# What does the 2.3 constant in e^Q/2.3RT come from?

• I
FQVBSina
TL;DR Summary
Many activation energy/temperature dependance equations have the term e^Q/RT and often it is written as Q/(2.3RT). Where did this mysterious 2.3 come from?
Ok, I have actually found the answer from http://www.bristol.ac.uk/phys-pharm...ch/ugindex/m1_index/med_memb/file/Nernst1.htm.

Basically, a convenient way to analyze these equations is to take the log of both sides. Since e takes the natural log and the equations are usually in log base 10, the conversion factor between natural log and log10 is 2.303, simplified to 2.3. Since I didn't find an explicit question on this and someone else may have the same question, I will leave this post here if you don't mind.

Many energy/temperature relationships are given as an exponential term, such as the diffusion equation:

$$D(T) = D_0*e^{\frac {-Q_{ID}} {RT}}$$

Where D0 is the initial diffusivity material constant, QID is the activation energy, R is the gas constant, and T is temperature. And often right after this, the book would write it as:

$$D(T) = D_0*e^{\frac {-Q} {2.3RT}}$$

Where did this 2.3 come from?

Example: This book on page 228: https://books.google.com/books?id=gCcSBQAAQBAJ&lpg=PA228&ots=tvZtxC9VW5&dq=diffusivity Q/(2.3RT) where did 2.3 come from&pg=PA228#v=onepage&q=diffusivity Q/(2.3RT) where did 2.3 come from&f=false