INDUSTRIAL AND ENGINEERING CHEMISTRY
1280
LITERATURE CITED
Vol. 47, No. 6
Mahin, E. G., "Quantitative Analysis," 4th ed., pp. 278-80, McGraw-Hill Book Co., New York, 1932. (5) Monsanto Chemical Co., St. Louis, Mo., "Phosphoric Acid, Its Physical and Chemical Properties," Tech. Bull. P-26,Table I, (4)
(1) Hoffman, J. I., and Lundell, G. E. F., Bur. Standards J.Research, 5 , 2 7 9 (1930). (2) International Critical Tables, Vol. 3, p. 61, McGraw-Hill Book Co., New York, 1928. (3) Knowlton, N. P., and Mounce, H. C., IND.ENG.CHEM.,13, 1157-8 (1921).
1946. RECEIVED for review April 2, 1954.
ACCEPTED November 29, 1954.
(Density of Aqueous Solutions of Phosphoric Acid) MEASUREMENTS AT 15" TO S O " C. E. P. EGAN, JR., AND B. B. LUFF Tennessee Valley Authority, Wilson Dam, Ala. *
I
N MEASUREMENTS of the heat capacities of phosphoric acid solutions a t 15', 25 ', 40 O , 60 O, and 80 C., t h e weights and volumes of the charges for the solution calorimeter were determined. Here was a n excellent opportunity for finding t h e densities of the solutions over the same range of temperature. T h e observed weight-volume relations, in conjunction with t h e precise composition-density relation a t 25' C. reported by Christensen and Reed in the accompanying paper (p. 1277) would yield values of density more accurate and, at concent'rations below 60% €13P04,more extensive th& those in the literature ( 1 , s ) . The densities thus determined, together with partial molal volumes derived therefrom, are presented here. T h e measurements cover concentrations of acid up t o 85% HaPOa.
-Table I.
O
Wt. yo
HsPOa
4.46 9.35 19.21 29.33 39.15 49.36 59.54 70.10 79.97 84.81
*
Table
50 55 60 65 70 75 80 85 SOU
95a
loo= t,
O
40.82' C. 1.0159 1.0428 1.1009 1.1667 1.2371 1.3183 1.4076 1.5096 1.6149 1.6695
60.81' C. 1,0064 1,0329 1,0910 1.1561 1.2256 1.3054 1.3938 1.4950 1.5989 1.6552
81.40' C. 0,9945 1,0210 1,0776 1.1415 1.2116 1.2911 1.3788 1.4794 1.5832 1.6378
IT. Smoothed D e n s i t i e s and D e n s i t y - T e m p e r a t u r e Coefficients of Phosphoric Acid Solutions, G./Ml.
Wt. % Hap04
45
25.18' C. 1.0213 1.0488 1.1072 1.1742 1.2461 1.3272 1.4176 1.5213 1.6271 1.6823
O
15' C.
0 5 10 15 20 25 30 35 40
15.85' C . 1.0232 1.0514 1.1114 1.1791 1.2511 1.3325 1.4239 1.5280 1.6345 1.6903
wit,h those from the densit,y measurements within an average of 0.02% HaP04. T h e observed densities are listed in Table I. Equations of t h e second degree in t, C., were fitted to t h e densities and temperatures at each concentration, and the densities at round values of temperature were calculated. T h e slope changed sharply between 60" and 80" C. Equations of t h e third degree in w, weight % H3P04,then were fitted t o t h e densities and concentrations at each temperature, The over-all average deviation in representing t h e densities was 0.2 mg. per ml. The densities a t uniform increments of concentration, t h e equations relating density
T h e charges of acid solution were measured in a volumetric flask t h a t held about 850 m1.-the required volume of solution for filling t h e calorimeter. T h e flask was made from a 1-liter flask by drawing t h e bottom inward and was, i n fact, a largecharge was brought to equiiibpycnometer* rium in a water bath, and t h e meniscus was adjusted t o t h e mark. Flask and contents then Rere weighed at room ternperature. The volume of t h e flask at each experimental temperature was found from t h e average weight of water used in determinations of t h e water equivalent of t h e calorimeter and t h e known density of water ( d l at t h e same temperature. ~ l weights l were corrented t o vacuum.
For convenience in subsequent correction of the calor i m e t r i c measurements, the temperature of the bath was held slightly above the respective nominal temperatures. Bath temperatures were read from a Beclrmann thermometer that was checked against a calibrated platinum resistance thermometer a t each temperature level. The temperature was regulated within =t0.003" C. The concentrations of phosphoric acid were found from duplicate measurements of the densities of the solutions a t 25' C. by the technique described by Christensen and Reed ( p . 1277). Careful volumetric analyses by the molybdophosphate m e t h o d yielded results t h a t agreed
Observed Densities of Phosphoric Acid Solutions, G./M1.
