To determine how many grams of HCl are needed to react with 6.5 grams of aluminum (Al), we need to follow a step-by-step approach:
1. Identify the molar masses:
- The molar mass of Aluminum (Al) is 26.98 g/mol.
- The molar mass of Hydrochloric acid (HCl) is 36.46 g/mol.
2. Calculate the moles of Al:
- We start by converting the mass of Al to moles using the molar mass.
- Moles of Al = [tex]\(\frac{\text{mass of Al}}{\text{molar mass of Al}}\)[/tex]
- Moles of Al = [tex]\(\frac{6.5 \text{ g}}{26.98 \text{ g/mol}}\)[/tex]
- Moles of Al = 0.24091919940696813 (mol)
3. Determine the stoichiometric ratio:
- According to the balanced equation [tex]\(2 \text{Al} + 6 \text{HCl} \rightarrow 3 \text{H}_2 + 2 \text{AlCl}_3\)[/tex]
- The stoichiometric ratio between Al and HCl is 2:6, which simplifies to 1:3.
4. Calculate the moles of HCl needed:
- Based on the stoichiometric ratio, 1 mole of Al requires 3 moles of HCl.
- Moles of HCl = Moles of Al [tex]\(\times\)[/tex] 3
- Moles of HCl = 0.24091919940696813 [tex]\(\times\)[/tex] 3
- Moles of HCl = 0.7227575982209044 (mol)
5. Convert moles of HCl to grams:
- Finally, we convert the moles of HCl to grams using the molar mass.
- Mass of HCl = Moles of HCl [tex]\(\times\)[/tex] Molar mass of HCl
- Mass of HCl = 0.7227575982209044 [tex]\(\times\)[/tex] 36.46 g/mol
- Mass of HCl = 26.351742031134172 (grams)
Therefore, to react with 6.5 grams of Al, you need approximately 26.35 grams of HCl.
