An aqueous solution of a mixture of salts is suspected to have one or more of these cations: NH₄⁺, Ba^2+, and Fe²⁺. The addition of sodium chloride to the solution does not result in any precipitate. A white precipitate is formed when sodium sulfate is added to the solution. The precipitate is filtered off and sodium carbonate is added to the obtained filtrate. Addition of sodium carbonate to the filtrate results in the formation of a greenish-brown precipitate. Write net ionic equations for the two observed precipitation reactions.