MICHAEL A. AURO’,
HOWARD M. HODGE, and NORMAN G. ROTH2
Chemical Corps, Fort Detrick, Frederick, Md.
Flasks
Oxygen Absorption Rates in Shaken
Only volumes of flask and of solution added are needed to predict conditions that will satisfy aeration requirements of certain microorganisms
VALUES
obtained in determinations of oxygen uptake rates ofsodium sulfite solutions in shake flasks are correlated to aeration requirements during the growth of certain microorganisms (2, 3 ) . T h e information presented here supports scale-up of data in shaken Erlenmeyer flasks of different sizes. T h e laboratory procedure was a modified version of the method of Bartholomew and others (7). T h e 0.5N sodium sulfite solution was prepared immediately prior to use; oxidation was catalyzed by 104M cupric sulfate. At the end of the test period, duplicate 5-ml. samples were withdrawn and placed in 50 ml. of 0.1N iodine solution. Excess iodine was back-titrated with 0 . 1 N sodium thiosulfate. From the amount of sodium thiosulfate solution required, the oxygen taken u p by the solution under test was calculated. T h e shaking machine was a reciprocating-type shaker, set to give a 3-inch amplitude and 96 cycles per minute. Oxygen uptake rates were determined when various amounts of sulfite solutions were shaken in Erlenmeyer flasks of different sizes. Replication of results was good. A good correlation is indicated between the oxygen uptake rates a t a fixed ratio of liquid to total flask volume, regardless of flask size. No statistically significant difference was found between oxygen uptake values a t constant liquid-flask volume ratios in the four sizes of flasks.
pressure of oxygen in the aerating gas, and Pz = partial pressure of dissolved oxygen in the solution being aerated. Values of PZfor absorption in sodium sulfite solutions are taken as zero because of the instantaneous interaction of oxygen with sulfite. As atmospheric air is used during aeration, PI = 0.21 atm., or 1GO mm. of mercury pressure. Either value may be used to convert absorption rate values to absorption coefficients, the choice depending on the units desired in the final coefficient.
Log A = m(VL)v, or (V L )
A = blOm
Logy = mx
(1 1
By taking antilogs of both sides of Equation 1, we get y = b lOmz
Logy = m log x
3.0
I
I
@a)
+ log 6
(3)
=
(3a)
bxm
T h e slopes obtained for the individual absorption rate lines are negative. Hence, it was necessary to plot negative slopes for the slope correlation, in order that they could be related (Figure 2). O n using the variables concerned Equation 3 becomes
(la)
I n terms of the variables used in this correlation, specifically for the plot of absorption rate, A , us. ml. of liquid in the flask, VL, a t constant flask volume, VF (see Figure 1 ) Equation 1 becomes:
v,
or by taking antilogs on both sides of the equation as: y
+ log b
(2)
If values of the slopes for the four Erlenmeyer flasks are plotted on log-log paper, they may be correlated with a straight line through them. T h e equation of a straight line on logarithmic paper is expressed as:
Derivation of Equations
T h e equation of a straight line on semilogarithmic paper is expressed as :
+ log 6
Log
- m = m, log V p + log 6 ,
(4)
and Equation 3a becomes: - m = bsVpma
or (4a)
m = -b,vFm’ I
I
Correlation of Data
Data obtained from oxygen absorption in Erlenmeyer flasks were plotted o n semilog paper (Figure 1). Straight lines were obtained for experiments with 250-, 500-, 1000-, and 2000-ml. flasks, when the volume of sulfite solution in the flask was plotted against the millimoles of oxygen absorbed per milliliter of solution. Values, in terms of a n absorption coefficient, KLA, may be obtained by dividing the rate values (millimoles of oxygen per liter per minute) by the oxygen transfer driving force (PI- PZ), where PI = partial Present address, n o w Chemical Co., Midland, Mich. * Present address, Whirlpool-Seeger Gorp., St. Joseph, Mich.
LOP A = m (VL) + L o p b
w
4 60
1I00
I
IW
I 200 VOLUME
Figure 1.
