calculate the number of atoms in the following masses.
a) 54.0g of aluminum
b) 69.45 g of lathanum
c) 0.697 g of gallium
d) 0.000 000 020 g of beryllium
The atomic mass of Al is 1 mol and it contains 6.02 x 10^23 atoms Al.
The atomic mass of La is 1 mol and it contains 6.02 x 10^23 atoms La.
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To calculate the number of atoms, we need to use the concept of molar mass and Avogadro's number.
Step 1: Find the molar mass of the given element.
The molar mass is the mass of one mole of atoms of a particular element. It is given in grams/mole (g/mol). You can find the molar mass of an element from the periodic table.
a) Aluminum (Al) has a molar mass of 26.98 g/mol.
b) Lanthanum (La) has a molar mass of 138.91 g/mol.
c) Gallium (Ga) has a molar mass of 69.72 g/mol.
d) Beryllium (Be) has a molar mass of 9.01 g/mol.
Step 2: Calculate the number of moles.
To calculate the number of moles, divide the given mass by the molar mass.
a) Number of moles of aluminum = 54.0 g / 26.98 g/mol = 2.00 mol
b) Number of moles of lanthanum = 69.45 g / 138.91 g/mol = 0.500 mol
c) Number of moles of gallium = 0.697 g / 69.72 g/mol = 0.0100 mol
d) Number of moles of beryllium = 0.000000020 g / 9.01 g/mol = 2.22 × 10^-9 mol
Step 3: Calculate the number of atoms.
To calculate the number of atoms, multiply the number of moles by Avogadro's number, which is approximately 6.022 × 10^23 atoms/mol.
a) Number of atoms of aluminum = 2.00 mol × 6.022 × 10^23 atoms/mol = 1.20 × 10^24 atoms
b) Number of atoms of lanthanum = 0.500 mol × 6.022 × 10^23 atoms/mol = 3.01 × 10^23 atoms
c) Number of atoms of gallium = 0.0100 mol × 6.022 × 10^23 atoms/mol = 6.02 × 10^21 atoms
d) Number of atoms of beryllium = 2.22 × 10^-9 mol × 6.022 × 10^23 atoms/mol = 1.34 × 10^15 atoms
Therefore, the number of atoms in the given masses are:
a) 1.20 × 10^24 atoms of aluminum
b) 3.01 × 10^23 atoms of lanthanum
c) 6.02 × 10^21 atoms of gallium
d) 1.34 × 10^15 atoms of beryllium