# Theoretical versus empirical equations

I'm familiar with the fact that theoretical formulae are based on already known theory and are very frequently simplified (some equations don't include interactions between molecules for example) while the purpose of empirical equations (like polynomial equations) is just to follow experimental measurements even if it doesn't make any chemical or physical sense.

Which of these yield more accurate results (compared to reality)? What are the upsides and downsides of each group? Which are more universal? Which would require less compound-specific data (constants) to use it?

Edit: Removed van der Waals equation as an example of theoretical equations since, as pointed out by others, it's actually an empirical equation.

• related question: chemistry.stackexchange.com/questions/342/… – Cohen_the_Librarian May 19 '15 at 16:00
• Note that the van der Waals equation requires two constants, in addition to the gas constant, that are unique to every gas and must be determined empirically. In general all theoretical models are attempts to generalize empirical models. – Ben Norris May 19 '15 at 16:10

## 1 Answer

As pointed out already, the van der Waals (vdW) equation is also an empirical equation. However, I think what you are saying is that the vdW equation is a physically motivated empirical equations where the empirical parameters in principle correspond to something "real" (e.g. molecular size and interaction strength) in contrast to a fit to an arbitrarily chosen fitting function such as a polynomial.

If you have lots of data points so that you can fit many parameters then a simple fit will be more accurate since it tends to have more fitting parameters than the physically motivated equation. However, the simple fit will likely only be accurate for interpolation, and is still likely to be comparatively less accurate for extrapolation.

• I would argue that e.g. a virial equation would be less physical, just because the vdW seems to (but in reality not) correspond something that is closer to a Chemist comprehension about small balls and big balls and their forces between them. From that point of view a viral equation is just a higher level of abstraction. – Greg May 20 '15 at 8:24
• Yes, my point was that vdW equation comes from physical background even if I put it in the wrong category. Thank you for your answer. – Chloris May 21 '15 at 14:55