1710
LAWRENCE JOSEPH HEIDT ?'AJ?I,E 7rlI13KMUDl"AMIC
t
oo 13'
25 :;go
C
CONSTANTS VOR 'I'FIIi
AC
0.0:3281 . 03283 .032'75 . 03262
0 , 704(1 1 . 1410 1,4401
1.8040
A,
0.97X1 !J7N
392. G 464.0
,9746 97.,;1
Harned and Emhree, THISJOURNAL, 6 6 , 1050 (1934). Stadie and Hawes. J. Rid. Chem., 77, 241 (1928). Cullen. Keeler and Robinson, i b i d . , 66, 301 (1925). Thomsen, "Thermochemische Untersuchungen," Leipzig,
I O N I Z A T I O S OF C A R B O N I C .4ClD
K,
24i.2 .4
that AH assumes a value of zero a t 58.1'. Consequently, pK1 would be expected to pass through a minimum (6.293) and K1 to reach a maximum (5.09 X a t that temperature. Such behavior is in accord with similar results on all other weak acids, so far as they have been studied." In the last column of Table IV are listed values for AH in calories, computed from equation (11'). The value a t 25' (AH = 2075 calories) is in excellent agreement with that derived from e. m. f . measurements a t 18 and 38' by Stadie and Hawes,'j and also by Cullen, Keeler and Robinson,16 both giving A H = 2050 calories. Direct calorimetric measurements by Thomsen17a t room temperature, probably 15-16', gave 2800 calories in reasonable agreement with our value of 2952 a t 15O. (14) (15) (16) (17) 188%.
Iv I;IRST
?.,
:m
Vol. 57
x
107
Ohsd.
2 . Cil;j ::,722 4.310
PKI
6 . .58:3() t i . 429;;
c,.3(i"5 7 3: 173
4.817
THE
A H , cal.
f i . ,5,88$)
4481
6 . 430(j 6 . 3654 6 . 3 173
2952 2075 1109
Summary New measurements have been made at 23' on the conductances of solutions of carbonic acid and of potassium bicarbonate. The relative conductances a t 0, 15,23 and 38' of saturated carbonic acid solution and of potassium bicarbonate, potassium chloride and hydrochloric acid a t 0.001 normal have also been determined. From these data the thermodynamic dissociation constant of carbonic acid as a monobasic acid has been obtained for the temperatures given. These values have been used in obtaining equations by means of which the ionization constant K1 and the heat A H of the reaction HzO COr = H HC03are expressed as functions of the temperature, The values of the constant K I are 4.31 X a t 25' and 4.82 X a t 38') in reasonable agreement with the corresponding values 4 . j X lop7 and 4.9 X low7obtained by MacInnes and Belcher a t these temperatures.
+
+
NEWYORK,N. Y .
[ COXTRIBETION FROM
Computed
RECEIVED JUNE 0, 1935
CHEMICAL LABORATORY OF HARVARD 1
7]
~
The Photolysis of Dry Ozone at XX 208, 254, 280 and 313 m,u. 11. Reaction Kinetics BY LAWRENCE JOSEPH HEIDT Recent data from this Laboratory1 on the photolysis of dry ozone, largely a t X 208 mp, gave quantum yields, 0, referred to ozone as large as 6.7. This strongly suggested a chain mechanism; but the decrease in 0 with po3/po2was not so great as that given by Beretta and Schumacher2 a t X 313 mu, nor was $J independent of the light intensity. Further interpretation of the data was therefore postponed until a check was made upon the work a t X 313 mp and until the influences of concentrations and wave length upon quantum yields were more fully established. Such data are presented here. The experimental procedure, precautions, and corrections were the same as previously followed. (1) Heidt and Forbes Trns J O U R Y A L 66, 2365 (1934) ( 2 ) R e i r t t a -1nd 5c 1 I ~ I I C ~ I C T9 ,hzrrk Chein 17B,417 ( i i l , L i
At X 313 mp an inverted U type quartz mercury arc lamp3 was used as a light source. The trap a t the top of the inverted U was omitted. Instead, the U was tilted so that the plane containing it made an angle of approximately 13' with the plane containing the plungers. The plunger connected to the upper positive electrode was seated; the other was slightly unseated. The luminous column was contained in a quartz tube 4 mm. inside diameter and 7 mm. 0 . d. The arc length was 60 mm. The lamp was operated on a 110-v. storage battery source a t from 2 to 4 amp. It was as intense, constant and durable for slit illumination as its higher voltage type predecessor. 3
I ,rh.
