a 50 g bracelet is suspected of being gold plated lead instead of pure gold.when it is dropped into a full glass of water,4cm of water overflows.is the bracelet pure gold?if not,what proportions of its mass is gold?determine also the amount of its materials are used:
using 4 cm^3
the density is ... 50g / 4 cm^3
... 12.5 g/cm^3
this is between lead (11.3 g/cm^3)
... and gold (19.3 g/cm^3)
gold plated lead is a good guess
G = fraction gold
19.3 G + 11.3 (1 - G) = 12.5
To determine whether the bracelet is pure gold or not, we can calculate its density. The density of an object can give us an indication of its material composition.
First, let's calculate the volume of water that overflows when the bracelet is submerged in a glass of water. The overflow represents the volume of the bracelet.
We know that 1 cm³ of water has a mass of 1 gram. Since 4 cm of water overflowed, the volume of the bracelet is 4 cm³.
Next, we'll use the given mass of the bracelet, which is 50 grams, to calculate its density. Density is calculated by dividing the mass of an object by its volume.
Density = Mass / Volume
Density = 50 g / 4 cm³
Density = 12.5 g/cm³
Now, let's compare this density to the densities of gold and lead. The density of pure gold is approximately 19.3 g/cm³, while the density of lead is about 11.3 g/cm³.
Since the density of the bracelet (12.5 g/cm³) is closer to that of lead than gold, it is likely that the bracelet is not pure gold. It is more likely to be gold plated lead.
To determine the proportions of gold in the bracelet, we can use the concept of relative density. The relative density of gold plated lead can be calculated by comparing its density to that of pure gold.
Relative Density = Density of the alloy / Density of pure gold
Relative Density = 12.5 g/cm³ / 19.3 g/cm³
Relative Density ≈ 0.648
This means that the bracelet is approximately 64.8% gold and 35.2% lead.
Finally, to determine the amount of each material used, we can calculate the actual mass of gold and lead in the bracelet. Since the bracelet has a total mass of 50 grams, we can multiply the total mass by the respective proportions:
Mass of gold = 50 g * 0.648 ≈ 32.4 g
Mass of lead = 50 g * (1 - 0.648) ≈ 17.6 g
Therefore, approximately 32.4 grams of gold and 17.6 grams of lead are used in the bracelet.