Find the mass of [tex]$AlCl _3$[/tex] that is produced when 25.0 grams of [tex]$Al _2 O _3$[/tex] react with excess HCl according to the following equation:
[tex]$Al_2 O_3(s)+6 HCl(a q) \rightarrow 2 AlCl_3(a q)+3 H_2 O(l)$[/tex]
A. 65.4 g
B. 72.9 g
C. 155 g
D. 16.3 g
E. 32.6 g
Answer (1)
Calculate the molar mass of A l 2 O 3 : 2 × 26.98 + 3 × 16.00 = 101.96 g/mol.
Calculate the moles of A l 2 O 3 : 101.96 25.0 = 0.24519 mol.
Determine the moles of A lC l 3 produced: 2 × 0.24519 = 0.49039 mol.
Calculate the mass of A lC l 3 : 0.49039 × ( 26.98 + 3 × 35.45 ) = 0.49039 × 133.33 = 65.38 g. The final answer is 65.4 g .
Explanation
Problem Analysis The problem states that 25.0 grams of A l 2 O 3 react with excess HCl according to the equation:
A l 2 O 3 ( s ) + 6 H Cl ( a q ) → 2 A lC l 3 ( a q ) + 3 H 2 O ( l )
We need to find the mass of A lC l 3 produced.
Molar mass of A l 2 O 3 First, we need to calculate the molar mass of A l 2 O 3 . The molar mass of Al is 26.98 g/mol and the molar mass of O is 16.00 g/mol.
So, the molar mass of A l 2 O 3 is:
2 × 26.98 + 3 × 16.00 = 53.96 + 48.00 = 101.96 g/mol
Moles of A l 2 O 3 Next, we calculate the number of moles of A l 2 O 3 using the given mass (25.0 g):
moles of A l 2 O 3 = molar mass mass = 101.96 g/mol 25.0 g = 0.24519 mol
Moles of A lC l 3 From the balanced chemical equation, we see that 1 mole of A l 2 O 3 produces 2 moles of A lC l 3 . Therefore, the mole ratio between A l 2 O 3 and A lC l 3 is 1:2.
So, the number of moles of A lC l 3 produced is:
moles of A lC l 3 = 2 × moles of A l 2 O 3 = 2 × 0.24519 mol = 0.49039 mol
Molar mass of A lC l 3 Now, we calculate the molar mass of A lC l 3 . The molar mass of Al is 26.98 g/mol and the molar mass of Cl is 35.45 g/mol.
So, the molar mass of A lC l 3 is:
26.98 + 3 × 35.45 = 26.98 + 106.35 = 133.33 g/mol
Mass of A lC l 3 Finally, we calculate the mass of A lC l 3 produced:
mass of A lC l 3 = moles × molar mass = 0.49039 mol × 133.33 g/mol = 65.38 g
Final Answer The mass of A lC l 3 produced is approximately 65.4 g.
Examples
In industrial chemistry, determining the mass of products formed in a chemical reaction is crucial for optimizing production processes. For instance, calculating the amount of aluminum chloride ( A lC l 3 ) produced from the reaction of aluminum oxide ( A l 2 O 3 ) with hydrochloric acid (HCl) helps in estimating the yield and efficiency of the reaction. This calculation is essential for cost analysis, resource management, and ensuring the desired quantity of the product is obtained. By accurately predicting the mass of A lC l 3 formed, chemical engineers can fine-tune reaction conditions to maximize output and minimize waste, leading to more sustainable and economically viable industrial practices.
