Plz Show Me How It Come About

write an ionic equatio in the reaction betwee CaCO3 & HNO3

CaCO3(s) + 2HNO3(aq) --> Ca(NO3)2(aq) + H2O(l) + CO2(g)

So, then putting in the aqueous ions:

CaCO3(s) + 2H+(aq) + 2NO3-(aq) --> Ca2+(aq) + 2NO3-(aq) + H2O(l) + CO2(g)

Cancelling the spectator ions:

CaCO3(s) + 2H+(aq) --> Ca2+(aq) + H2O(l) + CO2(g)