STABILITY GUIDANCE

The Arrhenius Equation of Svante Arrhenius (1903 Nobel Prize winner)

Common sense and chemical intuition suggest that the higher the temperature, the faster a given chemical reaction will proceed. Quantitatively this relationship between the rate are action proceeds and its temperature is determined by the Arrhenius Equation.At higher temperatures, the probability that two molecules will collide is higher. This higher collision rate results in a higher kinetic energy, which has an effect on the activation energy of the reaction. The activation energy is the amount of energy required to ensure that a reaction happens.

This calculator calculates the effect of temperature on reaction rates using the Arrhenius equation.

Where k is the rate coefficient, A is a constant, E_a is the activation energy, R is the universal gas constant, and T is the temperature (in degrees Kelvin).

R has the value of 8.314 x 10^-3 kJ mol^-1K^-1

Illustrative Data

To determine the incubation time necessary for stability claims using the Arrhenius equation

a) Q₁₀  = 2.0 (conservative; “Rule of Two”.  For every 10 degree increase in temperature the rate of degradation doubles)

b) Room temperature = 23C(Controlled  room temperature) RT is defined as 20 to 25C

c) Acceleration Time = Time at RT/Q₁₀^(T2-T1/10)

 

For T2= 45C, T1 = 23C and Q₁₀=2.0 and time at T1 = 12 months (365 Days)

T2-T1 = 22C

 

Acceleration Time =  12/2^22/10

          =  12/2^2.2

          = 12/4.6

          = 2.6 Months at 45C = 1 Year at 23C.

Time at Room Temperature (Years)	Time at 45C (Days)
1	79
2	158
3	237
4	316
5	395

If Q₁₀ = 4, then

Time at Room Temperature (Years)	Time at 45C (Days)
1	17
2	35
3	52
4	69
5	87