Given the temperature, pressure and density of a simple hydrocarbon, how would one go about find its identity, by using equations, and not empirical data.

i doubt it could be done. especially if you consider mixtures.

 

you might get it for simple ones like methane ethane ethene and so on but beyond that your not going to have much luck.

It might be possible to use statistical mechanics to work it out....but I'd expect the equations to far to hard to work out.

First, you want to assume that you have a pure substance. You can use the ideal gas law (another assumption) to calculate the number of moles. Assume any volume you like, eg 1 L, since it will cancel out.

 

Now you can get the molecular weight. So long as it is small enough and you know that it's made of only C and H (which should be, since it says simple hydrocarbon) you can work out the chemical formula.