736
LOYALCLARKE, L. S. KASSELAND H.H. STORW
Vol. 59
TABLEVI1 CORRECTIONS TO BE APPLIED TO CONDUCTANCE DATABASEDON KOHLRAUSCH STANDARD POTASSIUM CBLORIDE SOLUTIONS 18’
00
25”
200
1 N KC1 71.3828 g. KCl per 1000 g. of solution in vacuum Kohlrausch 0.06541 0.09822 0.10207 Parker’s values ,065312 ,098116 Parker’s corrections, % - .I50 .log ,065430 ,098201 ,102034 Our new values Recommended corrections, % ’ ,031 - ,019 - ,045
0.11180 ,111687 ,101 .111733 - ,060
0.1 N KCl 7.43344 g. KCl per 100 g. solution in vacuum Kohlrausch 0.00715 0.01119 0.01167 Parker’s values ,0071416 .0111846 Parker’s corrections, % - ,118 .04g Our new values ,0071543 .011191g .0116676 Recommended corrections, % 4- ,060 ,017 - .021
0.01288 .0128765 ,027 .0128862 -t- ,048
-
+
-
+
Kohlrausch Parker’s values Parker’s corrections, % Our new values Recommended corrections,
0.01 N KCI 0.746558 g. KC1 per 1000 g. solution in vacuum 0.000776 0.001225 0.001278 ,00077422 .00122238 - ,229 ,214 ,00077512 ,00122269 ,00127572 % - .I14 .189 - .179
-
Parker’s standards instead of the Kohlrausch standards originally used by most experimenters.
Summary 1. The absolute specific conductances of the 1, 0.1 and 0.01 N potassium chloride solutions recommended by Kohlrausch as a standard of
-
-
0.001413 .00141037
- .186
-
.00141145 ,110
reference for conductivity measurements have been redetermined. 2. The results indicate that the corrections used by the “International Critical Tables” in the recalculation of the conductance data are unreliable. CAMBRIDGE, MASS.
RECEIVED FEBRUARY 26, 1937
[CONTRIBUTION FROM THE PHYSICAL CHEMISTRY SBCTION, PITTSBURGH EXPERIMENT STATION, u. s. BUREAUOF MINES]
Kinetics of Activated Sorption of Hydrogen on Chromic Oxide Gel’ B Y LOYALCLARKE,~ L. s. KASSEL3 AND H.H.
Introduction Burwell and Taylor6 have recently presented more than usually complete data on the kinetics of activated sorption of hydrogen on a chromium oxide catalyst as a function of pressure and temperature. The present paper derives from their data an empirical relationship which is satisfactory, except for small and for very large (1) Publisher3 by permission of the Director, U. S Bureau of Mines. (Not subject to copyright). (2) Assistant chemist, Pittsburgh Experiment Station, U. S. Bureau of Mines, Pittsburgh, Pa (3) Formerly physical chemist, Pittsburgh Experiment Station, U S. Bureau of Mines, Pittsburgh, Pa : present address, Universal Oil Products C o , Chicago, Ill. (4) Principal physical chemist, Pittsburgh Experiment Station, U S Bureau of Mines, Pittsburgh, Pa. (5) R. L. BurwelI, Jr , and H. S Taylor, THISJOWRNAL, 68, 697705 (1936).
sTORCH4
sorption. The form of this relation suggests a model of the sorption process, which permits derivation of the equation for moderate sorptions, and accounts a t least qualitatively for its failure a t extreme conditions. When the amount of hydrogen sorbed computed by Burwell and Taylor is plotted against time and a smooth curve drawn through the points, it was found that extrapolation to the startirig time would, taken naively, indicate an appreciable amount of sorption coincident with the beginning of the experiment. The results of these extrapolations are given in Table I. It will be seen that for all the experiments a t 1 atmosphere this initial amount is about 1.3 c c , at onehalf atmosphereabout 0.8, and a t a quarter atmos-
April, 1937
ACTIVATED HYBROGEN SORPTIONON CHROMIC OXIDE GEL TABLE I
EXTRAPOLATION OF SORPTION DATATO STARTING TIME
737
and obscures the interpretation of Q as an activation energy.
