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Chapter 3: Problem 73

Which has more atoms: 3.0 g of iron, Fe, or 2.0 grams of sulfur, \(\mathrm{S} ?\)

Short Answer

Expert verified
2.0 grams of sulfur (S) has more atoms than 3.0 grams of iron (Fe).

Step by step solution

01

Finding moles of Fe and S

First, find the number of moles for both iron and sulfur. The molar mass of iron (Fe) is 55.845 g/mol and sulfur is 32.07 g/mol. Since the number of moles is equal to mass divided by molar mass, here we will find \( \frac{3.0g}{55.845g/mol} = 0.054mol \) of Fe and \( \frac{2.0g}{32.07g/mol} = 0.062mol \) of S.
02

Converting moles to number of atoms

Next, convert the amount of each substance from moles to atoms. This is done by multiplying the quantity in moles by Avogadro's number, which is \(6.022 \times 10^{23} atoms/mol\). By doing this calculation we find that the number of atoms in Fe is \(0.054mol \times 6.022 \times 10^{23} atoms/mol = 3.25 \times 10^{22} atoms\), whereas the number of atoms in S is \(0.062mol \times 6.022 \times 10^{23} atoms/mol = 3.73 \times 10^{22} atoms\).
03

Comparision of the number of atoms

Finally, compare the two quantites. We find that there are more atoms in 2.0 grams of sulfur (S) compared to 3.0 grams of iron (Fe). They have \(3.73 \times 10^{22}\) and \(3.25 \times 10^{22}\) atoms respectively.

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