Question

An allegedly gold nugget is tested to determine its density. It is found to displace 19.3 \(\mathrm{mL}\) of water and has a mass of 371 \(\mathrm{g}\) . Could the nugget be made of gold?

Short answer

After calculating the density of the nugget (371 g / 19.3 mL = 19.22 g/mL) and comparing it to the density of pure gold (19.32 g/mL), the nugget could be made of gold, as its density is very close to that of gold.

Step-by-step solution

Calculate the Density of the Nugget

To find the density of the nugget, use the formula for density which is mass divided by volume. In this case, the mass is 371 grams and the volume is 19.3 mL.

Compare Calculated Density with Density of Gold

The density of pure gold is approximately 19.32 g/mL. Compare the density of the nugget calculated in Step 1 to the known density of gold to determine if the nugget could be made of gold.

Conclusion Based on Density Comparison

If the density of the nugget is close to 19.32 g/mL, it is possible that the nugget is gold. However, if the density is significantly different, the nugget might not be pure gold.

Key concepts

Chemical Property

A chemical property is a characteristic of a substance that is observed during a chemical reaction and produces a change in composition. For instance, the reactivity of a metal with acids or the ability to oxidize are both chemical properties. One particularly useful chemical property for identifying substances, or determining their purity, is density.
Density is defined as mass per unit volume. It helps to distinguish different materials which may look similar but have different compositions. In the context of our problem, density serves as a crucial identifier to determine whether a nugget is indeed gold, which is often verified in authenticity testing.

• Density is an intrinsic property.
• It helps in the identification of substances.
• It is crucial in determining the purity of metals.

Density of Gold

Gold is a dense metal with a standard density of approximately 19.32 g/mL at room temperature. This high density is one of the reasons gold has been valued over time; not only does it have aesthetic appeal, but its weightiness is a key indicator of its authenticity and value.
When determining whether a substance is gold, comparing its calculated density with that of pure gold can indicate its likelihood of being genuine. A density significantly lower than 19.32 g/mL suggests that the nugget could be a gold alloy or a different metal altogether, possibly with a gold coating.

• The density of gold: approximately 19.32 g/mL.
• Gold’s density is key for authenticity tests.
• Deviation from this density suggests a substance is not pure gold.

Volume Displacement Method

The volume displacement method is a practical approach to determine the volume of an irregularly shaped object, like a gold nugget. By submerging the object in water, it displaces a volume of water equal to its own volume. This displacement can be measured to calculate the object's volume easily.
In the exercise provided, the nugget displaced 19.3 mL of water, which is directly taken as its volume for the density calculation. This method is part of Archimedes' principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid it displaces.

• Volume displacement determines the volume of irregular objects.
• It is based on Archimedes' principle.
• The method is ideal for measuring the volume for density calculations.

Thus, to summarize, by using the volume displacement method, we've ascertained the volume of the nugget to be 19.3 mL. When coupled with its mass of 371 g, we can calculate its density and compare it against the known density of gold to ascertain its genuineness.