&id
€ h d t T H YT o
RNU
63 4 ? * 0 ,1171
~
~
Sept., l!G5
REACTION KINETICSOF DRYOZONEPHOTOLYSIS
The actinometer solution a t X 313 mp was 0.003
1711
The average ten-degree temperature coeffi-
M in uranyl oxalate and 0.003 144 in oxalic acid. Its cient for the photolysis given in Series (j, a t A 813 = 1.15 over the range 0 to 60'. It quantum yield was taken as 0.57.4 The remain- m p u , is 6,,+ ders of the solutions and apparatus were the same is apparently independent of the mole fraction of as those employed a t XX 208, 254 and 280 mp.I ozone and of the temperature interval after 4 was corrected for the dark reaction between More than 97$$, by actual m e a ~ u r e m e n t con,~ sisted of light within 3 mp of the desired wave pressure readings before and after photolysis. There was no observable after-effect. Earlier length. work' gave 6,,.+ = 1.18 over the range -SO to Partial pressures of ozone, poJ. and oxygen, 0". B. and S. give 6,& = 1.23 over the range Po>, a t total pressure, P = pos Po?, were 0 to 3 5 O . calculated from the observed difference between The dark rates in Series (ifor which PI = P and total end pressure, Pf. To obtain Pf, the reaction cell was irradiated with light from an 3.84 mm. were as follows. At 23 * 2" they were Hanovia mercury arc lamp of quartz placed 2 cm. I . M / ~ O S O= 1.3 x IO-: mm./min. a t P = 446 at p from the front window of the cell until P became and Po, = 276 and 0.7/1300 = 0.6 X constant over eighteen hours. This was followed = 497. by flaming to a dull red heat, the cell, capillary At 30 * 1' they were 12/37 = 33 X connections and the quartz spiral pressure gage. at = 4iO; 2.3/310 = 8 X lo-: a t p = 4SO The system was then allowed to cool to room and 1.7/980 = 1.7 X lop3 a t p = .i23. temperature, whereupon Pfwas again determined. At 60 * I" theywere2.0/103 = 19 X at The difference between Pfas determined by irra- p = 530; O.S/SO = 16 X a t p = 540; diation and by flaming never exceeded 1 mm. 0.7/115 = 6 X lop3 a t P = 553 and 4.3/'940 = The volume of the system was 42 cc. The dead 4.5 x 10-3 a t P = 559. space outside the quartz reaction cell was 2.0 cc; These give a ten-degree temperature coetficient for the part a t room temperature was 1.3 cc. the dark rate of 3 * 0.1 between 20 and 60' for The results are tabulated in Tables I and 11. small mole fractions of ozone in oxygen. At corThe subscripts appended to the serial numbers responding mole fractions Glissmann and Schugive the number of experiments in the group if macher' give 3 * 0.1 between 70 and 110'. greater than one. Pressures were recalculated to Figure 1 shows plots of l/+ against po2 X 0' in mm. of mercury a t 0 ' . A barred quantity (Po2 @03)/Po,3.Circles represent the data of denotes an average. Quantum yields, 4, were re- B. and S.2 a t 7.5 + 3', X = 313 mp, and filled ferred to the number of ozone molecules decom- circles Series 3 of the previous work from this posed (calculated from 2 A P ) per quantum ab- Laboratory1 a t X 208 mp. Singly flagged circles sorbed. In representative cases, the subtracted represent the data of Table I, doubly flagged quantities under AP are the corrections for the circles, Table I1 a t A 313 mp and bisected circles, dark rate. For comparison, corresponding values Table I1 at AX 208 and 254 mp; all a t 22 * 2". of cp given by B. and S 2 are also included. At Although the initial partial pressure of pure dry XX 208, 234 and 2SO mp, absorption of light by ozone varied from 177 to 390 mm., the data of ozone was taken as complete.6 At X 313 mL:, (6 Tables I and I1 even a t X 313 mp, are in good is given for the value of the extinction coefficient, agreement with the earlier work of this Laborak = log Io/I/po,d(po,in rnm. and d in cm.), used tory. Plotted on a more condensed scale, they by B. and S.,2namely, 0.00092.6b are also in good agreement with the average of Table 11, Series 6, groups 1 and 2, and groups the data of Warburgs a t X 254 mp represented by 9, 10 and 11 show corresponding values of 4 to be the flagged filled circle. They agree with those approximately equal a t XX 20s and 313 mp. The of R . atid S. only if 4 is reduced by one-half. earlier work' also showed 4 to be approximately Possibly the latter referred their 4 to the increase equal a t AX ?OS, 2Y and ?SO mi: and freqiiently to iri the number ( I f molecules in the reacting system exceed 4 . per quantum absorbed ; the number of ozone molecules dcconiposcd is twice this number. Or they (4) Porbrs arid Heidt, 'l'iirs J O U K N A L . 56, 2:jli:j ,,I!): I 1
+
+
( 5 ) Method of Heidt and Daniels, i b i d . , 54, 2384 (1!):+2) (6) (a) Meyer, Ann. P h y s i k . 12, 849 (1903): (i,) Pabry and Buisson. Compt. rend., 156, 782 (1913); ( c ) N y and Choong, Chinere
J . Physics, 1, 38 (1933).
