Sounds like a bad catalytic converter usually that’s what rotten egg smell means but wait for other opinions before you go buy one there very expensive.
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Just to confirmed, I have my car check out at the dealer and the mechanic told me due to certain brand of gasoline have more sulfur. That will create the foul smell and it's normal under hard acceleration.
The smell you are smelling is hydrogen sulfide (H2S). It results from using fuel with high sulfur content. (Much of the fuel sold in the US contains a LOT of sulfur -- much more than is legal in Europe, for example, though the Govt. has mandated a reduction to Euro sulfur levels in Diesel fuel over the next several years). You can sometimes reduce or eliminate this problem by changing brands. That is often not a permanent cure since refineries usually buy from a variety of suppliers and the amount of sulfur in any one brand varies as a result.