If genes for different traits are on different chromosome pairs, they separate ______ of each other?

The appropriate word is "independently." If genes for different traits are on different chromosomes, they separate independently from each other. 

One of the key factors of inheritance discovered by Mendel (even though he didn't know about chromosomes) was that it's possible for traits to be transmitted independently of one another; for example, a tall brunette will not necessarily have tall brunette offspring, they might be tall, or brunette, or both, or neither. This indicated, at least in Mendel's time, that traits were distinct units of heredity and that there was no uniform "essence" of an organism, but rather that they were the composite representation of their many trait-units.

In more precise and modern terms, we can see how this quality is a result of how meiosis works. During meiosis, chromosomes pair up with their homologues (i.e. their matching partners) and swap some of their content. While it's entirely possible for non-homologous chromosomes to swap content, and this does happen, it is not favored because, more often than not, it leads to severe and irreparable genetic damage to the organism. Thus, under normal conditions, the swapping at chromosome A has nothing to do with the swapping at B, and neither has any influence over which allele will end up in which gamete.