Solid gold has a greater density than liquid gold what must happen to the volume of a given mass of solid gold when it becomes a liquid

There's an inverse relationship between density and volume. The higher the density, the smaller the volume occupied because the particles are compact; the lower the density the higher the volume - molecules are further apart. Hence objects with higher densities tend to have small volume but mass doesn't change. Since solid gold has a greater density than liquid gold this means solid gold occupies a smaller volume than the same mass of solid gold. If solid gold changes to liquid, now the particles are further apart and so the volume increases.

It's not the same dearthe first one is in grams per mole while the other is not