A 50.g bracelet is suspected pf being gold plated lead instead of pure gold. It was dropped into a full to the rim glass of water and 4cm to the third power overflowed. Is the the bracelet pure gold. Explain. (Density of gold=19 g/cm to the third power and lead=11 g/cm to the third power)
The volume of the bracelet is the amount that overflowed: 4.0 cm^3.
The density of the bracelet is 50/4 = 12.5 g/cm^3. What can you conclude from that?
To determine whether the bracelet is made of pure gold or gold-plated lead, we can use the concept of density. Density is defined as mass divided by volume. If we compare the density of the bracelet with the density of gold and lead, we can determine the material that the bracelet is made of.
Here's how we can proceed:
Step 1: Calculate the volume of the water that overflowed:
The volume of water that overflowed from the glass is 4 cm^3.
Step 2: Calculate the density of the water:
Water has a density of 1 g/cm^3.
Step 3: Calculate the mass of the water that overflowed:
Since the density of water is 1 g/cm^3 and the volume is 4 cm^3, the mass of the water that overflowed is 4 g.
Step 4: Calculate the mass of the bracelet:
Given that the bracelet caused 4 cm^3 of water to overflow, we can assume that the volume of the bracelet is 4 cm^3.
Step 5: Check the density of the bracelet:
Calculate the density of the bracelet by dividing its mass by its volume. The density formula is density = mass/volume.
Density of gold-plated lead = mass of the bracelet (50 g) / volume of the bracelet (4 cm^3).
Density of gold-plated lead = 50 g / 4 cm^3 = 12.5 g/cm^3.
Step 6: Compare the density:
Compare the density of the bracelet (12.5 g/cm^3) with the densities of gold (19 g/cm^3) and lead (11 g/cm^3).
If the density of the bracelet is closer to the density of gold (19 g/cm^3), then it is likely to be pure gold. If the density is closer to the density of lead (11 g/cm^3), then it is likely to be gold-plated lead.
In this case, since the density of the bracelet (12.5 g/cm^3) is closer to the density of lead (11 g/cm^3) than gold (19 g/cm^3), it suggests that the bracelet is gold-plated lead rather than pure gold.