Who was the second person to organize the elements on the periodic table and what property did he use to re-organize them?

Dmitri Mendeleev

Explanation:

He was a Russian Scientist who decided to reorganize the periodic table after other notable scientists such as Antoine-Laurent Lavoisier had also tried to organize it based on the states of matter of the elements.

Mendeleev reorganized the period in the order of increasing atomic mass although there were some other modifications by modern scientists.