A supposedly gold nugget displaces 19.3 mL of water and has a mass of 371 g. Could the nugget be made of gold?

검증된 단계별 안내

Determine the density of the nugget using the formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Substitute the given mass (371 g) and volume (19.3 mL) into the density formula.

Calculate the density of the nugget.

Compare the calculated density with the known density of gold, which is approximately 19.32 g/mL.

Conclude whether the nugget could be made of gold based on the comparison of densities.

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주요 개념

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Density

Density is defined as mass per unit volume and is a key property of materials. It is calculated using the formula density = mass/volume. For gold, the density is approximately 19.32 g/mL. By comparing the calculated density of the nugget with that of gold, we can determine if the nugget could be made of gold.

Displacement Method

The displacement method is a technique used to measure the volume of an irregularly shaped object by submerging it in water. The volume of water displaced by the object is equal to the volume of the object itself. In this case, the nugget displaces 19.3 mL of water, which provides the necessary volume measurement to calculate its density.

Mass and Volume Relationship

The relationship between mass and volume is fundamental in determining the identity of a substance. By knowing both the mass (371 g) and the volume (19.3 mL) of the nugget, we can calculate its density. If the calculated density matches that of gold, we can conclude that the nugget could indeed be made of gold.