If we consider the mass of carbon atom is taken for the relative atomic mass unit as 16, in place of 112 , the mass of one mole of a substance will
Remain unchanged
Let's call the new unit amu'. Taking this to be the standard, the mass of 1 atom would be 1/2 times the old amu. Hence, 1 amu = 2 amu' but, the mass of 1 mole of carbon will be the mass of carbon in amu' * mass of amu' * avagadro number = 2 amu' * 1/2 (mass of amu in g) * N = the old mass itself!
So mass remains unchainged.