To determine the mass of atoms of magnesium (Mg) that is equivalent to the number of atoms present in 54 grams of aluminum (Al), we need to use the concept of molar mass and Avogadro's number.
Calculate the number of moles of aluminum (Al): We know that the molar mass of aluminum (Al) is 26.98 grams/mol. Number of moles of Al = Mass of Al / Molar mass of Al Number of moles of Al = 54 g / 26.98 g/mol
Calculate the number of atoms in 54 grams of aluminum (Al): Avogadro's number states that 1 mole of any substance contains 6.022 × 10^23 particles (atoms, molecules, etc.). Number of atoms in 54 g of Al = Number of moles of Al × Avogadro's number Number of atoms in 54 g of Al = (54 g / 26.98 g/mol) × (6.022 × 10^23 atoms/mol)
Calculate the mass of atoms of magnesium (Mg) with the same number of atoms: Now, we can calculate the mass of Mg atoms with the same number of atoms as in 54 grams of Al. Since magnesium has a different molar mass, we'll divide the number of atoms in 54 g of Al by Avogadro's number and multiply it by the molar mass of Mg. Mass of Mg atoms = (Number of atoms in 54 g of Al / Avogadro's number) × Molar mass of Mg
The molar mass of magnesium (Mg) is 24.31 g/mol.
Substituting the values into the equation: Mass of Mg atoms = ((54 g / 26.98 g/mol) × (6.022 × 10^23 atoms/mol)) / (6.022 × 10^23 atoms/mol) × 24.31 g/mol Mass of Mg atoms = 54 g × (24.31 g/mol / 26.98 g/mol) Mass of Mg atoms = 48.91 g
Therefore, the mass of atoms of magnesium (Mg) with the same number of atoms as in 54 grams of aluminum (Al) is approximately 48.91 grams.