Phosphorus is obtained primarily from ores containing calcium phosphate. If a particular ore contains 35.1% calcium phosphate, what minimum mass of the ore must be processed to obtain 4.13 kg of phosphorus?

First, we determine the mass of calcium phosphate that is required. This is obtained by calculating the mass percentage of phosphorus in calcium phosphate, Ca₃ (PO₄) ₂

% Phosphorus = Mass of P x 100 / total mass

% Phosphorus = (31 * 2 * 100) / (310)

% P = 20%

The amount of calcium phosphate needed will be:

4.13 / 0.2 = 20.65 kg

Now, the ore has 35.1% calcium phosphate, so:

Mass of ore = mass of calcium phosphate required / percentage calcium phosphate

Mass of ore = 20.65 / 0.351

Mass of ore = 58.83 kg