High School

How many grams of [tex]$AlCl_3$[/tex] are produced when 30.0 g of [tex]$H_2$[/tex] are produced?

\[ 2 \text{Al} + 6 \text{HCl} \rightarrow 2 \text{AlCl}_3 + 3 \text{H}_2 \]

The molar mass of [tex]$AlCl_3$[/tex] is [tex]$133.33 \, \text{g/mol}$[/tex].

1. 0.0743 g
2. 0.167 g
3. 46.5 g
4. 1320 g
5. 5390 g
6. 655 g
7. 2970 g

Answer :

To find out how many grams of AlCl₃ are produced when 30.0 g of H₂ are produced, we'll go through the process of stoichiometry. Here are the steps:

1. Balance the Chemical Equation:
[tex]\[ 2 \text{Al} + 6 \text{HCl} \rightarrow 2 \text{AlCl}_3 + 3 \text{H}_2 \][/tex]

2. Understand the Stoichiometry:
According to the balanced equation, 3 moles of H₂ are produced along with 2 moles of AlCl₃.

3. Calculate the Moles of H₂ Produced:
First, find the moles of H₂ produced from the given mass.
- Molar mass of H₂ is approximately 2.02 g/mol.
- Moles of H₂ = [tex]\(\frac{\text{mass of } H_2}{\text{molar mass of } H_2}\)[/tex]
- Moles of H₂ = [tex]\(\frac{30.0 \text{ g}}{2.02 \text{ g/mol}}\)[/tex]
- Moles of H₂ ≈ 14.85 moles

4. Use Stoichiometry to Find Moles of AlCl₃ Produced:
Based on the balanced equation, 3 moles of H₂ are produced alongside 2 moles of AlCl₃.
- Moles of AlCl₃ = [tex]\(\frac{2}{3} \times \text{moles of H₂}\)[/tex]
- Moles of AlCl₃ = [tex]\(\frac{2}{3} \times 14.85\)[/tex]
- Moles of AlCl₃ ≈ 9.90 moles

5. Calculate the Mass of AlCl₃ Produced:
Now calculate the mass of AlCl₃ using its molar mass (133.33 g/mol).
- Mass of AlCl₃ = [tex]\(\text{moles of AlCl₃} \times \text{molar mass of AlCl₃}\)[/tex]
- Mass of AlCl₃ = [tex]\(9.90 \times 133.33 \text{ g/mol}\)[/tex]
- Mass of AlCl₃ ≈ 1320 g

Therefore, the amount of AlCl₃ produced when 30.0 g of H₂ are produced is approximately 1320 g, which corresponds to option 4 in the provided choices.