Aluminum reacts with chlorine gas to form aluminum chloride via the following reaction: 2Al(s)+3Cl2(g)→2AlCl3(s) What is the maximum mass of aluminum chloride that can be formed when reacting 32.0 g of aluminum with 37.0 g of chlorine? Express your answer to three significant figures and include the appropriate units.

To determine the maximum mass of aluminum chloride (AlCl_3) that can form, you need to follow the steps of a stoichiometric calculation. Here are the given values and molar masses you'll need:

Mass of aluminum (Al): 32.0 g - Mass of chlorine (Cl_2): 37.0 g - Molar mass of Al: 26.98 g/mol - Molar mass of Cl_2: 70.90 g/mol (35.45 g/mol for one Cl atom) - Molar mass of AlCl_3: 133.34 g/mol (26.98 g/mol Al + 3 × 35.45 g/mol Cl)

Stepwise Calculation:

1. Calculate the moles of aluminum and chlorine.

Moles of Al = mass of Al / molar mass of Al = 32.0 g / 26.98 g/mol = 1.186 mol - Moles of Cl_2 = mass of Cl_2 / molar mass of Cl_2 = 37.0 g / 70.90 g/mol = 0.522 mol

2. Use the balanced equation to find the limiting reactant.

The balanced equation tells us that 2 moles of Al react with 3 moles of Cl_2 to produce 2 moles of AlCl_3.

3. Determine the mole ratio from the balanced equation.

Since the ratio is 2 moles of Al to 3 moles of Cl_2, you compare the actual mole quantities you have: - For Al: 1.186 mol Al (from step 1) × (3 mol Cl_2 / 2 mol Al) = 1.779 mol Cl_2 is needed. - For Cl_2: You have 0.522 mol Cl_2, which is less than 1.779 mol. Therefore, Cl_2 is the limiting reactant.

4. Calculate the amount of AlCl_3 that can be formed from the limiting reactant.

From the balanced equation, 3 moles of Cl_2 produce 2 moles of AlCl_3, so you can calculate the moles of AlCl_3: - Moles of AlCl_3 = 0.522 mol Cl_2 × (2 mol AlCl_3 / 3 mol Cl_2) = 0.348 mol AlCl_3

5. Convert the moles of AlCl_3 to mass.

Mass of AlCl_3 = moles of AlCl_3 × molar mass of AlCl_3 = 0.348 mol × 133.34 g/mol = 46.4 g

Therefore, the maximum mass of aluminum chloride that can be formed from 32.0 g of aluminum and 37.0 g of chlorine is 46.4 g.