How many moles and how many grams of potassium alum, KAl(SO4)2 · 12 H2O, can be prepared from 5.00 g of aluminum?
To determine the amount of potassium alum that can be prepared from 5.00 g of aluminum, we need to consider the stoichiometry of the reaction.
The balanced chemical equation for the formation of potassium alum is:
2 Al + K2SO4 + 2 H2SO4 + 24 H2O → 2 KAl(SO4)2 · 12 H2O
From the equation, we can see that 2 moles of aluminum (Al) react to form 1 mole of potassium alum (KAl(SO4)2 · 12 H2O). Therefore, we need to convert the mass of aluminum to moles.
The molar mass of aluminum (Al) is 26.98 g/mol.
Number of moles of aluminum = Mass of aluminum / Molar mass of aluminum
Number of moles of aluminum = 5.00 g / 26.98 g/mol
Number of moles of aluminum ≈ 0.185 mol (rounded to 3 decimal places)
Since 2 moles of aluminum react to form 1 mole of potassium alum, the number of moles of potassium alum that can be prepared is half of the number of moles of aluminum.
Number of moles of potassium alum = 0.185 mol / 2
Number of moles of potassium alum ≈ 0.0925 mol (rounded to 4 decimal places)
Now, to determine the mass of potassium alum that can be prepared, we need to multiply the number of moles of potassium alum by its molar mass.
Molar mass of potassium alum (KAl(SO4)2 · 12 H2O) = (39.10 g/mol) + (26.98 g/mol) + (32.07 g/mol * 4) + (16.00 g/mol * 18) + (1.01 g/mol * 12)
Molar mass of potassium alum ≈ 474.39 g/mol
Mass of potassium alum = Number of moles of potassium alum * Molar mass of potassium alum
Mass of potassium alum = 0.0925 mol * 474.39 g/mol
Mass of potassium alum ≈ 43.90 g (rounded to 2 decimal places)
Therefore, from 5.00 g of aluminum, approximately 0.0925 moles and 43.90 grams of potassium alum can be prepared.
To find out how many moles and grams of potassium alum can be prepared from 5.00 g of aluminum, we need to do the following calculations:
1. Find the number of moles of aluminum:
- The molar mass of aluminum (Al) is 26.98 g/mol.
- We can use the formula: number of moles = mass / molar mass.
- Calculating the number of moles of aluminum: 5.00 g / 26.98 g/mol = 0.1851 mol.
2. Determine the stoichiometry of aluminum in the compound:
- The chemical formula of potassium alum is KAl(SO4)2 · 12 H2O.
- From the formula, we can see that for every 1 mole of aluminum (Al), we get 1 mole of potassium alum (KAl(SO4)2 · 12 H2O) since the coefficient is 1.
3. Calculate the number of moles and grams of potassium alum:
- The number of moles of potassium alum will be the same as the moles of aluminum, which is 0.1851 mol.
- To find the grams of potassium alum, we need to calculate the molar mass of KAl(SO4)2 · 12 H2O.
- The molar mass can be calculated by summing the molar masses of each element in the compound:
- The molar mass of KAl(SO4)2 is (39.10 g/mol) + (26.98 g/mol) + 2[(32.07 g/mol) + 4(16.00 g/mol)] = 258.2 g/mol.
- The molar mass of 12 H2O is 12[(1.01 g/mol) + 2(16.00 g/mol)] = 216.2 g/mol.
- Adding both molar masses together: 258.2 g/mol + 216.2 g/mol = 474.4 g/mol.
- Finally, calculating the grams of potassium alum: 0.1851 mol × 474.4 g/mol = 87.8 g.
Therefore, from 5.00 g of aluminum, you can prepare 0.1851 moles and 87.8 grams of potassium alum.