The reaction of magnesium with hydrochloric acid is:
\[
\text{Mg (s)} + 2 \, \text{HCl (aq)} \rightarrow \text{MgCl}_2 \, (aq) + \text{H}_2 \, (g)
\]
This reaction indicates that 1 mole of magnesium yields 1 mole of hydrogen gas.
At Standard Temperature and Pressure (STP), 1 mole of gas occupies 22.4 L. Consequently, 224 mL (0.224 L) of \( H_2 \) gas is equivalent to:
\[
\text{moles of } H_2 = \frac{0.224 \, \text{L}}{22.4 \, \text{L/mol}} = 0.01 \, \text{mol}
\]
Given the 1:1 molar ratio between magnesium and hydrogen gas, 0.01 mol of hydrogen necessitates 0.01 mol of magnesium.
The molar mass of magnesium (Mg) is 24 g/mol. Therefore, the required mass of magnesium is:
\[
\text{mass of Mg} = 0.01 \, \text{mol} \times 24 \, \text{g/mol} = 0.24 \, \text{g} = 240 \, \text{mg}
\]
The amount of magnesium required is 240 mg.