( 7 ) Glissrnann and Schumacher, Z. p h r s i k . Chem, 21B, :!2.3 (1'33H). (8) Warburg, Siizber. preuss. .Ikad. W i s s . , 644 (1913).
LAWRENCE 3 0 s HEIDT ~ ~
1712
Vol. 57
TABLE L Serial number
Cell
-
-
P
k i n mp
50%
PO7
5- 1 2 0 8 4 Zn 2 3 4 5 6 7 8 9 10 11 12 13 14 16 16 17 18 19
179 181 183 186 189 190 192 193 197 20A 209 211 225 226 236 238 247 248 249 Pt = 266
174 168 163 160 153 151 148 142 138 119 113 109 82
79 59 56 37 35 33
5 13 19 26 35 39 44 53
39 87 90 102 143 147 177 182 210 213 216
temp., ~ F / ~ O J OC.
Quanta
abs./mm. E D X 10-16
19.8 11.1 20.5 8.6 21.0 8.6 21.3 7.8 21.8 9.5 22.1 9.5 22.4 8.2 21.0 7.4 21.6 7.8 23.0 8.3 23.1 8.2 23.3 8.0 24.0 5.2 23.4 7.5 23.7 6.7 20.7 8.0 21.0 7.6 7.0 21.9 22.2 6.0 Average 7.8
5 14 21 30 43 49 57 73 84 151 178 I98 392 421 710 775 1400 1510 1630
pTime h t o l y sofi s ,
min.
12 10 15 13 7 9.3 15 19 15 19 18 19 17 23 22 21 25 24 24
AP
9
1/ 9
2.70 1.40 2.40 2.05 1.15 1.25 1.90 2.55 1.75 2.10 1.80 1.95 1.05 1.80 1.35 1.20 0.85 0.70 0.80
6.2 5.0 5.7 6.2 5.4 4.3 4.7 5.f1 4.5 4.1 3.8 :3 . 8 3 .ti 3.2 2.8 2.1 1.4 1.4 1.8
0.16 .20
.is .16 .19 .23
.21 .18
.22 .24 .26 .26 .28 .31 .36 .48
.72 .72 .56
TABLE I1 Serial number
6- l a b 2a b 3a b
-
Xin mp
208-4Zn 313
Hg
42 j2
6a b * {2
82
92 102 11s 1% 133 14a b c 15, 162 172
208-4 Zn 313 Hg
254--2 Zn
Pr
=
P
30a
421 424 434 437 444 447 449 473 477 481 488 494 496 500 517 522 529 542 546 551 568 570 581 584
325 319 299 293 279 273 269 222 213 205 191 180 175 166 133 123 109 83 75 65 31 27 5
PO?
3o2Fhoa
96 125 105 140 135 196 144 215 165 262 174 285 180 300 250 533 264 590 276 650 297 762 313 860 321 910 335 1005 388 1500 399 1697 420 2050 459 3000 471 3440 486 4120 537 9850 543 11500 576 67000
Cell Quanta t e y p . , abs./min.
c. Eo x l o - & $
22.5 22.6 20.9 20.9 0.2 .2 22.3 22.7 40.0 40.0 19.8 0.1 21.4 21.9 23.8 23.2 40.0 60.3 60.3 60.3
23.8 60.2 24.0
may have underestimated the amount of false light; they made use of filters t o render their light monochromatic. The decrease in 4 with increase in the light intensity and/or extinction as it varied with wave
12 9.5 8.6 4.1 11.2 6.6 6.7 3.1 9.5 8.4 9.2 5.8 7.2 16.2 5.2 7.6 4.5 8.2 7.4 7.7 3.1 4.3 18.6
Time of photo!ySlS, Rlrl.
