Final answer:
The required mass of Cl₂ to produce 21.4 g of HCl, first calculate the moles of HCl and then apply the molar ratio from the balanced equation. Upon calculation, 20.79 g of Cl₂ is required.
Step-by-step explanation:
To determine the mass of Cl₂ required to produce 21.4 g of HCl, we start by using the balanced chemical equation H₂ + Cl₂ → 2HCl. We know that the molar ratio of Cl₂ to HCl is 1:2; thus, 1 mole of Cl₂ produces 2 moles of HCl. The molar mass of Cl₂ is 70.90 g/mol. Using this information and the mass of HCl given, we can calculate the required mass of Cl₂.
First, we find out how many moles of HCl 21.4 g correspond to by dividing the mass by the molar mass of HCl (1 mol HCl = 36.45 g HCl):
21.4 g HCl ÷ 36.45 g/mol HCl = 0.5865 mol HCl.
Since the molar ratio between Cl₂ and HCl is 1:2, we need half the moles of Cl₂ to produce the amount of HCl we have, which is 0.5865 mol / 2 = 0.29325 mol Cl₂.
Finally, we calculate the mass of Cl₂ needed using its molar mass:
0.29325 mol Cl₂ × 70.90 g/mol Cl₂ = 20.79 g Cl₂.