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My guess is that most of the gold in any US vaults are tungsten bars with a gold plating thick enough for an impression test to pass. Same density, same x-ray, same hardness. Impossible to tell without literally sawing it in half.
The molecular weight of gold is 196.96655
The molecular weight of Tungsten is 183.84
So no, gold is about 7% heavier.
The difference in density between gold and tungsten is quite small. Tungsten is 19.25 g/cm3, while gold is 19.3 g/cm3. The difference is about .25%, so it is not something you'd be able to eyeball/feel. You'd need to do an immersion to accurately measure the actual volume as well as the weight, but it can be done. The only materials denser than gold are Iridium, Osmium, Platinum, Plutonium, and Rhenium, so you'd need to be able to blend one of those in with the Tungsten to exactly match the density.
Mike