388
I N D U S T R I A L AND E N G I N E E R I N G C H E M I S T R Y
Entomological tests ( 1 ) also indicate that the decomposition occurs very rapidly in pyridine, but less rapidly in acetone and other solvents. Conclusions
It is therefore seen that care must be exercised in the making and keeping of solutions of rotenone. Benzene may prove particularly valuable as a solvent because of its high solvent power and t,he fact that with it no appreciable decomposition of rotenone occurs. When a water-soluble solvent is desired, acetone may be used.
Vol. 23, No. 4
Solutions of rotenone should be freshly made, but if solutions are required to stand over a long period of time they should be kept in air-tight containers. Rotenone should be stored and shipped in the dry condition whenever possible, since dry rotenone undergoes no decomposition. Literature Cited Davidson and Jones, J . Econ. Entomol., 84, 257 (1931). (2) Gersdorff, Paper presented a t the Indianapolis Meeting of the American Chemical Society, March 30 to April 3, 1931. (3) Jones and Smith, J . Am. Chcm. Soc., 68, 2554 (1930). (4) Tattersfield and Roach, A n n . ApPZ. B i d . , 10, 1 (1923). (1)
~~
Free Energy of Some Copper Compounds' Merle Randall, Ralph F. Nielsen, and George H. West CHEMICAL
LABORATORY, UNIVERSITY
OF CALIFORNU,
BERKELEY,CALIF.
H E following review2 The chief obstacles faced today by practical metalby means of the Debye temlurgists, when called upon to solve their problems by of the e q u i l i b r i a in p e r a t u r e cube law is very the use of thermodynamics, are the lack of data from various r e a c t i o n s of small. Summing the areas, which to start and the difficulty of finding and appraiscopper c o m p o u n d s is prewe find ing such data when they do exist. An examination of sented, in the hope that it CU(S);S'2rs.i = 7.30; S O 2 s s . i = the available information, collected, sifted, and orwill greatly assist those who 7.815 calories per degree (1) ganized into a unified group by a competent authority, are interested in the metalFor the a l g e b r a i c heatpermits one to use what is set down therein with lurgy of copper. It has not capacity curve above 298.1 ' confidence. been possible to include all The previous tables of free energy 'by Lewis and Ranwe mention the determinathe compounds of copper for tions of Umino (93), Klinkdall were limited to a study of the non-metallic elewhich data are a v a i l a b l e . ments. This is the first extensive review consistent hardt (35), Wust, Meuthen, An effort has been made to with those data of the equilibria of a metallic element. and Durrer ( I O d ) , Naccari p r e s e n t a partial table of Most of the nineteen substances whose free energies are (53), Schubel ( 8 4 , Magnus free-energy values which are (47), and D o e r i n c k e l and tabulated are important compounds in the metallurgy reasonably consistent among of copper. The equilibria deal especially with the Werner (13). For comparithemselves and with those of high-temperature reactions of copper. The present son, their results were conLewis and Randall (42). The verted into heat content per values are consistent with the previously published agreement of the individual gram atom above 273.1' and free energies. determinations and the acplotted against the temperacuracy of the equations which have been derived may be judged from the constancy of the 'ture. It was at once apparent t h a t the heat content correvalues of the constant I , which we have given in all cases. The sponding to the solid a t the melting point (1083OC.) was about 7260 calories for all the investigators except Umino, who gave method of treatment will follow that of Lewis and Randall. 7720 calories. Fortunately both Umino (93) and White (98) Elementary Copper determined the heat capacity of nickel. Umino (93) obStandard Condition of Copper. Unstrained electrolytic tained 0.1294 and White (98)0.134 for the mean specific heat copper crystals, produced by the method of Lewis (40) and of nickel between 0" and 1452" C., or White's result is 3.5 of Lewis and Lacey (41) are taken as the standard condition per cent higher than Umino's. Umino gives 70.4 and White of copper. We shall probably ultimately adopt the single 73 calories per gram for the heat of fusion of nickel, again crystal as the standard condition. 