Final answer:
To find the mass of 242 atoms of cesium (Cs), convert the number of atoms to moles and then multiply by the molar mass of Cs. 242 atoms correspond to a tiny fraction of one mole, and by multiplying this number of moles by the molar mass of Cs (132.91 g/mol), the mass of the cesium atoms is calculated to be 5.38 × 10^-22 grams.
Step-by-step explanation:
To calculate the mass of 242 atoms of cesium (Cs), we first need to establish how many moles 242 atoms represent and then use the molar mass to find the mass in grams. The molar mass of cesium (Cs) is 132.91 g/mol, and we know that one mole of any substance contains Avogadro's number of atoms, which is approximately 6.022 × 1023 atoms/mol.
The number of moles of 242 atoms of Cs can be found using the formula:
- Calculate the number of moles: Number of moles = Number of atoms / Avogadro's number = 242 / (6.022 × 1023) moles.
- Calculate the mass in grams: Mass = Number of moles × Molar mass of Cs = (242 / (6.022 × 1023)) × 132.91 g/mol.
Performing the calculation yields the mass of Cs in grams:
Mass = (242 / (6.022 × 1023)) × 132.91 g/mol = 5.38 × 10-22 g.
Therefore, the mass of 242 atoms of cesium is 5.38 × 10-22 grams.