Write an equation for the precipitation reaction that occurs when the solutions lithium nitrate and sodium sulfate are mixed.

Lithium nitrate and sodium sulfate are both soluble in water so in an aqueous solution the salts will dissociate into their component ions.  A double replacement reaction would normally then proceed.

LiNO3 --> Li+ + NO3-

Na2SO4 --> 2Na+ + SO42-

2LiNO3(aq) + Na2SO4(aq) --> Li2SO4(aq) + 2NaNO3(aq)

The problem is that the products of the above reaction are both soluble in water so no precipitate is formed.  All of the reactants and products above will exist as ions in solution so there will be no driving force to push the reaction in the forward direction.  See the derivation of the net ionic equation below.

2Li+ + 2NO3- + 2Na+ + SO42- --> 2Li+ + SO42- + 2Na+ + 2NO3-

There are no changes in the substances involved in the reaction so there is no net reaction.  This is not a precipitation reaction.