3.7 per cent lower. White has the reputation for exceedingly Heat Capacity and Entropy of Solid Copper. The specific- careful work and we are thus led to the conclusion that the heat measurements of the various investigators indicate that heat capacity of copper is at least as high as that given by only one form of solid copper exists. The older work on the Umino and is perhaps a few per cent higher. Taking. Umino's specific heat of copper has been summarized by Harper (25), results we find: from which we have Cp273.1= 5.73, and Cp298.1 = 5.83 calories CU(S);C, = 4.91 0.00322 T - 0.000 000 54 Tz (2) per mol per degree. We have plotted these values and those of Nernst and Lindemann (55), Nernst (54),Keesom and Maier (49) recently used an equation based upon these same Onnes (34), and Griffiths and Griffiths (24) against log T in the conventional way (42). The curve extends to such results which does not differ greatly from Equation 2, but the coefficient of our T Zterm is more convenient and the low values of C, that the uncertainty (34) in extrapolation agreement near room temperatures is better with Equation
T
+
1 Received March 11, 1930; revised paper received February 11, 1931. Presented before the Division of Physical and Inorganic Chemistry at the 81st Meeting of the American Chemical Society, Indianapolis, Ind., March 30 to April 3, 1931. 2 The preliminary review was made in 1925 by Randall and Nielsen, whose results appear in the Free Energy Section, Vol. VII, International Critical Tables. The present publication includes supplemental work by Randall and West.
2 than with Maier's equation. Liquid Copper. For the heat capacity of liquid copper we have only the measurements of Wust, Meuthen, and Durrer (102), and of Umino (93). The former measurements 7.65 calories per degree for the mean heat capacity between 1083' and 1300" C. agree in magnitude with the latter but
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
April, 1931
give an unreasonable temperature coefficient, while those of Umino give: Cu(1); C, := 7.75 calories per degree
(3)
We shall accept this latter result for, although we should expect the heat capacity to decrease slightly just above the melting point, there should be a small positive temperature coefficient a t the higher temperatures. Umino's result, which gives a constant value between 1360" and 1780" K., is probably slightly low a t the higher temperatures. C 4 s ) = Cu(l). For the heat of fusion Glaser (22) found AH = 2650 calories; Richards (70) found 2750 calories; Wiist, Meuthen, and Durrer (102) give 2610 calories, but their value should be 3240 calories owing to a typographical error; Umino's measiirements (95) give 3210 calories, which we shall use. Honda and Ishigaki (30) studied the lowering of the freezing point in metallic systems and found about 2540 calories, but this value varies with the solute metal, and must be given little weight. Themeltingpoint of copper is (Q3a)1083" C.or (1356.1' K). From the above data we may therefore write
389
SE (single degree of freedom) = '/3 S E for solids as given in the tables (81) = 1.42. The value of Bv/T becomes unity a t about 430°K., a t which temperature the heat capacity of Cuz(g) has almost reached ( S I ) the limiting value of 9/2 R or about 9 calories per degree. Thus a t high temperature the heat capacity does not differ greatly from that of 2Cu(g). Vapor Pressure of Liquid Copper. Cu(Z) = Cu(g). The vapor pressure of liquid copper has been measured by Fery (17), Greenwood (23), Harteck (26), Jones, Langmuir, and hIackay (SS), Ruff and Bergdahl ( 7 4 , Ruff and Konschak (75), and Ruff and blugden (76). The data are given in Table I. Using the specsc heat equations of the previous paragraphs, we may write Cu(1) = Cu(g); A F o =
AH"0
+ 2.78 In T + I T
(8)
We may rearrange the general free-energy equation of Lewis and Randall, AFo/T =
- R In P
= AH"o/T
+ 2.78 In T + I
(9)
Cu(s) = Cu(1); A F ' = 1871 - 2.84 T l n T f 0.1101 61 T 2 0.000 000 09 T3 17.086 T; A H " z g s . i = 2580; ASo*!ps.i = 1.000; AF02ga.1 = 2282 (4)
and for convenience group the terms,
Gaseous Copper. Cu(l) = Cu(g). Von Wartenberg (95) measured the vapor density of a number of metals and found that most metallic vapors are monatomic. We may therefore assume copper vapor to be monatomic, take its heat capacity as constant, and write
If Z is plotted, as in Figure 1, against the reciprocal of the absolute temperature, we should be able to draw a straight line, the slope of which will be AHao. With the exception of the points of Fery ( l 7 ) , of Greenwood (23) at 2253' K., and of Jones, Langmuir, and Mackay (38), they seem to fall upon the line whose slope gives AH0' = 88,500 calories.
