What happens if you call the free function for a pointer that is equal to nullptr?

Nothing will happen. The C standard specifies that calling free with a nullptr argument has no effect.

C Standard, section 7.22.3.3:

The free function causes the space pointed to by ptr to be deallocated, that is, made available for further allocation. If ptr is a null pointer, no action occurs.

C++ Standard, section 21.6.7.3 (for std::free in <cstdlib>):

If ptr is a null pointer, the function does nothing.