A Theoretical Evaluation of Gas Chromatographic Isotopic Exchange and Column Efficiency SIR: I n a previous paper ( 1 ) the study of isotopic exchange in gas chromatography (GC) and its application to the labeling of inorganic compounds was described. The procedure is based on labeling the stationary phase with a radioactive ion common to the metal compounds to be chromatographed, followed by GC isotopic exchange between the ion of metal compound and that sorbed on the stationary phase. In continution of this study, it was interesting to see whether the volume of the stationary phase necessary for obtaining a certain percentage of isotopic exchange could be predicted from theoretical evaluations, for given chromatographic conditions.
-
32.5un3
1
I
5
0
I
or
dx
Let:
- WX)
- = K A (bx'
dz
x = isotopic exchange percentage in the solute sample x' = isotopic exchange percentage in the labeled compound adsorbed on the stationary phase z = distance in the column (cm.) A = cross section of column (sq. cm.) u = carrier gas flow rate (ml./min.) K = exchange constant a = amount of solute sample (mole) n = number of exchangeable atoms in solute sample b = amount of labeled compound adsorbed on the st'ationary phase (mole) Considering an element of the column between z and z dz, the following isotopic exchange balance in a unit of time can be written:
I
I
I
I
I
45
40
where V = A 2 = the volume of the column Integrating Equation 5, we obtain wx = Ce
If a
= 0,
x
- KV -u
+ bx'
u
(6)
= zo,and
nuxo = C
+ bx'
(7)
Equation 6 can then be written as 0.26 0.24 0.22 0.20
_ -- -KAZ (bx' dx da una
0.18
- nax)
0.16
or
+ dz) - u n a ( z ) =
dx -
~ U Z Adz )
(2)
This balance expresses the increment in the isotopic exchange percentage of the solute sample, as a function of the gradient between the degree of labeling of the stationary phase and solute sample. If we denote the total length of the column by Z and the ratio z/Z = a, where 0 6 ~ ~ 6 1Equation , 2 can be written :
+
K(bz' -
I
15 20 25 30 35 Carrier gas flow rate (mllrnin)
Figure 1. Gas chromatography isotopic exchange as function of carrier gas flow rate and volume of stationary phase
THEORETICAL
unax ( z
I
IO
da
(1)
KV una
= - (bx'
- na)
2
s"
0.12
010 0.08
loo -
0.06
u)
e
325 cm3
-2a
0.04
a02
.Y c
1
50-
I
I
2
4
B
B
s z
1
1
I
I
I
I
I
1
. I
I 6 Vlu
I
I
8
1012
Figure 3. Gas chromatography isotopic exchange as function of V/u ratio Carrier gas Row rate [ml./min.)
x s A 15
1624
0
ANALYTICAL CHEMISTRY
I
A 2 5
0 10
0 30
0
W 0
20
35 40
column and the percentage of exchange a t the end of the column (a = 1) is to be known, Equation 9 becomes
-
026 024 a22 0.20
or
0.16 -
048
8"
0.12
EXPERIMENTAL
-
:v0.10
0.02
0
20 40 60 80 100 120 N m h r GIthwrrtkd plates
Figure 4. Gas chromatography isotopic exchange as function of number of theoretical plates Carrier gas flow rates same as in Figure 3
nux
In order to verify the validity of Equation 11, a series of experiments was carried out using various amounts of labeled stationary phase and different carrier gas flow rates. The experimental conditions were similar to those described in Reference 1. The stationary phase consisted of Sil-0-Cel insulating fire brick (JohnsManville) of -10+12 US mesh size, labelled with C1M by adding a dilute solution of HC1W to the solid, prior to its introduction into the column (I). The solute sample was ASCla (BDH). The column temperature was 60" C. and its volume was 13 and 32.5 ~ m in. the ~ different experiments. Nitrogen was used as the carrier gas a t flow rates of 5-40 ml./min. Other parameters were as following: a = 2.4 X lO-'mole b = 4 X 10-4mole n = 3 X' = 9.2%
=
(nux,- bx')e
- K_v a
+ bx'
(8)
or nux=nazoe
- !Ea
+
bx' (1
- e-
KV
7T
(9) For the case where an unlabeled solute (2, = 0) is int,roduced into the
were used to plot log bx'/(bx' - naz)as function of V / u (Figure 3) and of the number of theoretical plates (Figure 4). Figure 3 shows that the plot of log bx'/(bx' - 3ax) as a function of V / u ,for a given u, is a straight line, thus verifying Equation 11. This makes possible the computation of the exchange constant, K , for a specific temperature and a given carrier gas flow rate. Thus, by prior determination of K , the volume of chromatographic column necessary for obtaining a certain isotopic exchange percentage, a t a given carrier gas flow rate, can be computed. Figure 3 also shows that K increases with increasing u. It is interesting, however, to note that in the carrier gas flow rate range of 25 to 40 ml./minute, no dependence of K on the carrier gas flow rate was observed. Nor was any dependence on the carrier gas flow rate observed in the plot of log b x ' / ( b d 3ax) as function of the number of theoretical plates in the column (Figure 4). The plot is a straight line, the standard deviation of the data being i17%. ACKNOWLEDGMENT
The assistance and criticism of Dr. Yehiel Lehrer-Ylamed are gratefully acknowledged.
RESULTS
LITERATURE CITED
Figures 1 and 2 show the isotopic exchange and number of theoretical plates as functions of the carrier gas flow rate and the volume of the chromatographic column. The data obtained in the experiments described in Figure 1 and a few others,
( 1 ) Tadmor, J., ANAL. CHEM.36, 1565 (1964).
JACOBTADMOR
Israel Atomic Energy Commission Soreq Nuclear Research Center Yavne, Israel
VOL 38, NO. 11, OCTOBER 1966
1625
