Page 357 - Excel for Scientists and Engineers: Numerical Methods

334 EXCEL: NUMERICAL METHODS

4. Autocatalytic Reaction. The data in Table 14-4 describes the time course of
an autocatalytic reaction with two pathways: an uncatalyzed path (A -+ B )
B
and an autocatalytic path (A +B). [A], = 0.0200 mol L-'. The rate law
(the differential equation) is
4Alt/dt = d[B]t/dt= ko[A]t + kl[A]tCBlt
Use any method from Chapter 10 to simulate the [B] = F(t) data, then use
the Solver to obtain ko and kl.

Table 14-4. Rate data for an autocatalytic reaction.

5. van Deemter Equation. Gas chromatography is an analytical technique
that permits the separation and quantitation of complex mixtures. The
mixture flows through a chromatographic column in a stream of carrier gas
(usually helium), where the components separate and are detected. In the
analysis of a sample of gasoline, for example, the components are separated
based on their volatility, the lowest-boiling emerging from the separation
column first. The degree of separation can be treated mathematically in the
same way as for fractional distillation: a column can be considered to have a
number of theoretical plates, just as a distillation tower in a refinery has
actual "plates" for the separation of different petroleum products (naphtha,
gasoline, diesel fuel, etc.). For gas chromatography, separation efficiency is
usually expressed in terms of HETP (Height Equivalent to a Theoretical
Plate), the column length divided by the number of theoretical plates.
Separation efficiency is a function of the carrier gas flow rate v, as shown in
the following figure. There is an optimum flow rate that provides the