+
Cu(g); C, = 4 97 calories per mol
(5)
L:= - R l n P - 2 . 7 8 l n T =
AH"olT+I
(10)
The critical temperature of copper vapor is very high. For copper vapor in the presence of no other vapor the saturated vapor is more perfect a t lower temperatures than a t high temperatures, especially above the boiling point. For the vapor in the presence of nitrogen or other gas a t atmospheric pressure the vapor of copper is probably far from perfect. For the entropy of copper vapor we have, from the Sackur equation (78, 91 , 43)
+
Cu(g); S O Z ~ ~=. ~3/2 R l n 63.57 26.03 = 38.41 calories per degree
(6)
Entropy and Heal Capacity of Diatomic Gaseous Copper. Although we will assume that copper vapor exists principally as monatomic vapor, it is desirable to consider the properties of diatomic copper vapor. These following calculations are estimates based upon spectroscopic data for various substances (44, 7 , 31, 87). T e writes
++
+
Cuz(g); S O Z ~ ~=. 3~ / 2 R In w 5/2 R In T - R In P - 2.30 R In 87r2I k T / h z - H In 2 R f SE = 40.48 15.98 f 1.42 = 58.88 calories per degree (7)
+
where the sum of the first four terms represents the entropy of translation, of the fifth, sixth, and seventh, the entropy of rotation (79, 91, 14) of a symmetrical molecule (symmetry reduces the entropy of rotation by R In 2), and the last the entropy of vibration (15, 16, 83). In Equation 7 w is the molal weight, I the moment of inertia, k the Boltzmann constant ( 7 ) , 1.372 x 10-'6, h is Planck's constant ( 7 ) , 6.554 x 10 - 2 7 , and S E is the entropy of vibration (15, 16, 85). The moment of inertia was estimated t o be about 500 X 1 0 - 4 0 by assuming that the distance between the centers of the copper atoms was twice the difference between the distance for normal CuH gas and one-half that between the hydrogen atoms in normal hydrogen gas (31). The characteristic frequency in the Einstein function was estimated v = 9 x 10l2,whence Bv/298.1 = hv/k 298.1 = 1.442, and 8 We wish to thank Prof IT. F Giauque for suggestions in making this calculation
I /'Y 0.3
1 I I 1 I 1 0.4 0.5 0.6 Reciprocal of Absolute Temperature X 1000 Figure 1-Sigma Plot for Cu (1) = Cu (g)
I
I
0.7
The values of I obtained by subtracting AHo$T = 88,50O/T from Z are given in column 6. Omitting the three very divergent starred points, the average value of I is -55.531. Column 7 gives the deviation from the mean, omitting the starred values, the average deviation being *0.304. From which we find Cu(1) = Cu(g); AF' = 88,500 f 2.78 T In T - 55.531 2"; A H O 2 9 8 . 1 = 87,672; AS'2gs.i = 36.912; AF'2gs.i = 76,662 (11)
The average deviation of the d u e of Z is only 0.304 entropy units. Considering the experiments as a whole, this would seem quite satisfactory. However, combining Equations 1 , 4 , and 6, we find Cu(1) = Cu(g); A S o ~ 9 = ~ .29.595 ~ (prelim.)
(12)
There is a discrepancy of 7.317 entropy units between Equations 11 and 12. This difference could arise in a systematic
I N D U S T R I A L A N D ENGINEERING CHEiVfISTRY
390
Table I-Cu(1) Ref. (26)
ij
(26)
26)
751
76) (23) (76) (75) (75) (76) (17) (74) (76) (74)
$3 (23) (7.5)
(33)
K. 1419 1420 1421 1430 1445 1449 1463 2138 2148 2253 2301 2328 2348 2368 2373 2448 2433 2488 2493 2518 2531 2573 2583 "43 3110
T,
log P a m .
