We consider the effects of power law scaling in the 1999--2000 Arctic lower stratospheric vortex from the point of view of the law of mass action and its application to the chemical kinetics of ozone loss embedded in a turbulent, macroscopic, fractal medium. The ER-2 observations of ClO obey power law scaling; the exponent varies with time in a manner shown to be consistent with the scaling of NOy and O3, via the influences of polar stratospheric clouds and actinic solar radiation. While the microscopic rate coefficient for ClO three-body recombination to the dimer applies as measured to three-dimensional volumes in which the sole transport mechanism is molecular diffusion, this cannot be true in the 2.56-dimensional space in which macroscopically fluctuating ClO reacts in the lower stratosphere. We show that the rate of loss of ozone via the ClO dimer mechanism is proportional to 2.20 in late January/early February and to 2.55 in March. Chemical ozone loss had already occurred by the date of the first flight, 20000120.