Influence of Pressure Grddients on Resolution in Gas Chromatography Sra: The height equivalent to a theoretical plate is usually assumed to be given for a gas chromatographic column as follows (8): H=A+B/pv+Cv+Dp,
(1)
where p and o are the local values of pressure and velocity, respectively, and A, B, C, and D are molecular and column constants for a given system. The measured value of H, fi, is obtained by the equation H = L(r/f)2, where L is the column length, t the retention time, and T is the standard deviation in retention time, or one fourth the peak width. For a column without gradients H = I?. The presence of an inlet pressure, pi, different from the outlet pressure, p., alters this equation. The correct equation, relating column performance fi to the microscopic parameters, A, B, C, and D,will now be obtained. If we consider the migration of a zone along the column, the variane of the peak, u2 (where u is the standard deviation in distance) will equal the sum of contributions along the entire column. However, any value of u acquired locally within the column is amplified by the ratio p / p . where p is the local pressure. This is an effect due to the decompression and subsequent expansion of the carrier gas as one proceeds along the column. The solute sone expands along with the gas. Hence u2is obtained as
Q’
=
f WP/P.)*
(2)
integrated over the length of the column. Once u2 is obtained, T ) can be written as d/R%,’ where R is the ratio of zone to gas velocity and v. is the outlet velocity. The foregoing integral requires a knowledge of pressure and velocity values throughout the column. Such information is obtained from the theory of James and Martin (3). The above integral is evaluated using this information, and thence used to obtain T* and fi. Formulating the column length, as L = f d z and the retention time as t = f dz/Rv, yields the expression
This equation rather than Equation 1 should be used for 2. W e under ordinary operating conditions f l ( P ) and ft(P) lead to an 3 only a few per cent different from that predicted by other equations, Equation 4 is useful, both in giving a theoretical basis for preesure gradient effects and in properly accounting for these effects when the pressure ratio is large. Furthermore, it is suspected that some recently observed anomaliea (1, 4)-negative A valuwmay stem in part from the use of an incorrect equation. We are compdmg and examining experimental dah to obtain a comparison of A, B, C, and D values from Equations 1 and 4 and from an equation due to Littlewood (4). LITERATURE CITED
(1) Bohemen,
(3)
Substitution of the terms of Equation 1 for the local H in this expreasion and integration over the lfngth of the column results in an expression for the observed A.
-
3 (P* 1). p , p ’ 2 (P’- 1)’ P.
J., $wneU, J. E., “Gas Chromatography, D. H. Derrty, ed., p. 6, Butterworths, London, 1958. (2) Golay, M. J. E.,Zbkf.,pp. 53,65. (3) James, A. T., Martin, A. J. P., Biochem. J . 50, 679 (1952). (4) Littlewood, A. B., “Gaa Chromatograph ” D. H. Desty, ed., p. 35, Butterwortk, London, 1958.
GEOBOE H. STEWART S P ~ C E1,.BSEAOER J. CALVIN GIUDINGS Department of Chemistry University of Utah Salt Lake City, Utah RECEIVEDfor review July 6, 1959. Accepted Jul 22, 1959. Work supppre Atomic Energy Commeslon by the U. under contract No.AT( 11-1 )-748.
8.
Determination of Surface Area Using a Gas Chromatograph SIR: Recently, Nelsen and Eggertsen ( 1 ) reported a new technique for deter-
mining surface area, which is basically an application of gas chromatography. (Since the preparation of the present communication, it has come to our attention that additional confirmation of Nelsen and Eggertsen’s technique was reported at the ACS meeting in Boston, April 9, 1959, by C. F. Lee and F. H. Stross, Shell Development Co.) This technique has stimulated considcrrrble interest because of its simplicity, speed, and freedom from the maintenance problems of a vacuum system. We have investigated this method usiug
In the original method of Nelsen and a commercislly available gas chromab Eggertaen, mixtures of helium and nitrograph and have made a number of modigen are compoeited from separate fications that simplify the operating procedure and calculations. By using source8 of these gases. This requires making absolute flow rate measurements prepared mixtures of helium and nitrogen, using a conventional scheme for of the helium, nitrbgen, and total flow. achieving constant flow, and making a These authors reported that flow rates were somewhat variable and had to be calibration with each desorption, we checked frequently. In our work we achieve a number of advantages: no use compressed mixtures of helium and necessity for controlling or metering the nitrogen obtained from the Mathesor. helium and nitrogen separately, no Co., East Rutherford, N. J. A Matheson necessity for measuring absolute flow two-stage regulator fitted with a prerate, no necessity for normalizing decision needle control valve is used on sorption peak areas, and minimieation of errors due to occasional drifts o l ~ the cylinder mixtures and gives a relatively long-term constancy of flow. A served in instrument output.
