Chalcopyrite, the principal ore of copper \((\mathrm{Cu})\) contains 34.63 percent Cu by mass. How many grams of Cu can be obtained from \(5.11 \times 10^{3} \mathrm{~kg}\) of the ore?

Extracting copper from its ores is a vital industrial process, given copper's widespread use in electronics, construction, and many other industries. One of the primary copper ores is Chalcopyrite, a mineral with a high copper content. When extracting copper from Chalcopyrite, the first step is to determine the amount of copper present in the ore.

Understanding the percentage composition is essential before beginning the extraction process. The percentage tells us how much of the total mass of the ore is actually copper that can be extracted. For instance, if an ore contains 34.63% copper by mass, it means that for every 100 grams of this ore, there will be about 34.63 grams of pure copper. The calculation starts with this fundamental concept to determine the yield from a given mass of ore.

When dealing with chemistry problems, especially involving solid substances, we often transition between different units of mass. Converting kilograms to grams is one such instance, relevant to our copper ore problem.

To perform a mass conversion, we must recognize that 1 kilogram is equal to 1000 grams. Thus, when we want to convert 5.11 x 10³ kg of ore to grams, we multiply by 1000, resulting in 5.11 x 10⁶ grams. Mass conversion is crucial as it ensures consistency in the units throughout the calculations, which is a cornerstone of accurate stoichiometry and problem-solving in chemistry.

Stoichiometry is the backbone of chemical calculations, translating the quantitative relationships between reactants and products in a chemical reaction into practical numerical solutions. It's based on the conservation of mass and the principle of balanced equations.

In the context of our copper extraction scenario, stoichiometry allows us to calculate the actual mass of copper that can be extracted from a known mass of ore. By understanding the percentage of copper (converted to a decimal for mathematical convenience), we apply stoichiometric principles to determine how much copper corresponds to the total mass of the ore.

Solving chemistry problems effectively involves a series of logical steps, each building on the previous to reach a solution. To decipher our copper ore calculation, we began with converting percentage to decimal – a crucial move to align the percentage with other numerical values. The next stride was mass conversion, ensuring that all measurements are in the same unit.

Finally, we carried out a straightforward multiplication to obtain the mass of copper from the ore. Problem-solving in chemistry demands meticulousness and a clear understanding of concepts like stoichiometry. Additionally, it's always beneficial to double-check each step for calculation errors and to confirm that the final answer makes sense in the context of the problem.