v~
-
-
I 51
100 Kn
100 Kfl
I
100 K n
100 Kn
71
I
I
L -,----J
I Figure 2. Electronic diagram far assembling the device.
OSC 4 OSC 1
OSC 5 OSC 2
OSC 3
OSC 6
Figure 3. Oscillograms produced by device for various flrst-arder reaction considerations,
Volume 61
Number 9
September 1984
809
integrators (OAl and OA3) and the other two as subtractors (OA2 and OA4).The voltages a t the integrators outputs are proportional to the concentrations of the reactant and of the product. The values of the voltages in their inputs are proportional to the net rate with which the concentrations of the reactant and of the product vary. Finally, the voltages in the inputs (+) of the subtractors are proportional to the direct and ~ k ~ are ) inverse rate reactions. The rate constants ( k and represented by two potentiometers. Figure 2 shows the electronic configuration of the device (5). Switches S are used for switching on the device (position 2). When these switches are in position 1, the voltages which represent the initial values of the concentrations of the corresponding chemical compounds can be selected by using the potentiometers P. Results
The oscillograms in Figure 3 show some of the recordings ohtained with this small electronic device. OSC 1and OSC 2 show how the concentrations of the reactant and the product, in equilibrium, are independent of one another. OSC 3 and OSC 4 show how the concentrations of the reactant and the product change in the case where the rate constants are equal
810
Journal of Chemical Education
and where the rate constant of the reactant is much greater than that of the product, respectively. In this last case, the reaction is almost complete. OSC 5 and OSC 6 show that the eauilibrium is reached when the rates ot'the forward and rev'& reactions become eounl. This noint is nearer the initial value of that reactant whose rate constant is smaller. OSC 7 shows that when the reaction reaches the equilibrium, its net rate, V = V A- VB,is equal to zero. OSC 8 and OSC 9, obtained with the oscilloscope in the XY mode, show the recordings of V Aversus [A]and V Bversus [B], respectively. Both show that when the equilibrium is reached V A= VB.By modulating the Z input of the oscilloscope with sharp pulses of known frequencies, it can be observed that when the reaction gets nearer the equilibrium, it progresses more slowly. Literature Cited (1)Braven, J.,Yeata.R. and M a u d e , E., Simulation,26,139 (1976). (2) Wunderlich, F.J. and Pesstrel, M., Am. J Phys., 46,189(1978). (3) Vega. J. M., PeSa,J.J.,Rmsell, M. A,, Galuez, M. andMahedero, 8.. Am. J Phya.,49, d m ,,om, -"" \."".,. (4)Shah, S. N..Simulofion, 29.88 (1977). (5) Millman.J. and Halkias, C. C.. '"IntegratedEloetmnier:h a l o g and Digital Circuit. and Systems," McCraw-Hill, New York. 1972,p. 545.
