Question

(a) $Mg + \frac{1}{2}O_{2} \rightarrow MgO$

$\frac{1}{2}\text{mole} \frac{1}{4} \times 32 = 8g$

∴ Mass of air needed = 8 + 1 × 28 = 36 g

(c) $3Mg + N_{2} \rightarrow Mg_{3}N_{2}$

$\frac{1}{2}\text{mole} \frac{1}{6}\text{mole}$

∴ Mass of air needed =$\frac{1}{6} \times 28 + \frac{1}{24} \times 32 = 6g$

(d) $Mg + \frac{1}{2}O_{2} \rightarrow MgO$

$x\text{mole} \frac{x}{2}\text{ mole}$

$3Mg + N_{2} \rightarrow Mg_{3}N_{2}$

$\left( \frac{1}{2} - x \right)\text{mole} \frac{1}{3}\left( \frac{1}{2} - x \right)\text{mole}$

From question: $\frac{1}{3}\left( \frac{1}{2} - x \right) = 4 \times \frac{x}{2} \Rightarrow x = \frac{1}{14}$

∴ Mass of air needed = $\frac{x}{2} \times 32 + \frac{1}{3}\left( \frac{1}{2} - x \right) \times 28$=5.14 g

Final mass of products = 12 + 5.14 = 17.14 g