Temp., O K . 383.5 405 427 457 491 457 Catalyst 9 9 9 9 9 1 0 Extrapolation in cc when pressure is: 1 atmosphere 1.34 1.42 1.26 1.30 1.20 1.21 1/a atmosphere 0.76 0.86 0.80 0.80 0.80 0.96 atmosphere .57 .50 .43 .50 .50 .43 1/1 atmosphere .15
Kinetic Model
The existence of a pressure effect definitely less than first order seems to force the assumption that the initial sorption process is followed by phere 0.5, or approximately 0.2 1.1p. It is quite some more or less slow rearrangement. We propossible that the dead-space determination using pose to investigate the consequences of this helium is not the correct dead space available for assumption in a relatively simple form. It will hydrogen,6 but regardless of cause it is believed be supposed that the sorbent contains n primary that a large fraction of these initial amounts adsorption centers and N secondary centers, represents a phenomenon other than the slow only the former of which are capable of capturing sorption process. Accordingly the amounts gas molecules. The secondary centers can take sorbed, as given by Burwell and Taylor, have molecules from, and give molecules to, the been corrected by subtraction of the extrapola- primary centers but have no kinetic relations tions given in Table I. The corrected figures with the gas. The fraction of primary centers appear to approximate the true amount of covered is e, that of secondary centers is a, and activated sorption. This is indicated by the the gas pressure is p . The rates of the various improved correlations obtained by means of the allowed transfers, in molecules per secondary are then taken to be as revised data. Burwell and Taylor observed that the data of gas +primary centers nPk1 ( 1 - e) the separate experiments would approximate a primary +secondary centers n N k B (1 - a ) / ( l Ra) common curve when the amount of sorption, secondary +primary centers S, is plotted against bt, where b is a constant n N k w ( 1 - e)/&+Ra) nk& whose relative value is characteristic of the primary centers +gas pressure and the temperature. This relation is, The significance of the factor 1 Ra will be as Burwell and Taylor themselves state, only discussed later in the paper. The controlling approximate, but it is improved somewhat by differential equations are then the use of our revised values instead of the undNa/dt = nN[R26 (1 - a ) - kaa ( 1 - e ) ] / ( l RCY) corrected data. The representation of b by the d(ne N a ) / d t = n[PRi (1 - e) - kre] equation b = pnAe'OIRT suggested by Burwell If n and N are of the same order of magnitude and Taylor is also improved but still inadequate, we proceed as follows: since the best values of n computed a t 383.5, (1) Define a new variable p , proportional to 405, 427, 457, and 491 OK. were, respectively : the total adsorption, by the relation 1.00, 1.00, 0.84, 0.74, and 0.60. Values of Q ne Na = nfl in the temperature range of 405 to 491°K. as and use this relation to eliminate a from the graphically computed from mean values of differential equations. a t sorptions of 1, 2, 3, 4, 5 and 6 cc. were, (2) Introduce for 8 the power series expansion respectively: 15.3, 18.3, 19.0, 19.2, 19.7 and e = p u a p ur03 . . . 21.0 kcal. Little impart may be attached to obtaining two differential equations of the form the 1 cc. value and the trend in the other values dfl/dt = f (8) is comparable with the accuracy of computation (3) Expand the two right-hand members and and would not be serious were it not that the determine the parameters ui by equating cofluctuation of n impairs the utility of the relation efficients of like powers of p. (6) Cf experiments reported by Benton at Pittsburgh meeting or American Chemical Society, September 7-12, 1936. (4) Solve the resulting single differential equa(7) Burwell and Taylor also suggested that a eertain amount of tion for t as a power series in p. the hydrogen loss was due to causes other than the one of interest and treated their data both with and without appropriate corrections The result is
+
+
+
+
+
+
+
therefore We found di5eulty in understanding the method of deduction of these values and have chosen the above method because it is direct. independently reproducible, and reasonably free from predisposition toward any particular relationship connecting the data at various pressures and temperatures.
t =
fl/Pki
+
+
+ (l/Pki $. k4/P2h2)((s2/2)+ . . .
The coefficients of /3 and p 2 do not have the form of pressure dependence necessary to give an
738
LOYALCLARKE, L. S. KASSELAND H. H. STORCH
apparent order less than unity and this model is thus unsatisfactory. The secondary centers, in fact, do not enter into these coefficients at all; kz first appears in the coefficients of B3, and k3 in that of 0‘.
VOl. 59
the form dq‘dt = f ( a ) which has as a solution the power series expansion
+ (N/kl + k4/k1Rz)(l/P)la + (1/2) (((R+ I)/& + [(R + 1)kdkikn + Nkslkikz + kskr/’kikz’)l (lip) + (Nksh/ki2kz + kskrz/klzkz2)(1/P2)) + . .
nt = [l/kz
When kq
