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Answer:
[tex]\boxed {\boxed {\sf 1.31 \ mol \ Fe}}[/tex]
Explanation:
We are asked to find how many moles of iron are in a sample containing 7.91×10²³ atoms of iron (Fe).
We convert atoms to moles using Avogadro's Number of 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are atoms of iron. There are 6.022 ×10²³ atoms of iron in 1 mole of iron.
Convert using dimensional analysis and set up a conversion factor using the molar mass.
[tex]\frac { 6.022 \times 10^{23} \ atoms \ Fe}{ 1 \ mol \ Fe}[/tex]
We are converting 7.91 ×10²³ atoms of iron to moles, so we multiply by this value.
[tex]7.91 \times 10^{23} \ atoms \ Fe *\frac { 6.022 \times 10^{23} \ atoms \ Fe}{ 1 \ mol \ Fe}[/tex]
Flip the ratio so the units of atoms of iron cancel.
[tex]7.91 \times 10^{23} \ atoms \ Fe *\frac { 1 \ mol \ Fe}{ 6.022 \times 10^{23} \ atoms \ Fe}[/tex]
[tex]7.91 \times 10^{23} *\frac { 1 \ mol \ Fe}{ 6.022 \times 10^{23} }[/tex]
[tex]\frac { 7.91 \times 10^{23}}{ 6.022 \times 10^{23} } \ mol \ Fe[/tex]
[tex]1.313517104 \ mol \ Fe[/tex]
The original value of atoms of iron has 3 significant figures, so our answer must have the same. For the number we found, that is the hundredth place. The 3 in the thousandth place tells us to leave the 1 in the hundredth place.
[tex]1.31 \ mol \ Fe[/tex]
There are approximately 1.31 moles of iron in 7.91×10²³ atoms of iron.