23.5 24.0 35.5 57.5 31.5 41.8 39.E 43.0 23.0 25.0 29.0 43.0 32.6 26.4 61.7 44.8 101.0 50.0 46.3 79.0 85.2 82.0 73.0
AP
3.36 2.95 3.55 2.50 2.70 2.10 2.20 1.20 2.8-0.6 2.7-0.3 1.90 1.05 1.23 2.8’) 1.90 1.85 2.60 4.5-0.7 4.6-1.4 5.4-0.8 1.10 2.35 0.90
4
3.6 4.0
3.5
2.1
3.3
2.3 2.3 2.9 3.1 3.1 3.5 2.1 1.3 1.7 1.0
1.15
2.0 1.2 1.14
1.1 1.18
0.9
1.9
1.7 2.1 3.9 2.8 2.3 1.3 2.1 0.2
1 .I4 1.14
1.15
Average
1.15
length a t AX 208, 254 and 280 mp,l does not alter the main trend of the increase in l/# with pap/ po3. At X 313 mp neither B. and 5.nor the author observed any dependence of $I upon light intensity.
REACTION KINETICSOF DRYOZONEPHOTOLYSIS
Sept., 1935
1713
3000
2000
is EL
i: a
1000
0.1
0.2
0.3
0.4
0.5
0.7
0.6
0.8
0.9
1.0
1.1
1.2
1.3
1.4
I/+. Fig. 1.-The curves are hypothetical. Circles represent the data of Beretta and Schumacher2 at X 313 mp; the flagged filled circle on the sub-plot, the average of the data of Warburgs at X 254 mp; and the remaining symbols, the data from this Laboratory at XX 208, 254, 280 and 313 mp.
The curves are hypothetical. Within the limits of experimental error they agree with the observed increase in 1/$ with Pot(Po2 f PO,>/ po3. At large mole fractions of ozone where the experimental accuracy in l/$ is best, the curves for Series 3 and 5 cross and follow the data very closely. They also approach asymptotically the straight lines drawn through the average of the data a t small mole fractions of ozone.
Discussion
+ h~
+0 2 ’
ka ks ks’ ksSs
02’
02’
02’
+ Os
+02’ +
02’
+S + +s + Oz -t +Oa + 02 + + Os + + 0s + + s +03 + 3 + + + +0 + Os + f + Oz + + 02
02‘
‘/*02
0 2
0 2
0 8
0 2
0 3
+S
0 2
0 2
0 2
0 3
0 2
+02 + S
To the left of the indicated reactions are given the corresponding rate constants. The reactions (k&) and (k&) involving the surface, have been added; and for absorption in the ultraviolet, 0 2 ’ in (k1) has replaced 02. The homogeneous recombination of oxygen atoms has been omitted because of their relatively small concentration in the presence of ozone and oxygen. If a02’ are produced in (k1) and PO,’ in (kz), equations I, I1 and I11 follow
s,
A reaction mechanism for the photochemical decomposition of ozone was postulated by Schumacherg in 1932, It was added to by Ritchie’O in 1934. A summary of their hypotheses follows. ki 03
0 kzSz 0 k3 0 k3’ 0 ksS8 0
kz
+0
(9) Schumacher, 2. ghysik. Chem., 17B,405 (1932). (10) Ritchie, Proc. Roy. Soc. (London), A146. 848 (1934).
