Effect of Instrumental Parameters on Atomic Absorption Spectrometric Method. The most sensitive absorption wavelength for molybdenum is at 313.3 mp. This resonance line was located by scanning in this wavelength region and recording relative intensity versus wavelength. The signal is then maximized for the 313.3 mp line. The flame profile for molybdenum in both fuel rich and fuel lean conditions has been reported (17). Because of small profile it is necessary to use care in making burner adjustments needed to obtain the maximum absorption. Proper alignment of the flame was accomplished by careful adjustment of vertical and horizontal adjustments on the burner. Synthetic Mixtures. A number of solutions containing known amounts of phosphorus as phosphate and silicon as silicate were prepared. These solutions were analyzed by the general recommended procedure with both the ultraviolet spectrophotometric and atomic absorption spectrometric methods of quantitation being utilized. The results of these analyses are given in Tables I and 11. These data demonstrate satisfactory results for the separation and determination of phosphorus and silicon. The indirect ultraviolet spectrophotometric method is more suitable for determining less than 0.4 ppm of either silicon or phosphorus, whereas the atomic absorption spectrometric method is more applicable to the 0.4 to 1.2 ppm range for each element. Un(17) C. S. Rann and A. N. Harnbly, ANAL.CHEM., 37,879 (1965).
less a mechanical shaker was employed, difficulty was often encountered for the higher concentrations of phosphorus and silicon because of the formation of a very cloudy aqueous phase following the ether extraction. The main disadvantage of the atomic absorption spectrometric method is the additional time required to prepare calibration plots at the time of each analysis. Precision. An estimate of the precision of the indirect ultraviolet spectrophotometric and atomic absorption methods was obtained by analyzing seven solutions containing 0.4 ppm of phosphorus and 0.35 ppm of silicon. Five values obtained for the ultraviolet spectrophotometric determination of phosphorus gave a mean absorbance value of 0.770, a standard deviation of 0.005, and a relative standard deviation of 0.65%. Seven values obtained for the ultraviolet spectrophotometric determination of silicon gave a mean absorbance value of 0.694, a standard deviation of 0.009, and a relative standard deviation of 1.3%. When the atomic absorption spectrometric method was used, a relative standard deviation of 0.65% was obtained for the determination of phosphorus and a relative standard deviation of 1.45 % for the determination of silicon. RECEIVED for review September 25, 1967. Accepted November 1 , 1967. Presented at the 154th Meeting, ACS, Chicago, Ill., Sept. 11-14, 1967.
Height Equivalent to a Theoretical Plate of an Open Tubular Column Lined with a Porous Layer A Generalized Equation M. J. E. Golay The Perkin-Elmer Corporation, Norwalk, Conn. The increased importance of open tubular columns lined with a porous layer makes the development of a suitably complete expression for the RFV of such columns desirable. The new formula, which can be considered as a generalized expression for the HETP of open tubular columns, makes allowance for the tortuosity of the porous layer and the degree of its porosity. Possibilities for experimental verification are also discussed.
IN A FORMER publication ( I ) , a formula for the HETP of an open tubular column lined with a porous layer was developed which contained no term for the resistance to mass transfer in the liquid phase, then assumed to be negligible. The purpose of this report is to complete this formula with such a term, as well as to make allowance for the tortuosity of the porous layer and the degree of its porosity. The starting point of the derivation will be Formula 31b in an earlier treatment (2) which can be written as: h = - 2Do + U
1
1 + + l l k 2 rzu - + f - - k3 + k)' Do 6(1 + k)' F'K'
6k 24 (1
r2u (1) DL
(1) M. J. E. Golay, Nature, 199, 370 (1963). (2) M. J. E. Golay, "Gas Chromatography 1958," D. H. Desty, Ed., Butterworths, London, 1958, pp 36-55.
382
ANALYTICAL CHEMISTRY
where h = HETP Do and D L = diffusion coefficients of the particular component considered in the gas and liquid phases, respectively k = capacity ratio K = partition coefficient r = radius of open tubular column F = ratio of the liquid phase surface over the equivalent surface of a smooth bore column u = average gas velocity
For our purpose, Equation 1 will be rewritten: 2Do h = - + U
1
+ 6k + l l k 2 r2u 24(1 + k)' 0, -t-
kT -(
u
(2)
where T designates the diffusion time of the component considered in the oil film of a smooth bore column of thickness d f / F . The equivalence of Equations 1 and 2 can be shown as follows :
The capacity ratio can be written as [see Formula 77 in (2)]:
which has the time constant:
k = 2 -dJK
(3)
r
wherefrom : dj
=
rk 2K
and the diffusion time can be written:
dJ2 k2rZ T = -3F2Dr, 12FZK2D~ which, when substituted in Equation 2, gives Equation 1. T can be considered also as the diffusion time of an openended telegraph cable of total distance R and total capacitance C,the input admittance of which is obtained from the equivalent circuits:
A
m +
?/qqc
c/5
k,, inert =
arz
+ 2ar
raz
=
+
2a2
xrZ
linear terms only in al,and a2being retained here and in what follows.
c/s
For components which are retarded by the actual capacity ratio, k , we shall have:
I+---
-
The problem consists now in expressing T and k in terms of suitable physical parameters for substitution in Equation 2. It will be stipulated that the porous layer of thickness a r can be characterized by a tortuous path of length a l r , where a1 > a, and by an average free volume of thickness azr, where a2 < a. It will also be stipulated that a
