Can someone help me with a precipitation reaction?
You do well to ask. This is actually a good test for nitrate, but the chemistry is very complicated. Nitrate is reduced to NO, nitrogen monoxide, which forms a complex with Fe(II), and this complex is responsible for the brown colour. Actually, this reaction is an example of a “colour test”, not a precipitation, since everything remains in solution. Chemical equations: NO3-+ H2SO4 = NO2+ + H3O+ + 2HSO4- (sulphuric acid reacts with nitrate to make the NO2+ (nitronium) cation; this reaction uses the strongly acidic and dehydrating properties of sulphuric acid) NO2+ + 3 Fe2+ + 2H+ = NO + 3Fe3+ + H2O (nitrogen reduced from +5 to +2; iron oxidised from +2 to +3) Fe2+ + NO = Fe(NO)2+ (formation of the brown ring complex) Every problem in science should be made as simple as possible, and no simpler (Einstein, attrib.) So please forgive me if I have told you more than you wanted to know.
