usual steep rise a t the equivalence point. In this particular instance phenolphthalein turned red when the 79th drop was added; interpolation using the methods developed by the present author (2-4) locates the end point a t 78.66 f 0.25 drops = 3.54 f 0.01 ml. in a titration of 5 ml. of borax solution. To check this result the same borax solution and the NaOH-sorbitol reagent were titrated with a 0.1N solution of hydrochloric acid; the result of this indirect comparison was: 5 ml. of borax solution = 3.55 ml. of XaOHsorbitol reagcnt. For the determination of any unknown borate, the solution is first titrated with acid and then with the NaOH-sorbitol reagent. Location of End Point by Interpolation. The bases for the calculation of the exact end point have been given (2-4); the ratio of the potential steps, occurring before and after the maximum, is related to the ratio of the lack of reagent a t the point just before and the excess just after the maximum. A correction has to be applied in certain cases to the potential steps immediately observed; as this fact is generally neglected, it may be explained as follow. If in the titration of a weak acid with sodium hydroxide or a iveak base with hydrochloric acid, x denotes the quantity of reagent required to attain exact equivalence, v and v’ are the quantities added a t two points, and V and V’ are the total volumes of the titrated
In the case of a titration of borax, z
of salt is already present at the start of the determination; so x v and z v’ should be inserted in Equation 1 in place of v and 8’. When calculating
+
+
the consequent correction, any approximate value of z may be used, as log (z v’ e)/(z v e) does not differ markedlyfrom log (x v ‘ ) / ( z u ) , provided that the possible error, e, is small relative to z v ,
+ +
+ + +
+
+
Figure 1. Titration of a borax solution
solution a t the same points, then the change of pH (absolute value, without considering the sign) is 2--2,
ApH
log 5 ~
- v 1
x u’-prior to the v
It is evident that in a titration of bivalent iron with permanganate or dichromate the potential steps after the equivalence point have to be multiplied by 5 or 6, respectively, in order to compare them with the steps occurring in the redox buffer formed before the end point by divalent and trivalent iron and that, in such cases, the maximum variation of the potential may be observed just before the equivalence point is reached. Taking account of these facts, known in theory but generally neglected in practice, an exact determination of the equivalence point is obtained in these cases too.
equivalence point (1) and x - u logx-
V’ X - after the equivalence
v
point
LITERATURE CITED
(1) Hahn, F. L., Anal.
(2)
Only when log v’/v or log V’/V, respectively, is deducted from the observed changes in p H are the steps before and after the maximum comparable.
Chim. -4cta 4, 583-94 (1950). (2) Ibid., 11, 396-9 (1954). (3) Hahn, F. L., Mikrochim. Acta 1958, 111,395-401. (4) Hahn, F. L., 2. anal. Chem. 163, 169-81 (1958). SOUTHWESTRegional Meeting, ACS, San Antonio, Tex., December 1958.
Modification of an Ionization Chamber Gas-liquid Chromatography Instrument 8. Theodore Cole, Biology Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. chamber gas-liquid instrument described by Farquhar and associates [Xutrition Reus. 17, 1-30 (1959)] was constructed in this laboratory for lipide analysis of biological systems. A vapor jacket contained in an aluminum housing lined with 1/4-inch asbestos and separated from the housing by 4 inches of glass wool was used initially to heat the column. I t was quickly determined, however, by appropriate location of thwmocouples, that the solvents boiling above 100’ C.-Le., toluene, propylene glycol, and ethylene glycol-were refluxing, the vapor having condensed in the vapor jacket, before reaching the cold water condensing coil built into the device. A constant temperature could be maintained, and solvents could be kept in a vapor phase throughout the length of the column until they condensed on the appropriate coil, by providing additional heat to the column. This was done by tightly wrapping the tubing housing column with two 30N
IONIZATION
A chromatographic
inch, 4 5 0 - ~ a t t Serpentine , (Tital Manufacturing Co.) units equipped with asbestos leads. The voltage t o each unit was independently controlled by separate Variac transformers. The temperature of the upper half of the column was maintained as close as possible to the boiling point of the solvent and was monitored by thermocouples placed between the packed column and the ‘/*inch steel tubing in which it was housed. Such an arrangement provided for an equilibrium between the actual column temperature and the boiling point of the solvent in the pot below the detector. Fatty acid samples placed in the carrier gas stream as originally described did not vaporize quickly. Temperatures high enough above that of the column to cause rapid vaporization of injected sample were provided for by wrapping the extreme top of the inch steel tube that protruded from the aluminum housing, and into which the column was inserted for use. with
flexible, 115-watt heating tape (E. H. Sargent and Co., 4647 West Foster Ave., Chicago 30, Ill.) insulated with glass fiber. The voltage to this tape was controlled by a variable transformer. The shape of the elution peak is strongly influenced by the manner in which the sample is introduced. The syringe method of sample introduction, in that it brings the sample into the column in the most concentrated form in a “closed” system of gas flow, will give narrowest elution peaks from a well packed column. Introduction of sample into an "open" system, which involves lowering the inlet pressure and interruption of gas flow, inevitably leads to poor quantitative control over injection of microliter and smaller amounts of sample, and to introduction of varying quantities of air and constituent water vapor. Any water or other polar compound in the gas flow tends to adsorb on most packings used for fatty acid analysis and VOL 33, NO. 2, FEBRUARY 1961
3 17
+:SLICONE
RUBBER GAS
