If 40.0 g of HCl react with an excess of magnesium metal according to the equation Mg + 2HCl → MgCl_2 + H_2, what is the theoretical yield of hydrogen gas (H_2) in grams?

• A. 11.1 g
• B. 40.0 g
• C. 20.0 g
• D. 2.02 g

Answer: (A)

Verified step by step guidance

1. Write the balanced chemical equation: \(\mathrm{Mg + 2HCl \rightarrow MgCl_2 + H_2}\).
2. Calculate the number of moles of HCl using its molar mass. The molar mass of HCl is approximately 36.46 g/mol, so use the formula: \(\text{moles of HCl} = \frac{\text{mass of HCl}}{\text{molar mass of HCl}} = \frac{40.0\,\mathrm{g}}{36.46\,\mathrm{g/mol}}\).
3. Use the mole ratio from the balanced equation to find the moles of \(\mathrm{H_2}\) produced. According to the equation, 2 moles of HCl produce 1 mole of \(\mathrm{H_2}\), so: \(\text{moles of } H_2 = \frac{1}{2} \times \text{moles of HCl}\).
4. Calculate the mass of \(\mathrm{H_2}\) produced by multiplying the moles of \(\mathrm{H_2}\) by its molar mass. The molar mass of \(\mathrm{H_2}\) is approximately 2.02 g/mol, so: \(\text{mass of } H_2 = \text{moles of } H_2 \times 2.02\,\mathrm{g/mol}\).
5. The result from the previous step gives the theoretical yield of hydrogen gas in grams.