# What's the source of “2.303” in Van't Hoff equation?

I've seen a "2.303" term multiplied to $R$ in Van't Hoff equation several times.

Here is one example:

http://en.wikipedia.org/wiki/Van_%27t_Hoff_equation#Error_propagation

$$\Delta H^\circ=2.303R\frac{\log K_1-\log K_2}{\frac1{T_2}-\frac1{T_1}}$$

What is this number and where does it come from?

• – Loong Sep 6 '16 at 10:29

## 2 Answers

It is the multiplier used when converting the equation to use a base 10 log instead of a natural log.

It comes out to be the natural log of 10.

To elaborate on Burak's answer, which states that 2.303 is the multiplier, the correct converison is:

$$\ln(x) = 2.303\cdot\log_{10}(x)$$

Or as a divisor to convert the natural logarithm to a base 10 log: $$\log_{10}(x) = \frac{\ln(x)}{2.303}$$

• Welcome to Chemistry.SE! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. For more information in general have a look at the help center. I have reformatted and reworded your answer in order to reflect the current situation. Please have a look and edit as needed. – Martin - マーチン Sep 6 '16 at 10:41