By SeanPublished On: December 8, 2022Last Updated: November 29, 2022
Pharmaceutical companies use stability studies to find the shelf life of their drug product and learn about its degradation pathways. However, many chemicals are stable under storage conditions. Here’s how we can use the Arrhenius equation to predict drug degradation rates using accelerated stability study data.
Table of Contents
Understanding the Arrhenius Equation
Long-Term vs. Accelerated Stability Data
Stability tests are an essential part of drug development, where possible degradation pathways and the shelf life of a drug product are studied. However, long-term studies can take several years since some drug ingredients are incredibly stable under normal storage conditions.
To shorten the development and estimate the shelf life of a drug, pharmaceutical companies can perform accelerated stability studies. Accelerated studies involve higher temperatures than the medicine would experience under normal storage and transport, producing valuable degradation data.
Using the Arrhenius equation, we can use this accelerated degradation rate and extrapolate it to estimate the degradation of a drug under normal conditions—without actually waiting for the medicine to degrade.
Forms of The Arrhenius Equation
We can measure a drug’s degradation rate using a number specific to a chemical: the rate constant (k). Drugs with a higher rate constant degrade faster (assuming everything else remains identical). You can read more about pharmacokinetics in our introductory pharmacology guide.
The rate constant is dependent on temperature, as seen from the Arrhenius equation:
Zero order: M time-1 First order: time-1 Second order: M-1 time-1
Rate constant (specific to the chemical and temperature)
Same as the corresponding rate constant (k)
Arrhenius constant (independent of temperature)
Joules per mole (J mol-1)
Activation energy (minimum energy requirement)
8.314 Joules per Kelvin per mole (J K-1 mol-1)
Ideal gas constant
We can rewrite the Arrhenius equation in different ways:
Calculating the Rate Constant for Unknown Temperature
The Arrhenius equation is useful to estimate rate constant data for temperatures not experimentally obtained. In accelerated stability studies, we use data measured at higher temperatures and extrapolate it back to find the rate constant at storage conditions.
For example, a drug requires freezing storage conditions (-20 °C/253 K). However, because it is so stable at these temperatures, we might have to wait years to get usable degradation data. To get around this, we can get experimental data at higher temperatures:
Rate Constant (hr-1)
This is the same data as the example above, which means we can use the same activation energy (Ea) and Arrhenius constant (A) values. To calculate the rate constant (k) at temperature 253 K, we substitute these known values into the Arrhenius equation:
This tells us that the rate constant at freezing (253 K) is 40 times smaller than the rate constant at room temperature (298 K)!
Moisture-Corrected Arrhenius Equation
As we extrapolate further away from experimental values, the accuracy of the Arrhenius estimate worsens. This is because drug molecules degrade through different pathways under different conditions, while this extrapolation assumes that the pathway remains the same, but at temperature-dependent rates.
Humidity plays a significant role in the stability of a drug product since water can hydrolyze molecules while providing a solvent that accelerates other degradation reactions. This poses a problem as the original Arrhenius equation doesn’t consider humidity. This leads to poor shelf-life estimates, which can have a negative impact on the drug product’s regulatory approval process.
Sean is a consultant for clients in the pharmaceutical industry and is an associate lecturer at La Trobe University, where unfortunate undergrads are subject to his ramblings on chemistry and pharmacology.