What is the mass of 7.21 x 10^24 atoms P?
Understand the Problem
The question is asking for the mass of a specific number of phosphorus atoms given in scientific notation. To solve this, we need to use the atomic mass of phosphorus and convert the number of atoms into moles, then find the mass using the mole-to-grams conversion.
Answer
The mass of $7.21 \times 10^{24}$ atoms of phosphorus is approximately $370.44$ g.
Answer for screen readers
The mass of $7.21 \times 10^{24}$ atoms of phosphorus is approximately $370.44$ g.
Steps to Solve
- Determine the number of moles of phosphorus atoms
To find the moles of phosphorus atoms, use Avogadro's number, which is approximately $6.022 \times 10^{23}$ atoms/mol.
[ \text{Moles of P} = \frac{7.21 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} ]
- Calculate the moles
Now perform the division to find the number of moles:
[ \text{Moles of P} \approx \frac{7.21 \times 10^{24}}{6.022 \times 10^{23}} \approx 11.98 \text{ moles} ]
- Find the molar mass of phosphorus
The molar mass of phosphorus (P) is approximately $30.97$ g/mol.
- Calculate the mass using the moles calculated
To get the mass of phosphorus, use the formula:
[ \text{Mass} = \text{Moles} \times \text{Molar mass} ]
Substituting in the values:
[ \text{Mass} = 11.98 \text{ moles} \times 30.97 \text{ g/mol} \approx 370.44 \text{ g} ]
The mass of $7.21 \times 10^{24}$ atoms of phosphorus is approximately $370.44$ g.
More Information
The calculation can be useful in fields like chemistry and materials science, where determining the mass of elements in a sample is crucial for various experimental setups and reactions.
Tips
- Forgetting to use Avogadro's number for conversion between atoms and moles.
- Miscalculating the division when finding the number of moles.
- Not using the correct molar mass for the element.
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