Final Answer:
16 karat gold contains 16/24 parts pure gold. To find the mass of pure gold in 8.11 kg, calculate (16/24) * 8.11 = 5.407 kg. Subtracting this from 8.11 kg yields 2.703 kg, indicating the impurities. Therefore, the mass of gold is 8.11 kg - 2.703 kg = 9.66 kg. Therefore the correct answer is option b.
Step-by-step explanation:
To find the mass of pure gold in 8.11 kilograms of 16 karat gold, first, understand that 16 karat gold is 16/24 parts pure gold. The formula to calculate the mass of pure gold is given by: Mass of gold = Total mass of gold alloy × (karat purity/24). Therefore, for 16 karat gold, the pure gold content is (16/24) × 8.11 kg = 5.407 kg. This represents the mass of pure gold within the 8.11 kilograms of the 16 karat gold. To find the total mass of gold present (including impurities), subtract the mass of the impurities from the total mass of the alloy: 8.11 kg - 5.407 kg = 2.703 kg. Thus, the mass of gold present in 8.11 kilograms of 16 karat gold is 9.66 kg.
In this scenario, the given 8.11 kilograms represents the total weight of the 16 karat gold, but not all of it is pure gold. Since 16 karat gold denotes that 16 out of 24 parts are gold, we calculate the pure gold content using the ratio of the karat purity (16/24) and the total weight. Multiplying these values yields the mass of pure gold in the given quantity. Subtracting this from the total weight of the alloy then gives the mass of impurities. This calculation indicates that 9.66 kilograms out of the 8.11 kilograms is the actual mass of gold present within the 16 karat gold alloy, while the remaining weight accounts for other metals or impurities.
Gold alloys of different purities contain varying amounts of pure gold, and understanding the karat system helps determine the actual mass of pure gold in a given quantity of an alloy, aiding in assessing its value or utility. Therefore the correct answer is option b.