Step-by-step explanation:
Aluminum will react with chlorine gas according to the following reaction:
2 Al (s) + 3 Cl₂ (g) ----> 2 AlCl₃
We have to find the mass of Cl₂ that will completely react with 13.5 g of Al. First we have to convert the mass of Al to moles using its molar mass.
molar mass of Al = 26.98 g/mol
moles of Al = 13.5 g * 1 mol/(26.98 g)
moles of Al = 0.500 mol
2 Al (s) + 3 Cl₂ (g) ----> 2 AlCl₃
Now, according to the coefficients of the reaction, 2 moles of Al will react with 3 moles of Cl₂. So the molar ratio between them is 2 to 3. We can use that relationship to find the number of Cl₂ that will react with 0.500 mol of Al.
2 mol of Al : 3 moles of Cl₂ molar ratio
moles of Cl₂ = 0.500 mol of Al * 3 moles of Cl₂/(2 moles of Al)
moles of Cl₂ = 0.750 mol
And finally we can convert back to grams using the molar mass of Cl₂.
molar mass of Cl₂ = 70.91 g/mol
mass of Cl₂ = 0.750 moles * 70.91 g/(1 mol)
mass of Cl₂ = 53.2 g
Answer: a. 53.2 g of Cl₂ for complete reaction.