Accelerated Stability Calculator

Formula

The formula to calculate the Shelf Life is:

\[ \text{Shelf Life} = \frac{e^{\left(\frac{E_a}{R \cdot T}\right)}}{k} \]

Where:

\(\text{Shelf Life}\) is the shelf life of the product
\(k\) is the Arrhenius rate constant
\(E_a\) is the activation energy in J/mol
\(T\) is the temperature in Kelvin
\(R\) is the universal gas constant (8.314 J/(mol*K))

What is Accelerated Stability?

Accelerated stability testing is a method used to estimate the shelf life of a product by storing it at elevated temperatures. The increased temperature accelerates the rate of chemical degradation or physical changes, allowing predictions to be made about the product's shelf life under normal storage conditions. This method is widely used in the pharmaceutical and food industries to ensure product quality and safety.

Example Calculations

Example 1:

Arrhenius Rate Constant (k) = 0.1
Activation Energy (Ea) = 50000 J/mol
Temperature (T) = 298 K

Using the formula:

\[ \text{Shelf Life} = \frac{e^{\left(\frac{50000}{8.314 \cdot 298}\right)}}{0.1} \approx 5.81 \times 10^{9} \]

The Shelf Life is approximately \(1.66 \times 10^{8}\) units of time.

Example 2:

Arrhenius Rate Constant (k) = 0.05
Activation Energy (Ea) = 60000 J/mol
Temperature (T) = 310 K

Using the formula:

\[ \text{Shelf Life} = \frac{e^{\left(\frac{60000}{8.314 \cdot 310}\right)}}{0.05} \approx 2.58 \times 10^{11} \]

The Shelf Life is approximately \(2.58 \times 10^{11}\) units of time.