An organic food color is a complex organic dye with a broad-banded absorption spectrum. In the case of a Helium-Neon (He-Ne) laser at 632 nanometers (nm), the dye of choice is one with a spectrum with a reasonably strong absorption at the red 632 nm line; i.e., blue or green. The transmission of the beam through a volume of absorbing dye solution is governed by the Beer-Lambert law:

It = Io exp (-s C L) (1)

where It = transmitted intensity, Io = incident intensity, s = absorption cross section, C = dye concentration, and L = optical path length (i.e. distance laser beam passes through dye solution). Typically, Eq. (1) is rewritten as:

A = ln () = s C L (2)

where A = absorbance. Since there is a negligible absorption by water at 632 nm, Io can be taken to be the intensity of the laser beam exiting the reactor.

The oxidation reaction can be written as:

A + b B -----> products (3)

where A = dye, B = oxidant, and b = overall stoichiometric coefficient indicating the number of moles of B consumed for each mole of A oxidized. It is assumed that Eq. (3) probably represents an overall stoichiometry; i.e., the dye oxidation occurs via a mechanism of several elementary reactions. However, overall reaction kinetics can be determined (6).

The rate of reaction (- rA) can be written as:

- rA = - = k CAn CBm (4)

where k = global rate constant; CA and CB = concentrations of dye and oxidant, respectively (mole/cm3); n and m = overall reaction orders. If the reaction is performed whereby the concentration of oxidant is in considerable excess over that of the dye (i.e. CA << CB), then CB is effectively constant. Equation (4) can then be rewritten as:

- rA = - = k' CAn (5a)

where

k' = k CBm (5b)

Combining Eqs. (5a) and (2) results in the first working relation needed to model the experimental data:

- = k* An (6a)

where

k* = k' (s L)1-n (6b)

and is a constant for a given experiment with a specific amount of excess bleach. Taking the logarithm of Eq. (6a) yields:

ln(- ) = ln(k*) + n ln(A) (6c)

Using a differential approach, curves of A vs. time are generated from a signal traces. Slopes of these curves, representing the time rate of change (-dA/dt) are determined, and then plotted vs. absorbance A according to Eq. (6c). The "best fit" slope is the order n, with intercept giving k*.

Alternatively, using an integral approach, two cases can be derived from Eq. (6a) depending on the value of n. If n = 1, then Eq. (6a) integrates to:

ln () = k* t (7)

where Ao = the absorbance measured initially with water and dye but before the oxidant is added. If n not equal to 1, then Eq. (6a) integrates to:

A1-n = (n-1) k* t + Ao1-n (8)

Eqs. (5b) and (6b) are combined:

k* = k CBm (s L)1-n (9)

Absorbance data are correlated with either Eqs. (7) or (8) to determine the "best fit" reaction order n and rate constant k*.

Whether a differential or integral approach is taken, the series of k* values from runs with different volumes of excess bleach are then correlated with bleach concentrations using Eq. (9) to determine the "best fit" reaction order m. Taking the logarithm of Eq. (9) yields:

ln(k*) = ln[k (s L)1-n] + m ln(CB) (10)

A plot of k* vs. CB according to Eq. (10) should yield a slope of m and the rate constant k to within a constant (s L)1-n.

NOTE: You are limited to 1/2 of an optical table as a working space.

The suggested overall layout for this experiment is given in the figure. The major components include: plastic container, magnetic stirrer (with stirring bar), HeNe laser, photodiode detector, chopper, lock-in amplifier, and data computer.

Fogler, Elements of Chemical Reaction Engineering, Prentice-Hall.

Jenkins and White, Fundamentals of Optics, McGraw-Hill.

Dye Bleach

Buret Buret

Attenuator Transport

(if necessary) Reactor

Photo

Chopper Diode

Magnetic Stirrer