1. Write the balanced chemical equation:

S(s) + 3F₂(g) → SF₆(g)

2. Convert grams of sulfur to moles:

* Molar mass of sulfur (S) = 32.06 g/mol

* Moles of S = (17.8 g) / (32.06 g/mol) = 0.555 mol

3. Use the mole ratio from the balanced equation to find moles of fluorine:

* From the equation, 1 mole of sulfur reacts with 3 moles of fluorine.

* Moles of F₂ = (0.555 mol S) * (3 mol F₂ / 1 mol S) = 1.665 mol F₂

4. Convert moles of fluorine to grams:

* Molar mass of fluorine (F₂) = 38.00 g/mol

* Mass of F₂ = (1.665 mol F₂) * (38.00 g/mol) = 63.27 g

Therefore, 63.27 g of fluorine gas is needed to react completely with 17.8 g of sulfur to form sulfur hexafluoride.