1. Write the balanced chemical equation:

H₂ + Cl₂ → 2HCl

This equation tells us that 1 mole of hydrogen (H₂) reacts with 1 mole of chlorine (Cl₂) to produce 2 moles of hydrogen chloride (HCl).

2. Calculate the moles of each reactant:

* Hydrogen:

- Molar mass of H₂ = 2.016 g/mol

- Moles of H₂ = (0.490 g) / (2.016 g/mol) = 0.243 mol

* Chlorine:

- Molar mass of Cl₂ = 70.906 g/mol

- Moles of Cl₂ = (50.0 g) / (70.906 g/mol) = 0.705 mol

3. Determine the limiting reactant:

The limiting reactant is the one that gets used up first, limiting the amount of product that can be formed. To find the limiting reactant, compare the mole ratios of the reactants to the balanced equation:

* H₂: We have 0.243 mol H₂. The balanced equation shows a 1:1 mole ratio between H₂ and Cl₂. If we had enough chlorine, this amount of hydrogen could react with 0.243 mol of chlorine.

* Cl₂: We have 0.705 mol Cl₂. This is more than enough chlorine to react with all the hydrogen.

Therefore, hydrogen (H₂) is the limiting reactant.

4. Calculate the moles of HCl produced:

The balanced equation shows a 1:2 mole ratio between H₂ and HCl. Since hydrogen is the limiting reactant, we'll use its moles to calculate the moles of HCl:

- Moles of HCl = 2 * Moles of H₂ = 2 * 0.243 mol = 0.486 mol

Answer: 0.486 moles of hydrogen chloride can be produced.