To determine the mass of sodium that contains the same number of atoms as 27 grams of aluminum, we need to compare their molar masses and use Avogadro's number.
The molar mass of aluminum (Al) is 26.98 g/mol, which means that 26.98 grams of aluminum is equal to one mole of aluminum atoms.
Avogadro's number, denoted as NA, is approximately 6.022 × 10^23 atoms/mol. This number represents the number of atoms or molecules in one mole of a substance.
To find the number of aluminum atoms in 27 grams of aluminum, we divide the given mass by the molar mass and multiply by Avogadro's number:
Number of aluminum atoms = (27 g / 26.98 g/mol) × (6.022 × 10^23 atoms/mol)
Now we need to find the mass of sodium that contains the same number of atoms. We divide the number of aluminum atoms by Avogadro's number to find the number of moles of aluminum atoms. Then, we multiply this by the molar mass of sodium to find the mass of sodium.
Mass of sodium = (Number of aluminum atoms / Avogadro's number) × Molar mass of sodium
The molar mass of sodium (Na) is 22.99 g/mol.
Let's calculate the mass of sodium:
Number of aluminum atoms = (27 g / 26.98 g/mol) × (6.022 × 10^23 atoms/mol) Number of aluminum atoms ≈ 6.728 × 10^23 atoms
Mass of sodium = (6.728 × 10^23 atoms / 6.022 × 10^23 atoms/mol) × (22.99 g/mol) Mass of sodium ≈ 25.6 grams
Therefore, the mass of sodium that contains the same number of atoms as 27 grams of aluminum is approximately 25.6 grams.