K. J. Miller Bell Telephone Laboratories, Inc.
Murray Hill, New Jersey
1
I
Prediction of Maximum Reaction Yield Examples for elementary physical chemistry
General discussions of the prediction of reaction yield are given in most physical chemistry texts, but few specific elementary examples have been available. One excellent treatment of this subject can be found in Denbigh's "The Principles of Chemical Equilibrium."' The purpose of this paper is to present some examples of the calculation of the maximum theoretical yield of some reactions of industrial importance. Yield prediction is based on the determination of the equilibrium value of the product for a given reactant quantity, usually one mole.
for vapor deposition of thin films for use in electronic devices. I n such processes the advantageous factors of purity and control outweigh the relatively low yields obtained. I n addition, the yield may be increased by adjusting the total gas pressure or by inert gas dilution if there is an increase in the number of moles of products over those of the reactants.
Figure 2. 0 Ol 0 2 03 0 4 0 5 06 07 0 8 09 10 YIELD OF BORON, (9-ATOMS B i M O L E SXII,AT EOUliERlUM 4T 1000%
-
Figure 1. Yield or a function of total gor pressure for the reaction 2BXa(gl 3Hdg) 2B(sl+ 6HX(gl, where X = CI or Br.
+
Frequently a reaction of interest will have a large positive free energy change, AGO, and consequently a small value of the equilibrium constant, K,, can be expected. However, a significant reaction yield may still be achieved and this yield may be of practical importance, particularly when a steady-state flow system is used and reacted products are removed. This yield condition exists in the newly developing processes 1 DENBIGH, K., "The Principles of Chemical Equilibrium," Cambridge University Press, London, 1961, pp. 173, 174.
386
/
Journal o f Chemical Education
Br.
-
Yield as a function of total gar presure for the reactions Mi11 4HX(gl, where M = Si or Ge ond X = CI or
+ 2Hdgl
+
Reactions extensively used for thin film deposition from the gas phase are the hydrogen reduction reactions of the halides of boron, silicon, and germanium2:
+ 3 H 4 d - 2B(s) + 6IIX(g) M X k ) + 2Hdd M(s) + 4HX(d
2BXdg)
-
(1) (2)
where X = C1 or Br and M = Si or Ge. If a signifies the fraction of each mole of BX8 or MX, that reacts, then for reactions (1) and (2), a will also signify the yield of B or M. The mole fractions of the reacting gases at equilibrium are: a
MILLER, K. J., and GRIECO, M. J., J. Electroehem. Soc.,
1252 (1963).
110,
2 - 2a 5 + a
1-
where An is the number of moles of products less those of the reactants. From the foregoing relations and the known values of AGO for reactions (1) and ( 2 ) 8 the solution of the equation for ru may he obtained by solving for the mots
by the usual algebraic methods. Figures 1 and 2 show plots of yield as a function of total gas pressure for reactions (1) and (2). The calculated yield results given in Figures 1 and 2 are useful in comparing the relative reactivity of these bromides and chlorides. At P = 1 atmosohere and T = 1000°K, the approximate yield ratios bf bromides to chlorides are BBr3:BCla,6: 1; SiBr4:SiC14,2: 1; and GeBr4:GeC4, 1:1. These ratios make quite evident the greater reactivity of the bromides in comparison with the chlorides for these boron and silicon compounds and indicate no appreciable difference in yield between GeBr4 and GeC14. These results are not uuexpected for BC13and BBr3and for SiCIPand SiBr4when their bond euereies are considered.' but could not be predicted from The bond energy values for GeC14 and GeBr4. Figures 1 and 2 also show the appreciable increases in yield with dilution; if kinetic considerations could be ignored, this would indicate the desirability of gas dilution.
J A t 1000'K and 1 atmosphere, the values af AGO for reactions (1) and (2) for the various hdide reactants have been calculated from data in the literature to be: BCla, 24.8 k c d ; BBrs, 0.2 kcal; GeCh, -4.0 kcd; GeBrc -4.4 kcal; Sic4 18 kcal; and SiBr,, 11.5 kcal.
'Cottrell, T. L., "The Strengths of Chemicd Bonds," 2nd ed., Butterwarths Scientific Publications, London, 1958, pp. 273-87, gives bond energies for these compounds as follows: B-C1, 109 kcal; R B r , 90 kcal; Si-CI, 91 kcal; Si-Br, 74 kcal; Ge-Cl, 81 kcal; and Ge-Br, 66 kcd.
ZBXa
=
3 - 30 28"
ZHX =
ZYX.
(18)
6~ 5+ a
a
= -
=a, =
3+a
2 - 2a
3+a
ZHX =
(24
4a -3 f a
The equilibrium constants for reactions (1) and (2) respectively are K, =
Z-a XSX,'
2x11
(Ih)
Ks =
ZHX* ZMX,
(2h)
ZE,'
~t equilibrium the relations between AGO, K , and K , are: AG" = -RT In K, = -RT in K,PAn
(3)
Volume 43, Number 7, July 1966
/
387
