The limiting factor is the solubility of PbS in an increasing concentration of HNO3, not the the solubility of H2S in H2o.
In other words, given high enough concentrations of HNO3, the PbS would redissolve in the HNO3, yes. THAT is when you have reached equilibrium. Until
then, you start accumulating lots of PbS. PbAc2 paper is used for H2S detection for that very reason, and HAc is a much stronger acid than H2S.
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