Do chemists count atoms and molecules?

Of course, that would be a LOT of fun! We'd count atoms/molecules all day, losing track of time (and them), and having to start over a few thousand times!

No, I'm kidding. We let detector technology do that for us!

For example, a Faraday cup is one possible detector that can be placed at the end of a mass spectrometer to count charged particles (such as ions) that collide with it.

The basic process then is:

1. Load the sample.
2. Hit it with an ionization source. Some examples are electron beams, ESI, or MALDI. This has to occur, for the Faraday cup to be able to count ions.
   
   (depicted is a simplified MALDI setup)
3. Make it go through some analysis process. Fragmentation, perhaps, like in all mass spectrometry? Maybe you'll have a filtering process to choose the kinds of ions you want.
   
   (depicted is a quadrupole filter)
4. Send the ions at the detector to generate a count signal.
5. Amplify the signal if necessary (such as some sort of operational amplifier), and then convert it into a spectrum able to be read by people. This converter is called a transducer.

(In fact, it's common in mass spectroscopy to have a detector count ions, send the signal to a transducer, which returns a mass spectrum of ion abundances.)