by substituting a value of y found by some other method, together with the appropriate values for the related quantities, and solving for k'. For this purpose we chose Randall and Vietti's value of y + in 0.01 m KBr soln, and found the value of k' to be 0.0058411. Using this value, y A for the other concentrations of KBr was calculated. The values thus obtained for the concentrations 0.025, 0.05 and 0.1m are as follows:
*,
'
Gerke: Chem. Reviews, 1, No. 4, 377 (1925). Braune and Koref: 2.anorg. Chem., 87, 175 (1914). Thomsen: Landolt-B6rnstein Tabellen, 2, 1533 (rg23); J. prakt. Chem., (2), 12, 92 (187.5). ._ 13 Lewis and Randall: "Thermodynamics and the Free Energy of Chemical Substances," 371 (1923); J. Am. Chem. SOC.,43, I I I Z (1921). l4 Ref. 12, p. 355. 10
2620
JESSIE Y. CASN AND RUTH A. SCYSER
m KBr
-/=k E.M.F.
y i
0 025
o 51661
0
0
05
0.1
0.48936 0
43543
Sol’y.
5165 0.4894 0 4355
The solubility data are listed for purposes of comparison. It will be seen that these values of y A from electromotive force measurements are practically identical with those obtained from solubility measurements. Too much weight, possibly, should not be laid upon this identity because the method of calculation was relative, not absolute. Nevertheless the agreement is remarkable. We also calculated the product, Ks p. = 4 m i 3 y i 3 ,for PbBrz, and found it to be 0.0000389. Recent papers by Fromherd5 discuss the activity coefficients of the lead halides in great detail. He states repeatedly that the true activity coefficients of an electrolyte like PbBrz agree closely with those of the strong electrolyte BaC12. Our results are in general accordance with this statement.
Summary We have calculated the values of AF, AH and AS for the formation of lead bromide from its elements. Our values of A F and A H agree reasonably well with those found in the literature. Our value of AS differs from Latimer’s value because the coefficient dE/dT would seem to be too large. We have also calculated the values of the activity coefficient from both electromotive force measurements, using our own data, and from solubility measurements, using the data of Randall and Vietti. A relative method of calculation was used. Chemical Laboratory of Smith College, Northampton, Massachusetts. 25
Fromherz: Z. physik. Chem., 153, 376;
321 (1931).
