Question

How many grams of phosphorus are in a sample of Ca3(PO4)2 that contains 50.0 grams of calcium

Answer 1

Mass of calcium \(=50 \mathrm{~g}\) Molar mass of calcium \(=40 \mathrm{~g} / \mathrm{mol}\)

$$ \begin{aligned} \text { Moles of calcium } &=\frac{50 \mathrm{~g}}{40 \mathrm{~g} / \mathrm{mol}} \\ &=1.25 \mathrm{~mol} \end{aligned} $$

In \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) formula, 2 moles of phosphorus is present for every 3 moles of calcium.

$$ \begin{aligned} \text { Moles of phosphorus } &=\frac{2 \times \text { moles of calcium }}{3} \\ &=\frac{2 \times 1.25 \mathrm{~mol}}{3} \\ &=0.833 \mathrm{~mol} \end{aligned} $$

Molar mass of phosphorus \(=31 \mathrm{~g} / \mathrm{mol}\) Mass of phosphorus \(=\) Moles \(\times\) molar mass

$$ \begin{array}{l} =0.833 \mathrm{~mol} \times 31 \mathrm{~g} / \mathrm{mol} \\ =25.8 \mathrm{~g} \end{array} $$