LAWRENCE JOSEPH HEIDT
li14 (I)
[ O ] :=
and, as
C$
= -d[o'1,/Iab8.,
VOl. 57
it follows that
dt
Term I
From 111, l/# is equal to the sum of two terms, the first of which increases to 1/(2 f &/(os)) or '/2 (very nearly) as Poz approaches (PO% Po3), and the second of which increases to a constant k3/2h (very nearly) times po2(po2 $ 0 3 ) / h The experimental work (see Fig. 1) shows a similar increase in 1/# with this ratio." The constant, k3/2k2, is the reciprocal of the slope of the straight line (Fig. 1, solid line) which the data approach a t small mole fractions of ozone. Its intercept on the l/# axis equals the maximum value of the first term, :i. e., 1/2 (very nearly), as Po2-+ (Po2 po3). From the data of this Laboratory a t 22 * 3' its slope is 7500 * 800 mm./l/q5 corresponding to 680 given by B. and S. a t 7.5 j = 3') Fig. 1 dotted line. If the wall effect is negligible, Sn = 0. Then, when Po? == 0, term I1 = 0 and from term I for
hence, i t is not possible to assign from the data unique values to a and 0. The work of this Laboratory, however, gives cp >4 when po,P/po, is less than 100. Therefore, /3 must be greater than zero; otherwise, if the postulated mechanism is correct, # couM not exceed 4 even though all the primary products of the photo dissociation subsequently decomposed ozone. A plausible assumptiong is to set p = 2. We may evaluate CY in the following way. At XX 208, 254, 280 and 313 mp, the approximate equivalence of # suggests that the primary act is essentially similar a t these wave lengths, i. e., CY remains unchanged. The energy available a t X 313 mp (91 kcal.) is sufficient to dissociate ozone into an oxygen atom and an oxygen molecule in its first electronically excited lZ state (24 37 kcal.). It is not sufficient, however, t o dissociate a n ozone molecule into oxygen k g = kg' ks atoms (24 117 kcal.).12 Also, the energy of the - - 2i(l a ) - (1 - a) k4 1 - 2i 32 to 2 transition, 37 kcal., corresponds almost where i is the intercept of the plots on the l/+ exactly with the difference between the long wave axis. The data of this Laboratory give i = 0.14 length limits of the ultraviolet6b and visibleg ab* 0.1. sorption spectra of ozone, X 350 and X 650 mp, reThe values assigned t o CY and B ,also determine spectively, or 82-44 = 38 kcal. In addition the in part the rate of increase of l/cp with P o ~ ( P o ~ lZ state of oxygen is metastable as evidenced by @o,)/po,. Variations in the calculated value the very weak absorption of oxygen a t X 760 mp of l / # for (Y = 0 or 1 and /? = 1 or 2, using corre- corresponding to the transition 38to ' 2 . A plausponding Tralues of kg/k4 determined from i, do sible assumption, therefore, for absorption by not fall outside the limits of experimental error ; ozone in the near ultraviolet is to set a = 1. (11) I f t h e synthesis of ozone from oxygen atoms and ozone mole+- ki'['&] + k35'3) in 111 would Thereupon, k5/k4 = 2 for N = I,$ = 2 and i = cules were bimolecular, [O?](k3[0-] 0.14. become ka"[O?]. However, plotsof I/# with Doz/.bor differ greatly a t small mole fractions of ozone with changes in t h e initial pressure of The rate of arrival of the chain carriers a t the pure ozone, thereby implying corresponding variations in the rate
+
+
+
+
+ +
+
constants.
(12) Lewis and von Elbe, THISJ O U R N A L , 117, 612 (1935)
Sept., 1935
1715
REACTION KINETICSOF DRYOZONEPHOTOLYSIS TABLE 111
Serial number
3-7 3-6 3-8 3-9 3-8
P
903
50: PopF/;/Poa
10-16
Av. obsd. value of 114
525
222
303
716
3.0
0.39
624
224
300
700
14.4
.47
530
212
318
795
3.3
.4 3
Xin mp
254-2211
EQX
Term I
Term I1
12
0.28
0.11
0 39
50
.28
.20
.&Y
13
.29
.12
.4L
64
.29
.23
.%j2
A(l14)
0. os
.10 530
212
16.8
705
318
1/+ calculated from Equation 111; a: = 1; p = 2;
3-3 3-5 3-4
Sn
Calcd. value of l/+
502
208
506
260
234
440
246
l/+ calculated from Equation 111;
= 1;
k5 k4
12.0
p
= 2.
’
2kz
= k3
7500; k7b = 0.16; A = 6
.27
2.1
480 01
..it?
.41
k5 k4
= 2; - = 2 ;
,154
x
A(l/+)
0.09
.I1
10-15
8
.24
,06
. 30
47
.26
.I:;
, ,‘;:j
0.0
2k = 7500; k’‘ = 0.013; A = 5 X ka
The “constant” A , depends among other things upon the temperature, the nature of the surface and the distribution of incident light flux over the surface. With our apparatus the latter varies widely with wave length. I t is approximately constant, however, st a given wave length and temperature, for Eo was diminished by stopping down the collimation lens; the slits and source were left unchanged. As k3S3 and k5Ss enter equation I11 as additive terms to the total pressure, term I of I11 increases with EOand kp,,. Also, that part of term I1 of I11 where k’ = 2.3 k = the absorption coeEcient of containing k8 in the numerator, briefly, (K3p,,P ozone, and d is the depth of the absorbing layer.14 k 2 S ~ ) , ’ ( k ~ p o ~ k&) increases with k,Sz for all Their rate of diffusion according to the kinetic values of k3$0,P,’kz$0, less than 1. (lVhen the theory of gases, is inversely proportional t o latter exceeds 1, k& is negligible for S, -+ 0 as 1/Dv-z 1,’Dg-z ... P+ 05; also ka/kz