-5.839 -5.816 -5.839 -5.839 -5.780 -5.669 -5.538 - 1,677 - 1.580 -0.881 - 1.066 -0 856 -0,868 -0,871 0.000 -0.561 -0 471 -0.404 -0 296 -0 274 -0.136 - 0.0052 0.000 +0.0034 0 000
I / T x 104 7.0472 7.0423 7.0373 6.9930 6.9204 6.9013 6.8353 4.6773 4.6555 4.4385 4.3459 4.2955 4.2589 4.2230 4.2123 4.0850 4.0766 4.0193 4.0112 3.9714 3.9510 3.8865 3.8713 3 7836 3.2154
log fi(atm.) =
- 3140 a / T + 4.97 + log a
- 14,60O/T + 5.64
--
-
-
-
-
-
AH' (Eq. 16) 77,726 77,628 77 831 78:299 78,687 78 152 77:997 73,924 73 289 69:363* 72,653 71,189 71,879 72,465 63,143* 71,210 70 336 70:473 69,371 69,748 68,467 67,948 61(,123 69,495 80,415*
Mean
-0.276 -0.341 -0.192 0.182 0.524 0.175 0.137 0.498 0.235 -1.178* 0.430 -0.120 0.180 0.544 3.354* 0.253 -0 089 0.070 -0.357 -0.132 -0,598 -0.672 -0,574 0.125
-
-
(13)
Dev. from
1 (Eq. 11) -55.807 -55.872 -55.723 55.349 55.007 -55.356 55.394 55.033 -55.296 56.709, -55.101 -55.651 -55.351 54.987 -58.885* -55.278 -55.620 55.461 -55.888 -55.663 56.129 56. 203 56.105
6,5604 6.4521 6.6565 6.5392 6.2395 5.7200 5.0976 13.6389 14.0854 17.4281 -16.6402 17.6357 17.6022 17.6131 -21.6060 -19.1260 - 19.5415 19,8898 -20.3886 -20.5156 21.1634 21.8069 - 2 1.8415 -21 9211 - 2 2 3681
The equation of Hildebrand presupposes a constant value of AH ( AC, = 0). The single constant a, which is characteristic of each metal, and the constant 4.97 were determined by a consideration of the vapor-pressure curves of mercury, cadmium, zinc, lead, and thallium. For copper, using Greenwood's (63) value of the boiling point, which is not far from that calculated below, Hildebrand found a = 4.65, AH = 66,900, whence log @ =
-Cu('g)
z
error or a trend in the vapor-pressure measurements, thus giving a value of A.H which is too large. We may compare the value of aH (column 8) calculated on the basis of Equations 12 and 16 with the value to be expected on the basis of Hildebrand's formula (68) for the vapor pressure of copper.
Vol. 23, No. 4
-55 406 - 50,814*
4 717*
+ In T ) + Arl T - I
Ref.
(14)
(15)
where Are, Ar1, etc., are the summations of the coefficients in the algebraic heat-capacity equations. We may calculate a theoretical value of I which is really based on the low-temperature specific-heat measurements of solid copper, the Sackur equation, and the entropy of fusion of solid copper, which of course involves the measurements of Umino (93) on the specific heat and heat of fusion. However, any probable error in Umino's measurements would not make an error in the entropy of fusion of more than a few entropy units. Whence from values in Equations 12 and 8 substituted in Equation 15, I = -48.380. Now, using the values of Z in Table I and I = -48.380, we may calculate a value of A.Ho/T based upon each of the pressure measurements of Table I. Giving equal weight to all the experiments, we find an average value, AHo = 73,040. On the basis of the entropy calculation of I and the measured values of the pressure, we have the equation
+
Cu(1) = cu(g); AF" = 73,040 2.78 T1n T - 48.215 T; A.H"ap8.l = 72,211; AS'2gs 1 = 29.595; AF'zps.1 = 63,386 (prelim.) (16)
We may easily calculate the pressure corresponding to this equation by means of the above equation, which gives 2792" K. for the boiling point. Thevalues of AH corresponding to Equation 16 are given as the dotted curve of Figure 1. Solving Equation 11for AB'" = 0, by the method of approximations we find for the boiling point of copper, 2632" K. Equation 14 gives 2588" K. as compared with 3110" K. as calculated by Jones, Langmuir, and Mackay (33). Vapor Pressure of Solid Copper. Cu(s) = Cu(g). The
