How many phosphorus atoms are present in 158 kg of elemental phosphorus (P)?

• A. 1.97 × 10^{26} atoms
• B. 9.51 × 10^{25} atoms
• C. 3.08 × 10^{27} atoms
• D. 6.02 × 10^{28} atoms

Answer: (C)

Verified step by step guidance

1. Identify the given quantity: 158 kg of elemental phosphorus (P). Convert this mass into grams because molar mass is typically expressed in grams per mole. Use the conversion factor: 1 kg = 1000 g.
2. Determine the molar mass of phosphorus (P). Since phosphorus is an element, use its atomic mass from the periodic table, which is approximately 30.97 g/mol.
3. Calculate the number of moles of phosphorus in 158,000 g using the formula: \(\text{moles} = \frac{\text{mass in grams}}{\text{molar mass}}\).
4. Use Avogadro's number, \$6.022 \times 10^{23}\( atoms/mol, to convert moles of phosphorus to number of atoms. The formula is: \)\text{number of atoms} = \text{moles} \times 6.022 \times 10^{23}$.
5. Perform the multiplication to find the total number of phosphorus atoms in 158 kg. This will give you the answer in atoms, which you can compare to the given options.