What is the mass of 7.21 x 10^24 atoms of phosphorus (P)?
Understand the Problem
The question is asking for the mass of a specific number of phosphorus (P) atoms, which involves using the concept of moles and atomic mass to calculate the total mass from the given number of atoms.
Answer
\( \text{mass of P} = \frac{\text{number of atoms}}{6.022 \times 10^{23}} \times 31 \)
Answer for screen readers
The mass of phosphorus for the given number of atoms is calculated as ( \text{mass} = \frac{\text{number of atoms}}{6.022 \times 10^{23}} \times 31 ).
Steps to Solve
- Identify the atomic mass of phosphorus
The atomic mass of phosphorus (P) is approximately 31 grams per mole (g/mol). This information will be used to convert moles of phosphorus into grams.
- Convert atoms to moles
To convert the number of atoms to moles, we use Avogadro's number, which is approximately $6.022 \times 10^{23}$ atoms per mole.
The formula to convert atoms to moles is:
$$ \text{moles of P} = \frac{\text{number of atoms}}{6.022 \times 10^{23}} $$
- Calculate the mass of phosphorus
Once we have the moles of phosphorus, we can find the mass using the formula:
$$ \text{mass of P (g)} = \text{moles of P} \times \text{atomic mass of P (g/mol)} $$
- Substitute and solve
By substituting the calculated moles into the mass formula, we can find the total mass of phosphorus in grams.
The mass of phosphorus for the given number of atoms is calculated as ( \text{mass} = \frac{\text{number of atoms}}{6.022 \times 10^{23}} \times 31 ).
More Information
To find the mass of atoms, we always need to convert the number of atoms into moles using Avogadro's number, then multiply by the atomic mass. This approach applies to any element when calculating mass from the number of atoms.
Tips
- Confusing the number of atoms with moles; remember to convert using Avogadro's number first.
- Not using the correct atomic mass for phosphorus; ensure to check the reference used.
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