(Eq.19) -88.-723 -88.815 -88.636 -88.241 87.874 88.208 -88.223 -87.945 88.203 -89.591 -87.974 -88.519 -88.161 -87.831 -91.748 -88.135 -88.477 -88.317 -88.745 -88.521 -88.986 - 89.064 -88.967 -88.276 - 83,749
--
vapor pressure of solid copper has been measured by Langmuir and Mackay (38), Mack, Osterhof, and Kraner (46), and by Rosenhain and Ewen (76). The last-mentioned investigators measured the rate of evaporation in a vacuum, but we have reduced their measurements by means of an equation given by Langmuir (37). The results are given in Table 11, where the columns designate the same quantities as in Table I. The result a t 1273" K. by Mack, Osterhof, and Kraner (46) is given as the vapor pressure of CuO(s), but seems to be rather that of Cu(s). T 1083 1273 1186 1298 1288 1288 1288 1288
Table 11-Cu(s) log Patm. -9.158 -6.946 -8.546 -7.371 -7.814 -7.634 -7.621 -7.527
= Cu(8)
z
I (Eq. 17)
40.715 30.330 37.769 32.244 35.779 34.952 34.892 34,462
-42.723 -40.661 -38.429 -37.379 34.385 -35.212 -35.272 35.702
From an equation given by Lewis and Randall (46), A S o t g ~ . l= AI'&
I
-
-
I (Eq.20) -59.631 -56.ao2 -55.132 -53.620 -521146 52.973 53.053 - 53.462
-
-
The values of 2 are plotted against 1/T in Figure 2. Curve 17 corresponds to Equation 17, which is the sum of Equations 4 and 11. Curve 18 corresponds to Equation 18, which is the sum of Equations 4 and 16.
+
= 90,371 - 0.06 T In T 0.00; 61 T 2 0.000 000 09 T3 - 38.445 T; AH"2gs.l 90,251; A S 298.1 = 37.912; AF'zos.1 = 78,944 (17)
Cu(s) = Cu(g); AF'
-
+
CU(S) = cu(g); AF" = 74,911 - 0.06 T h T 0.00: 61 Tz 0.000 000 09 Ta - 31.129 T; A H O Z ~ S=. ~74,791; A S 298.1 = 30.595; AF0zg8.1 = 65,668 (prelim.) (18)
-
The two points of Langmuir and Mackay give A H " 0 = 75,945, which agrees very well with the value calculated from Equation 12, but their pressure is tenfold too large. It is not easy to account for these differences, for some unpublished calculations by Randall and others show that the entropies of vaporization of mercury, cadmium, zinc, and thallium are in excellent agreement with such calculations w were made in Equations 16 and 18. We prefer to use Equations 11 and 17 since, although the entropy is not properly accounted for, these equat,ions will reproduce the average of the experimental measurements of the vapor pressure. Evidence f o r Existence of Cu2(g). We shall not give any detailed calculations, but we wish to point out that if the formula of copper vapor is Cua rather than Cu, then we must reduce Harteck's calculated log P by log 2. Recalculating the data of Table I, we find
+
-
2Cu(l) = Cul(g); A F ; = 97,880 6.5 T In T 88.410 T; 95,942; A S pe8.1 = 44.874; AF'29s.i = 82,565 (19) AH'zoa.~
The individual values of I (Equation 19) are given in the last column of Table I. Combining Equations 1, 4, and 7,
ISDUSTRIA I, AND ENGINEERISG CHEMISTRY
April, 1931
we calculate the entropy of vaporization of liquid copper to diatomic copper vapor to be 41.25 entropy units. The difference between this value and that of Equation 19 is only 3.63 entropy units, a better agreement than that obtained on the assumption of monatomic copper vapor. Combining Equations 4 and 19, we find
+
?cu(s)= Cuz(g); A F ' = 101,622 0.82 T In T $. 0.003 22 T ? - 0.000 000 18 T 3 - ,54.238 T; hHozss.l = 101,102; AS0?98 1 = 46 874; 9 F O z s s . 1 = 87,129
(20)
