Lab safety - Long vs. Short Sleeves on Lab Coats
The short sleeve has no place in a chemistry lab. 

Considering the coats purpose as personal protective equipment (PPE) is to reduce or eliminate the potential or risk of exposure to materials then the long sleeve coat would be the correct PPE to wear in a chemistry laboratory along with extra PPE which should have been assessed prior to performing the procedure. 

Even in a microbiology or molecular biology lab, where a lot of the solutions might not seem harmful, the cellular material in suspension is classed as a bio hazard, which the long sleeve will provide better protection. 

Hazardous chemicals are still commonly used in these labs, too, and will most likely be present whether you using them or not. It's not just for chemical exposure either also for general protection.