To determine how many grams of aluminum are required to produce 8.00 moles of aluminum chloride (AlCl₃), we will break this problem into a few steps using stoichiometry and molar mass.
### Step 1: Analyze the Chemical Equation
The balanced chemical equation given is:
[tex]\[ 2 \text{Al} + 3 \text{Cl}_2 \rightarrow 2 \text{AlCl}_3 \][/tex]
This equation tells us that 2 moles of aluminum (Al) react with chlorine gas to produce 2 moles of aluminum chloride (AlCl₃).
### Step 2: Determine the Moles of Aluminum Needed
Since the stoichiometric coefficients for Al and AlCl₃ are both 2:
[tex]\[ \text{Moles of Al needed} = \text{Moles of AlCl}_3 \times \left( \frac{\text{Coefficient of Al}}{\text{Coefficient of AlCl}_3} \right) \][/tex]
Given that we need to produce 8.00 moles of AlCl₃, using the stoichiometric coefficients from the balanced equation, we can write:
[tex]\[ \text{Moles of Al needed} = 8.00 \text{ moles AlCl}_3 \times \left( \frac{2 \text{ moles Al}}{2 \text{ moles AlCl}_3} \right) \][/tex]
[tex]\[ \text{Moles of Al needed} = 8.00 \text{ moles Al} \][/tex]
### Step 3: Convert Moles of Aluminum to Grams
We know the molar mass of aluminum (Al) is given as 26.98 g/mol. To find the mass in grams, we use the formula:
[tex]\[ \text{Mass (g) of Al} = \text{Moles of Al} \times \text{Molar mass of Al} \][/tex]
[tex]\[ \text{Mass (g) of Al} = 8.00 \text{ moles Al} \times 26.98 \text{ g/mol} \][/tex]
### Step 4: Calculate the Mass
Multiplying the moles of Al by the molar mass gives us:
[tex]\[ \text{Mass (g) of Al} = 215.84 \text{ grams} \][/tex]
So, to produce 8.00 moles of aluminum chloride (AlCl₃), you need 215.84 grams of aluminum (Al).
