Which action changes the identity of the substance referenced?
a. breaking an ice cube
b. running an electric current through copper
c. melting gold
d. corroding iron

Corroding iron.  The reason why iron corrodes is that it reacts with the oxygen in the air to create iron oxide which is what we call rust.  when iron turns to rust, the chemical identity of the iron changes.  
when you break ice, the ice is still ice.  that water did not change into something else.  when you run a current through copper, the electrons in the copper move due to the voltage but the copper is not changing.  After the circuit stops, the copper wires are still made out of copper (the copper did not undergo a chemical change).  When you melt gold, the gold is only going from solid form to liquid form.  The gold has not changed chemically, it just underwent a phase change.
I hope this helps.  Let me know if anything is unclear.