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

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• FQVBSina
In summary, it is convenient to take the log of both sides of energy/temperature relationships given as exponential terms, and the conversion factor between natural log and log base 10 is approximately 2.3. This can be seen in the diffusion equation, where the book writes it as ##D(T)=D_0 \cdot e^{\frac{-Q}{2.3RT}}##. This is also mentioned in a book on page 228, where the equation is written as ## D(T)=D_0 \cdot 10^{\frac{-Q}{2.3RT}} ##.

#### 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

It would appear, when it has the ## 2.3 \approx \ln{10} ##, the equation is written as ## D(T)=D_o \cdot 10^{\frac{-Q}{2.3 RT}} ##. Your "links" might contain this info, but it is difficult to scroll through the pages of your "links".

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