Phosphorus is obtained primarily from ores containing calcium phosphate. If a particular ore contains 57.8% calcium phosphate, what minimum mass of the ore must be processed to obtain 1.00 kg of phosphorus?

Verified step by step guidance

1. Identify the chemical formula of calcium phosphate, which is Ca3(PO4)2.
2. Calculate the molar mass of calcium phosphate, Ca3(PO4)2, using the atomic masses of calcium (Ca), phosphorus (P), and oxygen (O).
3. Determine the mass percentage of phosphorus in calcium phosphate by calculating the total mass of phosphorus in one mole of Ca3(PO4)2 and dividing it by the molar mass of Ca3(PO4)2, then multiply by 100%.
4. Calculate the mass of calcium phosphate needed to obtain 1.00 kg of phosphorus by using the mass percentage of phosphorus in calcium phosphate.
5. Determine the minimum mass of the ore required by dividing the mass of calcium phosphate needed by the percentage of calcium phosphate in the ore (57.8%).

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate how much of a substance is needed or produced based on the amounts of other substances involved. In this question, stoichiometry will help determine the mass of ore required to yield a specific mass of phosphorus.

Calcium Phosphate Composition

Calcium phosphate is a chemical compound with the formula Ca3(PO4)2, which is a significant source of phosphorus. Understanding its composition is crucial for calculating the amount of phosphorus that can be extracted from a given mass of calcium phosphate. The percentage of calcium phosphate in the ore directly influences the calculations needed to find the minimum mass of ore required.

Mass Percent and Conversion

Mass percent is a way of expressing the concentration of a component in a mixture, calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100. In this context, knowing that the ore contains 57.8% calcium phosphate allows us to convert the desired mass of phosphorus into the total mass of ore needed, using the mass percent to find the relationship between the two.