A crown is determine to weigh 2.65 kg. When this crown is submerged in a full basin of water, the overflow is found to be 145 mL. Is the crown pure gold or a gold-silver alloy? The density of silver is 10.5 g/mL and gold that of gold is 19.3 g/mL. Show work.
VolumeCrown=145ml
density crown=2650g/145ml=18.27g/ml
looks like someone slipped a little silver into it.
Same answer I gave you yesterday.
To determine if the crown is pure gold or a gold-silver alloy, we need to compare its density with the density values of gold and silver.
Let's begin by calculating the volume of the crown using the information given.
Given:
Weight of the crown = 2.65 kg
Density of water = 1 g/mL
Overflow volume of water = 145 mL
Using the density formula, we can calculate the volume of the crown:
Density = Mass / Volume
Volume = Mass / Density
Volume of the crown = 2.65 kg / 1 g/mL
Now, let's calculate the volume of water displaced by the crown:
Volume of water displaced = Overflow volume of water - Volume of the crown
Volume of water displaced = 145 mL - (2.65 kg / 1 g/mL)
Next, we'll determine the mass of the water displaced. Since the density of water is 1 g/mL, the mass of 145 mL of water is 145 g.
Now, we'll calculate the mass of the crown using the formula:
Mass = Volume x Density
Mass of the crown = Volume of the crown x Density of water
From the given information, we know that the density of silver is 10.5 g/mL and the density of gold is 19.3 g/mL.
If the mass of the crown is closer to the expected mass of a pure gold crown, then it is likely a pure gold crown. However, if it is closer to the expected mass of a gold-silver alloy, then it is likely an alloy.
To determine which one it is, we'll compare the calculated mass of the crown with the expected masses of both a pure gold crown and a gold-silver alloy crown.
Expected mass of a pure gold crown = Volume of the crown x Density of gold
Expected mass of a gold-silver alloy crown = Volume of the crown x (Mass fraction of gold x Density of gold + Mass fraction of silver x Density of silver)
Now, compare the calculated mass of the crown with the expected masses. If the calculated mass is closer to the expected mass of a pure gold crown, then the crown is likely pure gold. If it is closer to the expected mass of a gold-silver alloy crown, then it is likely an alloy.
By following these steps and performing the calculations, you can determine whether the crown is pure gold or a gold-silver alloy.