Two methods have been proposed for the analysis of sulfur in impure samples of pyrite, FeS₂. Sulfur can be determined in a direct analysis by oxidizing it to SO₄ ^2– and precipitating it as BaSO4. An indirect analysis is also possible if the iron is precipitated as Fe(OH)₃ and isolated as Fe₂O₃. Which of these methods will provide a more sensitive determination for sulfur? What other factors should be considered in deciding between these methods?