chemistry is so developed now that the big questions are specific to the different fields. the literature is evolving so fast, so much is being discovered by so many independent labs that "big questions" are really questions about finding efficient solutions to problems.
a few examples from different fields that come to mind:
>main group
preparation of 2D materials like black phosphorus
persistent tripet carbenes and congeners
catalysts that compete with transition metal catalysts
fundamentally new chemistries, recent examples include frustrated lewis pairs, sigma-holes, and just low valent main-group chemistry in general
>catalysis
nitrogen fixation
CO2 reduction
polymerization catalysis
depolymerization
>materials
self-assembly of molecular electronics, pretty far off it seems
earth abundant replacements for standard materials like tin-doped indium oxide, tellurides, etc.
self-healing materials, soft electronics
chemistry is all around us, none of it is hidden. Physics tends to deal with things on the extremes of reality, chemistry is more practical. I honestly think it's sad that both sides don't appreciate each other enough.
