Answer:
[tex]\boxed {\boxed {\sf 4.685 \times 10^{24} \ Fe \ atoms}}[/tex]
Explanation:
We are asked to convert grams of iron to atoms of iron.
First, we convert grams to moles. We use the molar mass or the mass in 1 mole of a substance. This is found on the Periodic Table because the molar mass is equal to the atomic mass, but the units are grams per mole instead of atomic mass units. Look up iron's molar mass.
We convert using dimensional analysis, so we must set up a ratio using the molar mass.
[tex]\frac {55.84 \ g \ Fe}{ 1 \ mol \ Fe}[/tex]
We are converting 434.52 grams to moles, so we multiply by this value.
[tex]434.52 \ g \ Fe *\frac {55.84 \ g \ Fe}{ 1 \ mol \ Fe}[/tex]
Flip the ratio so the units of grams of iron cancel.
[tex]434.52 \ g \ Fe *\frac { 1 \ mol \ Fe}{55.84 \ g \ Fe}[/tex]
[tex]434.52 *\frac { 1 \ mol \ Fe}{55.84}[/tex]
[tex]\frac { 434.52}{55.84} \ mol \ Fe[/tex]
[tex]7.781518625 \ mol \ Fe[/tex]
Next, we convert moles to atoms. We use Avogadro's Number or 6.02 ×10²³. It is the number of particles (atoms, molecules, formula units, etc) in 1 mole of a substance. For this problem, the particles are atoms of iron. We set up another ratio using this number.
[tex]\frac {6.02 \times 10^{23} \ atoms \ Fe }{ 1 \ mol \ Fe}[/tex]
Multiply by the number of moles we calculated.
[tex]7.781518625 \ mol \ Fe *\frac {6.02 \times 10^{23} \ atoms \ Fe }{ 1 \ mol \ Fe}[/tex]
The units of moles of iron cancel.
[tex]7.781518625 *\frac {6.02 \times 10^{23} \ atoms \ Fe }{ 1 }[/tex]
[tex]4.68447421 \times 10^{24} \ atoms \ Fe[/tex]
The correct answer choice is Choice 3: 4.685 × 10²⁴ atoms of iron.
