The karat scale used to describe gold alloys is based on mass percentages. (b) If an alloy is formed that is 50 mol% copper and 50 mol% gold, what is the karat number of the alloy? What is the color of this alloy?

검증된 단계별 안내

Determine the molar masses of copper (Cu) and gold (Au).

Calculate the mass percentages of copper and gold in the alloy using their molar masses and the given molar percentages (50 mol% Cu and 50 mol% Au).

Locate the mass percentages of copper and gold on the triangular diagram provided.

Identify the karat number of the alloy by comparing the mass percentage of gold to the karat scale on the diagram.

Determine the color of the alloy by finding the corresponding region on the diagram based on the mass percentages of copper and gold.

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주요 개념

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Karat Scale

The karat scale is a measure of the purity of gold alloys, where 24 karats represents pure gold. The karat number is calculated based on the mass percentage of gold in the alloy. For example, an 18-karat gold alloy contains 75% gold and 25% other metals, while a 14-karat alloy contains 58.3% gold. Understanding this scale is essential for determining the quality and value of gold jewelry.

Mole Fraction and Mass Percentage

Mole fraction is the ratio of the number of moles of a component to the total number of moles in a mixture, while mass percentage is the mass of a component divided by the total mass of the mixture, multiplied by 100. In the context of the question, the alloy is composed of 50 mol% copper and 50 mol% gold, which can be converted to mass percentages to determine the karat number. This conversion is crucial for accurate calculations.

Color of Gold Alloys

The color of gold alloys is influenced by the types and proportions of metals mixed with gold. Copper imparts a reddish hue, while silver contributes a yellowish tint. The triangular diagram illustrates how varying the mass percentages of gold, copper, and silver affects the resulting color of the alloy. For the given alloy of 50% gold and 50% copper, the color is expected to be reddish, indicating a significant copper content.