Question

A supposedly gold nugget displaces \(19.3 \mathrm{~mL}\) of water and has a mass of 371 g. Could the nugget be made of gold?

Short answer

The density of the nugget is \( \frac{371 g}{19.3 mL} = 19.22 g/mL \). Since this is very close to the density of pure gold (19.32 g/mL), the nugget could be made of gold.

Step-by-step solution

Calculate the Density of the Nugget

Determine the nugget's density by using the formula for density which is density \( = \frac{mass}{volume} \). Using the given mass of 371 g and the volume of 19.3 mL the calculation will be \( density = \frac{371 g}{19.3 mL} \).

Compare with the Density of Pure Gold

Find the standard density of pure gold, which is approximately 19.32 g/mL. Compare the calculated density of the nugget with this value to ascertain if they match.

Determine the Composition of the Nugget

If the density of the nugget is close to 19.32 g/mL, it suggests that the nugget could be made of gold. A significant difference would imply that the nugget is not pure gold.

Key concepts

Understanding Chemical Density

Chemical density is a fundamental concept in chemistry that describes how much mass of a substance is contained in a given volume. It is an essential property that can distinguish between substances and serves as a valuable tool for identifying materials.

How It Works

At the microscopic level, density can be thought of as how closely packed the atoms or molecules of a substance are. For example, in metals, atoms are typically closely packed together, which results in higher densities. The importance of understanding the chemical density lies in its wide range of applications, from material science to everyday uses such as cooking, where density can affect how certain ingredients behave when mixed.

Conducting a Gold Purity Test

Gold purity tests are crucial in assessing the value and authenticity of gold items. One of the traditional methods for testing gold purity includes density measurement.

Practical Methodology

Testing the purity of gold through density involves a few steps. The object's mass is measured on a scale, and then it is submerged in water to measure the volume of water displaced. The density is calculated and compared against the density of pure gold (approximately 19.32 g/mL). If they match, the gold is likely pure. Deviations suggest the presence of other metals. This non-destructive test is particularly favored in the jewelry industry, where the integrity of the gold pieces must be maintained.

Applying the Density Formula

The density formula, given by the equation \( density = \frac{mass}{volume} \) is a simple yet powerful tool in calculating the density of a material. The formula allows for the determination of whether an object might be made of a specific material based on its density.

Use in Real-World Applications

Suppose you have a mystery nugget as described in our exercise. By measuring how much water the nugget displaces, you determine its volume. Weighing the nugget gives its mass. Applying the density formula, if the result is close to that of pure gold's density, the nugget may very well be genuine. This formula is pivotal in fields like material identification, science education, and manufacturing.