can the chemical composition of a single mineral vary. explain your answer

An interesting question.  The short and simple answer
would appear to be "no" because a mineral is supposed to be a unique designation. 
However, minerals are made up of many atoms and even single element minerals like
gold,iron, or silver, may contain inclusions that with very sophisticated tools might
show up in chemical analysis.  So,in fact, minerals do vary in chemical composition. 
This fact is often used to determine the genesis and subsequent metamorphism of
minerals. The effect of different compositions is within very narrow ranges and usually
in very small amounts but make for some fascinating studies.