1 I I 2w 300 a5Ia 400 OF L l O U l D IN FLASK ml. (V,)
I
460
I 400
I a60
I
600
Relation of absorption rate to volume of liquid in flask VOL. 49, NO. 8
0
AUGUST 1957
1237
0 008
-
0 006
-
0005
-
with no great effect on the final values. However, in the examples given in this discussion, the equations were used as presented. Sample Calculation
0004-
What absorption rate may be expected when 200 ml. of 0.5N sodium sulfite are agitated in a 1000-ml. Erlenmeyer flask on a shaker producing 96 3-inch strokes per minute? Using Equation 7: VF = 1000
I
W 4
0003
9
INTERCEPT
I 657
SLOPE - 0 9403 m = I 6 5 7 VP-O 9 4
-
0 002 -
,
I
0 001 100
,
,
8
200
xx)
#
400
l
,
500
FLASK VOLUME
Figure 2.
l
,
700
l
, , , 1x4
,
,
l
,
,
,
,
~
2000
Log A
- ml (VF)
=
VL = 200 (_ - 1 657)(200) _Lioooo.~4
+
(7.9 X 10""'")(1000)
Relation of flask volume to slope Log A
=
- 331 __ 661
+ 0.079 -+ 0.167
Comparison of Calculated Absorption Rates with Those Obtained from Curves Flask Liquid A Curve, A Calcd., Difference, Volume, Volume, Mmoles 02/ Mmoles 02,' M1. M1. Liter/Min. Liter/Min. % 20 1.03 1 .oo - 3.0 250 0.1805 - 16.0 100 0.215 50 300
0.860 0.041
0.915 0.0551
loo0
100 350
1-01
Q.99 0.233
- 2.00
0.263 1.18 0.470
1.16 0.465
- 1.9 - 1.1
2000
200
500 a
++34Q 6.5
500
95% confidence limit.
Oxygen uptake = 0.04 i 0.06.
Intercept values were found to correlate best in a form similar to Equation 1 ; this is presented in Figure 3. I n terms of the variables we are dealing with, the intercept correlation may be written as: Log b
=
-11.5
+
~ , V F log b,
(5)
or (54
b = bi
slope correlations resulted in the following values: ' b, = 1.657 m, = -0.94 mi = 7.9 X 10-6
log bi = 0.167 bi = 1.468
When these values are incorporated into Equations 6 and 6a, the final relationship is:
Equations 5 and 4a are substituted in Equation 2, or 4a and 5a in 2a, and the complete correlation becomes :
7.9 X
+ 0.167
(7)
or ( E'L) V F
Log A
=
-bay,
+ mcVF + log b i (6)
A
bi 1OrntVP10-b8vFm"("L)VF
(6a)
A statistical fit for the intercept and
FLASK
Figure 3.
1 238
INDUSTRiAL AND
For simplicity, these equations may be rounded off to one decimal place
VOLUME mi
Relation of flask volume to intercept
ENGINEERING CHEMISTRY
=
0.501 - -0.255 Aonlcd = 0.556 mmole Oe/iitt:r/minutr A curve (Figure 1) = 0.590 mmole Os/fitci /minritc 0.590 - 0.556 yoerror = ____--o.590 x 100 -- 5.75% 0.246
Table 1.
+ 0.16'
I -
Conclusions Only the volumes of the Erlenmeyrr flask and of the solution to be added t o it are required to predict the absorption rate for surface aeration under the experimental conditions described. Table I shows the results of calculations performed on several flask volume-liquid volume ratios chosen a t random in an effort to check the vaiidity of Equation 7. These results correlate favorably with the observed laboratory data. Nomenclature A = absorption rate, mmoies of oxygen absorbed per liter per minute ( VL)I.F= volume of liquid being aerated, milliliters m, = slope of slope correlation line b , = intercept of slope correlation line m, = slope of intercept correlation line b t = intercept of intercept correlation line I/, = volume of Erlenmeyer flask, milliliters Acknowledgment
T h e authors wish to express their appreciation to Mary E. Ready for statistically analyzing and fitting curves to the laboratory data. Literatu re Cited (1) Bartholomew, W. H., Karow, E. O., Sfat, hl. R., Wilheim, R. H., IND. EKG.CHEM.42, 1801 (1950). ( 2 ) Roth, N. G.! Lively, D. H., Hodge, H. M.: J. Bactariol. 69, 455-9 (1955). ( 3 ) Smith, C. G., Johnson, M. J., Ibid., 68, 346-50 (1954). RECEIVED for review August 25, 1956 ACCEPTEDFebruary 7, 1957 Division of Agricultural and Food Chemistry, Symposium on Fermentation Process and Equipment Design, 130th Meeting, ACS, Atlantic City, N . J., September 1956.
