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Chapter 3: Problem 46

What number of \(\mathrm{Fe}\) atoms and what amount (moles) of Fe atoms are in \(500.0 \mathrm{~g}\) of iron?

Short Answer

Expert verified
In 500 grams of iron, there are approximately 8.95 moles of Fe atoms and \(5.39 \times 10^{24}\) individual Fe atoms.

Step by step solution

01

Find the molar mass of iron (

Begin by finding the molar mass of iron, which is the mass of one mole of iron atoms. Based on the periodic table, the molar mass of iron (Fe) is approximately 55.84 g/mol.
02

Calculate the amount of iron in moles

Next, divide the mass of iron by the molar mass to find the amount of iron in moles: moles of Fe = (mass of Fe) / (molar mass of Fe) moles of Fe = \( \frac{500}{55.84} \) Now, calculate the moles of Fe: moles of Fe = \( \frac{500}{55.84} \) ≈ 8.95 moles
03

Calculate the number of iron atoms using Avogadro's number

Avogadro's number (Nₐ) is the number of atoms (or molecules, ions, etc.) in one mole of a substance, which is approximately \(6.022 \times 10^{23} \) entities per mole. To find the number of iron atoms, multiply the moles of iron by Avogadro's number: Number of Fe atoms = (moles of Fe) × (Avogadro's number) Number of Fe atoms = (8.95 moles) × \(6.022 \times 10^{23}\) atoms/mol Now, calculate the number of Fe atoms: Number of Fe atoms ≈ 5.39 × \(10^{24}\) iron atoms To summarize, there are approximately 8.95 moles of Fe atoms and \(5.39 \times 10^{24}\) individual Fe atoms in 500 grams of iron.

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