You would like to determine if a set of antique silverware is pure silver. The mass of a small fork was measured on a balance and found to be 80.56 g. The volume was found by dropping the fork into a graduated cylinder initially contain-ing 10.0 mL of water. The volume after the fork was added was 15.90 mL. Calculate the density of the fork. If the den-sity of pure silver at the same temperature is 10.5 g/cm3, is the fork pure silver?

Verified step by step guidance

1. Determine the volume of the fork by subtracting the initial volume of water from the final volume after the fork is added: \( \text{Volume of fork} = 15.90 \text{ mL} - 10.0 \text{ mL} \).
2. Calculate the density of the fork using the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Use the mass of the fork (80.56 g) and the volume you just calculated.
3. Compare the calculated density of the fork to the known density of pure silver, which is 10.5 g/cm^3.
4. If the calculated density is approximately equal to 10.5 g/cm^3, then the fork is likely pure silver. If not, it may be an alloy or a different material.
5. Consider any potential sources of error in the measurements that could affect the density calculation, such as measurement precision or temperature effects.

Key Concepts

Density

Density is defined as the mass of an object divided by its volume, typically expressed in grams per cubic centimeter (g/cm³). It is a physical property that helps identify substances, as different materials have characteristic densities. In this case, the density of the fork can be calculated using the measured mass and the change in water volume to determine its volume.

Volume Displacement

Volume displacement is a method used to measure the volume of an irregularly shaped object by observing the change in liquid level when the object is submerged. In this scenario, the initial water level in the graduated cylinder was 10.0 mL, and after adding the fork, it rose to 15.90 mL, indicating that the volume of the fork is the difference, which is 5.90 mL.

Comparison to Known Densities

To determine if the fork is pure silver, its calculated density must be compared to the known density of pure silver, which is 10.5 g/cm³. If the calculated density of the fork matches or is very close to this value, it suggests that the fork is likely made of pure silver. If the density differs significantly, it indicates that the fork may contain other materials or alloys.