Question

You are asked by the King of Allegesia to determine if the crown he was given for his birthday is pure gold. The density of pure gold is 19.32 g/mL; the density of water is 0.998 g/mL at 20ºC. There is a container when filled to the mark contains 1900.0 mL. When the container is filled with water to the mark, it has a mass of 2499.5 g. The crown is placed in the container and filled to the mark with water and now weighs 15,113.3 g. The crown has a mass of 13,910.0 g. What is the density of the crown? Is the crown pure gold?

Answer 1

The density of the crown is 10,71 g/mL. Thus, the crown is not pure gold.

Step-by-step explanation:

As volume of container is 1900 the mass of water when filled to the mark is:

1900,0mL×
`(0,998 g)/(1mL)` = 1896,2 g of water

The mass of 2499,5 g is the mass of container with water. As the mass of water is 1896,2 g the mass of container is:

2499,5 g - 1896,2 g = 603,3 g -container-

When the crown is placed in the container and this is filled with water the mass of this water is:

15113,3 g - 13910,0 g - 603,3 g = 600 g of water

Total mass - crown - container

This 600,0 g occupy a volume of:

600,0 g×
`(1 mL)/(0,998)` = 601,2 mL

Thus, volume of the crown is:

1900,0 mL - 601,2 mL = 1298,8 mL

Total volume - Water

The density of the crown is:

`(13910,0 g)/(1298,8 mL)` = 10,71 g/mL

As density of the crown is different to density of pure gold, the crown is not made of pure gold.

I hope it helps!