\\-e reduce log P found by Mack, Osterhof, and Kraner ( ; G ) by log 2 and by the others (38, 7 2 ) by l/z log 2, whence we find the values of I (Equation 20) given in the last column of Table 11. The value of I calculated from the entropy (AS"298.1 calcd. = 43.25) is -50.614. We see that the agreement is again better when we assume copper vapor to consist largely of CUZmolecules. Copper Amalgam. The difference in potential between metallic copper and copper amalgam has been found by several investigators (11, 60, 59, 57) to vary from 0.0001 to 0.005 volt. We shall make no large error in provisionally assuming that the difference in free energy is negligible. Oxides of Copper
+
?CuO(s) = C U Z O ( S ) Oz(g). The dissociation pressures of cupric oxide have been carefully studied by Smyth and Roberts (89) and Roberts and Smyth ('?I),who showed that up to the eutectic point, 1080.2' C., cupric oxide and cuprous oxide do not form solid solutions. They thus confirm the earlier results of Foote and Smith (19) and contradict the still earlier results of Wohler and Foss (101), who claimed
I
I
I
l
l
I
/
I
1
1
0.75 0.80 0.85 0.90 Reciprocal of Absolute Temperature X 1OO(l Figure 2-Sigma Plot for Cu(8) Cu(&
-
different dissociation pressures for different mixtures of cupric and cuprous oxides. Roberts and Smyth (71) found that false equilibria in these systems were common. The early measurements of Debray and Joannis (12) are also in fair agreement with the results of Foote and Smith (19) and Smyth and Roberts (89). Measurements by Moles and Pay6 (52) and Ruer and Nakamoto (73) are also given. The heat capacity of cuprous oxide was studied by Magnus (@), who found the mean heat capacity to be 16.41 between 17" and 100" C. and 17.78 calories per degree between 18" and 541" C. Neuman (49) gives 15.3 for the heat capacity at 291" K., while Rlillar (51) has found accurate values at low temperatures. Maier (49) used the equation CuzO(s); C, = 11.75 0.01 T based upon Millar's low-temperature results and Magnus' measurements a t higher temperatures, but his equation gives values a t high temperature which are much too high. We prefer to use a linear equation passing through the mean of Magnus' points, and this equation again gives a slope which must be a little too large:
+
391
CU,O(S); C, = 14.34
+ 0.0062 T
(21)
The heat of formation of cuprous oxide is found by Thomsen (92) to be 40,810 a t 291" K., from which we have the value Cu20(s); AHOO = -41,166 calories as given in Equation 30. The heat capacity of cupric oxide from the data of Magnus (48) is CuO(s); C, = 8.32
+ 0.0071 T
(22)
Millar (51) also gives accurate values a t low temperatures in essential agreement with those of Magnus a t high temperatures. The heat of formation of cupric oxide from Thomsen (92) is -1H02el= 37,160, whence we find 4H"o = -37,353 calories as given in Equation 96. For oxygen gas we have O l ( g ) ; C,
6.50
+ 0.001 T
(23)
from Lewis and Randall (42). The data are given in Table 111. The value of AH",, found by plotting Z (-R In P1la 0.95 In T - 0.00375 2') against l / T is 34,500 calories, in fair agreement with l H o o = 33,550 calories, calculated from Thornsen's data, which give 33,490 calories at room temperature. We have adopted the calorimetric value of AH"0. I n calculating the average value of I we have omitted the starred values. Whence,
+
= 2.5,610 calories
s23 1 1058 1 111 9 1118 1 1118 1 1173 1 1173.1 1178 1 1188 7 1223.1 1229.2 1233.1 1233.1 1234.1 1234.1 1256.5 1273.1 1273.1 1273.1 1273.7 1283.1 1290.8 1293.1 1303.1 1303.1 1304.1 1311.9 1313.1 1316.2 1323.1 1332.2 1333.1 1344.4 1348 1 1349 8 1360. J 1351 0 1353.2 1363.3 e 1363 8 m 1364.6 m 1358.1 m 1378.1 m 5 40 per cent CuO, 60 per cent Cu20 b Pure(?) CuO e Eutectic point rn Metastable
(34)
',io*
0.00132 0 00026
-.Z
