The excess reactant is the reactant in a chemical reaction with a greater amount than necessary to react completely with the limiting reactant. It is the reactant(s) that remain after a chemical reaction has reached equilibrium.
How to Identify the Excess Reactant
The excess reactant may be found using the balanced chemical equation for a reaction, which gives the mole ratio between reactants.
For example, if the balanced equation for a reaction is:
2 AgI + Na2S → Ag2S + 2 NaI
You can see from the balanced equation there is a 2:1 mole ratio between silver iodide and sodium sulfide. If you start a reaction with 1 mole of each substance, then silver iodide is the limiting reactant and sodium sulfide is the excess reactant. If you are given the mass of reactants, first convert them to moles and then compare their values to the mole ratio to identify the limiting and excess reactant. Note, if there are more than two reactants, one will be a limiting reactant and the others will be excess reactants.
Solubility and Excess Reactant
In an ideal world, you could simply use the reaction to identify the limiting and excess reactant. However, in the real world, solubility comes into play. If the reaction involves one or more reactants with low solubility in a solvent, there's a good chance this will affect the identities of the excess reactants. Technically, you'll want to write the reaction and base the equation on the projected amount of dissolved reactant.
Another consideration is an equilibrium where both the forward and backward reactions occur.