Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 90

Chapter 1, Problem 90

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry. (a) Consider a piece of gold jewelry that weighs 9.85 g and has a volume of 0.675 cm3. The jewelry contains only gold and silver, which have densities of 19.3 and 10.5 g/cm³, respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry. (b) The relative amount of gold in an alloy is commonly expressed in units of carats. Pure gold is 24 carat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is 50% gold is 12 carat. State the purity of the gold jewelry in carats.

Verified step by step guidance

Identify the given percentage of gold in the alloy.

Understand that pure gold is 24 carats, which corresponds to 100% gold.

Use the relationship: \( \text{Carats} = \left( \frac{\text{Percentage of gold}}{100} \right) \times 24 \).

Substitute the given percentage of gold into the formula.

Calculate the carats to determine the purity of the gold jewelry.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Alloy Composition

An alloy is a mixture of two or more metals, where the properties of the resulting material differ from those of the individual components. In jewelry, gold is often alloyed with metals like copper or silver to enhance its hardness and durability. The composition of an alloy is crucial for determining its physical properties and applications.

Carat System

The carat system is a unit of measurement used to express the purity of gold. Pure gold is defined as 24 carats, meaning it contains 100% gold. The carat value decreases as the proportion of gold in the alloy decreases, allowing for a straightforward way to communicate the quality of gold in jewelry.

Percentage Calculation

Understanding percentage calculations is essential for determining the carat value of gold alloys. The percentage of gold in an alloy can be converted to carats by using the formula: Carats = (Percentage of Gold / 100) * 24. This relationship allows jewelers and consumers to assess the quality and value of gold jewelry based on its gold content.

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