Question

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 \(80.56 \mathrm{~g} .\) The volume was found by dropping the fork into a graduated cylinder initially containing \(10.0 \mathrm{~mL}\) of water. The volume after the fork was added was \(15.90 \mathrm{~mL}\). Calculate the density of the fork. If the density of pure silver at the same temperature is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), is the fork pure silver?

Short answer

The fork is not pure silver, as its density of 13.65 g/cm³ is higher than pure silver's 10.5 g/cm³.

Step-by-step solution

Calculate the Volume of the Fork

The volume of the fork can be calculated using the formula:\[ \text{Volume of fork} = \text{final volume} - \text{initial volume} \]In this scenario: \[ \text{Volume of fork} = 15.90 \text{ mL} - 10.00 \text{ mL} = 5.90 \text{ mL} \]Since 1 mL is equivalent to 1 cm³, the volume of the fork is \(5.90 \text{ cm}^3\).

Calculate the Density of the Fork

Density can be calculated using the formula: \[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]Using the mass and volume of the fork: \[ \text{Density} = \frac{80.56 \text{ g}}{5.90 \text{ cm}^3} = 13.65 \text{ g/cm}^3 \]This gives the density of the fork as \(13.65 \text{ g/cm}^3\).

Compare the Density of the Fork with Pure Silver

The density of pure silver is given as \(10.5 \text{ g/cm}^3\). \(13.65 \text{ g/cm}^3\) (calculated density of the fork) is significantly higher than \(10.5 \text{ g/cm}^3\). Therefore, the fork is not pure silver.

Key concepts

Pure Silver

Silver is a precious metal known for its lustrous appearance and remarkable conductivity. Pure silver is defined chemically as having a purity level of 99.9%. This level of purity ensures that the metal does not contain significant amounts of other elements that might alter its natural properties. In terms of physical characteristics, one of the key identifiers of pure silver is its density. Density is the mass per unit volume of a material. For pure silver, this density is around \(10.5 \, \text{g/cm}^3\), providing a reliable standard against which other silver-like materials can be measured. If an object claiming to be pure silver deviates from this density, it could contain impurities or be a different metal altogether. Thus, knowing the density of pure silver aids significantly in identifying the authenticity of silver items.

Volume Displacement Method

The volume displacement method is an easy and effective way to measure the volume of irregularly shaped objects. It comes handy when dealing with items that do not have straightforward geometrical shapes, like antique silverware or other household objects. Here's how it works:

• Start with a graduated cylinder filled with a known volume of water.
• Carefully submerge the object whose volume you wish to determine.
• Measure the new volume level of the water.

By simply recording the initial water volume and the final water volume, you can find the object's volume through simple subtraction. This method leverages the fact that the object will displace an amount of water equal to its own volume. For instance, if the initial water volume is \(10.0 \, \text{mL}\) and the final volume after submersion is \(15.90 \, \text{mL}\), the object's volume is \(15.90 - 10.00 = 5.90 \, \text{cm}^3\). This technique is not only precise but also efficient, making it a preferred choice in many scientific and educational applications.

Density Comparison

Once the density of an object is determined, comparing it to the density of pure substances becomes an important step to understand its purity or composition. To compare densities:

• Calculate the density of the object using the formula: \( \text{Density} = \frac{\text{mass}}{\text{volume}} \).
• Compare this calculated density to the known standard density.

For pure silver, the standard density is \(10.5 \, \text{g/cm}^3\). If you calculate an object’s density, like the fork in the example, and find it is \(13.65 \, \text{g/cm}^3\), you can determine that it does not match the density of pure silver. Since \(13.65 \, \text{g/cm}^3\) is significantly higher, the fork is not pure silver and likely contains denser impurities or is made of a different metal. This approach of density comparison provides a straightforward method to verify the purity or authenticity of a material.

Mass and Volume

Understanding both mass and volume is essential for performing a density calculation. Mass refers to the amount of matter in an object and is measured in grams (g). It tells us about the weightiness of the object in relation to a standard measurement scale. Volume, on the other hand, refers to the amount of space that an object occupies. It is typically measured in cubic centimeters (cm³) or milliliters (mL), and it shows how much space an object takes up regardless of its weight. To find density, you need both mass and volume. The formula is straightforward: \[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]For the fork example, the mass was already known: \(80.56 \, \text{g}\). Using the volume displacement method, we calculated the volume as \(5.90 \, \text{cm}^3\). Plug these values into the formula, and the resulting density tells us more about the composition of the fork. By systematically understanding mass and volume, you can tackle a wide array of scientific questions, particularly those involving the identification of materials.