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I'm solving a quantitative problem involving the process of making oleum from pyrite.

The problem specifies that, at the end of the reaction, we find sulfur which does not come from the impurities present in pyrite.

Where is that sulfur coming from? Is it from the thermal decomposition of $\ce{FeS2}$?

$$\ce{FeS2 -> Fe + 2S}$$

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    $\begingroup$ What reaction? There is more than one, if I remember correctly. $\endgroup$ – Ivan Neretin Nov 29 '15 at 14:46
  • $\begingroup$ @Ivan Well, I didn't include the reactions used for obtaining sulfur trioxide (which is used for obtaining oleum) because the products ($SO_2,\ SO_3, \ H_{2}SO_4$) are unlikely to decompose into sulfur. $\endgroup$ – L3ul Nov 29 '15 at 15:31
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Guilin Hu, Kim Dam-Johansen, Stig Wedel, Jens Peter Hansen. Decomposition and oxidation of pyrite, Progress in Energy and Combustion Science, Volume 32, Issue 3, 2006, Pages 295-314, ISSN 0360-1285, http://dx.doi.org/10.1016/j.pecs.2005.11.004.

"In inert atmospheres, the transformation of pyrite proceeds through a multi-step process in the sequence of pyrite→pyrrhotite→troilite→iron. The whole process is determined by the temperature and the total sulfur gas pressure in the system."

Since there isn't any oxygen in an inert atmosphere, the sulfur in the pyrite must be converted to elemental sulfur to maintain charge neutrality and mass balance as you proposed.

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