25' C.
0.4991 1.0268 1,0553 1.0852 1,1165 1.1493 1.1837 1,2198 1.2577 1 ,2974 1.3391 1 3828 1.4287 1.4768 1.5271 1,5798 1.6350 1.6928 1.7532 1.8163 1.8823
..
23 29
..
32
..
39
..
53
..
56
..
62
73 , .
76
..
80
si
c.
15 25 40 60 80 a Extrapolated.
p
0.9971 1.0241 1.0523 1,0819 1.1129 1,1453 1,1794 1 2151 1 ,2527 1 2920 1,3334 1.3767 1 ,4223 1.4700 1.5200 1,5725 1.0275 1,6850 1.7482 1.8082 1.8741 p,
p = p = p = p 3 p =
400
0,9995 0,9971 0.9923 0.9833 0,9720
x
c. dp/dt
dp/dt
dp/dt x 105
105
P
0,9922 1.0189 1.0468 1.0759 1.1065 1.1385 1,1721 1,2074 1.2444 1,2834 1.3242 1.3672 1.4122 1.4596 1.5092 1.5613 1.6159 1 6732 1.7331 1,7969 1.8616
29 34
..
38
45 .. 56 .. 59 64
73
..
77
so. . 84
x
105
, .
39 43 , .
46
..
53
..
62
..
62
..
67
..
74
..
78
..
81
84
60' C. dddt P x 105 0.9832 .. 1.0097 52 1.0373 53 ,. 1,0661 1.0963 58 1,1280 .. 1.1611 63 1,1960 .. 1.2326 68 1.2710 .. 1.3114 67 1.3539 1.3985 7i , 1.4453 1 ,4945 75 1,5462 .. 1.6003 78. 1.6672 1.7168 , . 1 7792 1.8446 85
G./M1. = f ( w , Wt. % HaPOa) 0 , 0 0 5 3 3 6 ~ 0.042334~2f 0 . 0 6 1 1 5 8 ~ ~ 0 . 0 0 5 2 8 5 ~f O.O.g2276u;2 f 0 . 0 ~ 1 2 0 9 ~ 3 0 . 0 0 5 2 1 6 ~4- O . O d 2 2 1 4 ~ ~ 0.061263~3 0 . 0 0 5 1 7 6 ~f 0 . 0 a 2 1 0 9 ~ ~f2 0 . 0 ~ 1 3 2 8 ~ 3 0 . 0 0 5 0 2 2 ~f 0.0a2387w2 f 0 . 0 ~ 1 1 2 8 ~ 3
++ + ++
+
+
si
80" P
0.9718 0.9977 1.0247 1.0531 1,0829 1.1142 1.1472 1.1818 1.2183 1.2566 1.2969 1.3392 1.3836 1.4303 1.4792 1.5305 1.5843 1,6406 1.6996 1.7612 1.8257
c. dp/dt x 106 .. 64
64
..
69 74
..
76
.. , .
72 75
.
,
75
..
80
k3 86
fAv. O ,00024 Dev. 10.00013 i0,00007 *0.00019 = k O . 00040
1281
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1955
m = - 1000 .--
M z
Table 111. Partial Molal-Volume, Fz,of HsPO4 in Phosphoric Acid Solutions, Cc./Mole HaPo4 Wt. yo HsP04 LO
20
30 40 50 60 70 80 90 100
1 5 O C.
25OC. 47.12 47.92 48.68 49.43 50.16 50.84 51.43 51.90 52.18 52.29
46.64 47.47 48.28 49.08 49.85 50.57 51.19 51.66 51.96 52.06
40°C. 47.77 48.52 49,23 49.91 50.59 51.24 51.81 52.25 52.54 52.64
6OoC.
48.26 49.09 49,80 50,48 51.14 51.75 52.30 52.74 53.03 53.13
80°C. 49.16 49.63 50.20 50.83 51.52 52.18 52.78 53.26 53.57 53.68
dm =
wt. % HsPOa 10
L
20 30 40 50 00
70 80 90 100
15OC.
25OC.
4OOC.
60’C.
