Because the MKRH is analogous in concept to the MKT, it is helpful to provide a brief review of the MKT. The definition of
MKT provided above describes how the MKT concept is an attempt to provide a single temperature which, if the product were
stored at this constant temperature, would age the product to an equal degree to that obtained from storing the product at
a variable temperature over the same period of time. The MKT is derived directly from the Arrhenius equation that relates
reaction rate with temperature (Equation 1):
where k = the rate constant of the degradation reaction, A = the 'pre-exponential factor', Ea = activation energy (KJ·mol-1), R = universal gas constant = 8.314 J·K-1·mol-1, and T = temperature (K).
The MKT can be calculated as shown in Equation 2:
where MKT = mean kinetic temperature (K), T
1 to T
n = the variable temperature (K) measured at constant intervals, and n = the number of temperature measurements.
In the solid state, the rate of the degradation reaction has been shown to vary with temperature and relative humidity according
to the humidity-corrected Arrhenius equation in Equation 3 (8–12):
where B = the moisture-sensitivity term and RH = relative humidity (%).
It can be seen from the humidity-corrected Arrhenius equation that reaction rates increase exponentially with RH; the additional
B term is the magnitude of the effect of RH on the rate of degradation. The B term varies from product to product (as does
Ea) and can be typically determined from a short (e.g., 2 week) accelerated stability study as described by Waterman et al. (9–12). The B term is most simply expressed as the logarithm of the ratio of the degradation rates obtained at two different
relative humidity conditions (at the same temperature) divided by the difference in relative humidity as shown in Equation 4:
where k1 is the rate constant of reaction at relative humidity RH1, and k2 is the rate constant of reaction at relative humidity RH2 at the same temperature.
The B term is typically in the range of 0 to 0.09. A B term of 0 indicates that RH has no effect on reaction rate, whereas
a B term of 0.09 indicates a high dependency on RH: the degradation rate would double for every 8% increase in RH.
On the basis of the humidity-corrected Arrhenius equation, the isothermal MKRH can be calculated as shown in Equation 5:
where MKRHisothermal = mean kinetic relative humidity (%), RH
1 to RH
n = the variable relative humidity (%) measured at constant intervals, and n = the number of relative humidity measurements.
A complication that arises as a consequence of the humidity-corrected Arrhenius equation is that the established MKT equation
holds true only for samples held at constant relative humidity, and Equation 5 for MKRH holds true for samples held at constant temperature.