# Archermedes was commissioned to determine if the crown given to the king was pure gold or not. If the crown had a mass of 882 grams and displaced 50.0 mL of water, was the crown pure gold?

Jul 23, 2017

Gold has a density, $\rho = 19.3 \cdot g \cdot m {L}^{-} 1 ,$ which is approx. 20 times as much water.
The density of the gold crown (given to the tyrant of Syracuse, not the king), was $\rho = \frac{882 \cdot g}{50 \cdot m L} \equiv 17.6 \cdot g \cdot m {L}^{-} 1$. So the goldsmith, whoever he was, has substituted a baser metal than gold, and was probably headed for the high jump, or at least no more royal commissions. Had the goldsmith been a chemist, he might have substituted tungsten, which, I recall, has almost the same density as gold. Of course, tungsten, was unknown in the 3rd century BC.
Archimedes discovered a way of measuring the VOLUME of the gold crown, by immersing it in water, and noting the fluid displacement. Given the mass, he was then able to get the density of the crown......$\rho = \text{Mass"/"Volume}$.