0.0164 0,0434 0.0932 0.1730 0.2893 0.4517 0,6639 0,9247 1.2427 1.5825
o.oo90 0.0360 0.0827 0.15711 0.2675 0,4209 0,6233
0.0104 0.0347 o.0780 0.1462 n.2489 0.3948 0,5896 0.8347 1.1377 1.4900
0.0115 0.0380 o.0820 0.1495 0.2491 0.3875 0.5761 0.8190 1.1161 1.4880
0.8814
1.1827 1.5112
o.oo811 0.0586
0.1222 0.2264 0,3756 0.5815 0.8477 1.1719 1.5014
t o concentration, and t h e corresponding density-temperature coefficients are shown in Table 11. T h e present measurements a t 25” C. are included in Table 11 for comparison with the more accurat,e values in Table 111 of Christensen and Reed (p. 1277). For simplicity in calculation, the equations ( 2 ) relating partial molal quantit.ies t o molality
1000 M P [(loo loo - w)’] d w
&fz
+[o
-
9v =
(100 PO W
a@t v* = + w(100 - w )aw @v
-
(VI
8OOC.
0.0235
- 20)
T h e constancy of T,P , . a n d n1 permitted a substitution of the partial derivatives for t h e total derivatives t o yield, after simplification of terms
Table IV. Relative Partial Molal Volume, -(TI - T:), of HzO in Phosphoric Acid Solutions, Cc./iMole HzO c
W
(100
-
-
V:) =
M I
wz
a@ =
- M-n 100 aw
wz
-0.183839 -
a@
100 a w
where p is the density of t h e acid solution, po is the density of water at the same temperature, and t h e other terins have their usual significance. T h e density and & were calculated a t 2.5y0intervals for each temperature. T h e slope, a&,/aw, was determined b y means of seven-point first-derivative coefficients (6). Calculated values of and of (71 a t concentration intervals of 10% are given in Tables I11 and IV, respectively. Values of for concentrations below 5% H3P04 a t 25’ C., as calculated from the density measurements reported in the preceding article approach = with a rapidly increasing slope that vitiates an extrapolation to Although this relation of t o w is not evident from t h e present measurements, it is assumed to hold at the other temperatures and is the reason for putting values of v z instead of ( v z - 72)in Table 111.
vy)
vz
v2
vz
LITERATURE CITED
V2 =
@u
(1) Farr, T. D., “Phosphorus-Properties
of the Element and Some of Its Compounds,” TVA Chem. Eng. Rept. No. 8, 1950. ( 2 ) Glasstone, S., “Thermodynamics for Chemists,” Chap. 18, Van
a@ + m dm 2
( V I - v:) = - ~.m2
55.51
were converted t o a basis of weight the relations
b& bm
yo,w,by substituting therein
Nostrand, New York, 1947. (3) International Critical Tables, Vol. 3, p. 61, McGraw-Hill Rook Co., New York, 1928. (4) Ibid., p. 24. ( 5 ) Salzer, H. E., Natl. Bur. Standards, Washington 25, D. C., Applied Mathematics Ser. 2, 1948. RECEIVED for review April 2, 1954.
ACCEPTED November 29, 1951.
Combination of Rubber and Carbon Black on Cold Milling W. F. WATSON British Rubber Producers’ Research Association, 48 Tewin Road, Welwyn Garden City, Herts, England
T
HE mechanism for the degradation of elastomers by cold milling (3) can be represented by:
+
Scission by shear forces Radical recombination Z. Radical acceptor reaction Termination to noncross-linked products R - R ++ Termination to cross-linked products
R - R + R. R. R. R. + R - R R. + X + RX. or RY RX. or Z.
+
-+
R., R X . , or Z.
+
where the term “radical acceptor” denotes a substance competing significantly with recombination. Although t h e structure of carbon black is imperfectly known, x-ray analysis has shown it t o consist of layers of condensed rings of carbon atoms. Unsaturation and discontinuities in t h e layers a r e likely t o provide sites for attack of free radicals, and thus
make carbon black a radical acceptor of a special polyfunctional type. hssuming combination of rubber radicals and carbon black, a particle could terminate more than one sheared rubber chain. Furthermore, rubber chains attached to a carbon black particle could also undergo scission by shear and be terminated by combination with other particles. T h e result anticipated on this picture is a network of rubber and carbon black held together by chemical bonds. I n rubber solvents such a network would be insoluble and merely become swollen gel. Insolubiliaation of rubber on milling with carbon black has been reported on occasion, but t h e evidence is not sufficiently extensive t o draw reliable conclusions as t o its cause. This paper reports a systematic investigation of t h e occurrence of rubber-carbon black gel on cold milling. This gel has been shown t o form, and t h e conditions for its formation and its prop-
