DETERMINATION OF THE SPECIFIC RATE CONSTANT FOR THE LOSS OF A YELLOW INTERMEDIATE DURING THE FADING OF ALIZARIN LAKE
Robert L. Feller, Ruth M. JohnstonFeller, & Catherine Bailie
2 FIRSTORDER RATE EQUATIONS
ANALYSIS OF THE DECLINE in the computed concentration of alizarin lake during exposure of these opaque mixtures of alizarin lake and titanium white revealed that, within the narrow zone in which fading took place, a constant fraction of the alizarin lake tended to be lost during any given period of exposure.
The loss of a fixed fraction of the material present at any point in time corresponds to rate behavior known as firstorder kinetics. This is expressed mathematically as
Fig. .

In the integrated form this becomes
Fig. .

In these equations, A represents the weightpercent concentration of alizarin at any time, t [alizarin + white + yellow (see below) = 100], dA/dt is the instantaneous change in concentration of A with time, and A0 the initial weight concentration of alizarin; InA is the logarithm of A to the base e.4
Because the intensity of illumination diminishes with the age of the xenon lamps, instead of time we used the product of intensity times time, or exposure, for t. Thus, instead of reporting the fraction of alizarin lake lost per hour, the rate, in a sense, is expressed in terms of the fraction lost per footcandle hour or, in our case, per kiloJoule/cm2. The irradiance was monitored at a wavelength of 420 nm.
As reported,2 the specific rate constant, k1, was found to be essentially constant throughout a range of initial concentrations of alizarin lake pigment of from 50 to 2.5% relative to the titanium white and a range of pigment volume concentration (PVC) of titanium white from 19 to 2.5%. This is indicated by the identical slopes of the plots of log A (equivalent to lnA/2.303) vs. exposure in Figure 1 regardless of initial concentration.
Fig. 1.
Semilog “firstorder” plot of the loss of concentration of alizarin lake formulated at three different initial concentrations, showing also the accompanying rise and fall of a yellow component. Exposure carried out in a xenonarc Fadeometer¯ monitored in terms of kJ/m2 at 420 nm.

