Question

How many moles of Fe contains 3.41 x 1023 Fe atoms?

Answer 1

`\boxed {\boxed {\sf 0.566 \ mol \ Fe}}`

Step-by-step explanation:

We are asked to convert a number of atoms to moles.

We can convert atoms to moles using Avogadro's Number, which is 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this problem, the particles are atoms of iron (Fe). There are 6.022 ×10²³ atoms of iron in 1 mole of iron.

We use dimensional analysis to convert atoms to moles. This involves setting up ratios. Use Avogadro's Number and the underlined information to make a ratio.

`\frac {6.022 * 10^(23)\ atoms \ Fe}{1 \ mol \ Fe}`

We are converting 3.41 × 10²³ atoms of iron to moles, so we multiply by this value.

`3.41 * 10^(23) \ atoms \ Fe *\frac {6.022 * 10^(23)\ atoms \ Fe}{1 \ mol \ Fe}`

Flip the ratio. It stays equivalent, but it allows the units of atoms of iron to cancel.

`3.41 * 10^(23) \ atoms \ Fe *\frac{1 \ mol \ Fe} {6.022 * 10^(23)\ atoms \ Fe}`

`3.41 * 10^(23)*\frac{1 \ mol \ Fe} {6.022 * 10^(23)}`

`\frac{3.41 * 10^(23)} {6.022 * 10^(23)} \ mol \ Fe`

`0.5662570575\ mol \ Fe`

The original measure ment of iron atoms ( 3.41 × 10²³ ) has 3 significant figures, so our answer must have the same. For the number we calculated, that is the thousandths place. The 2 in the ten-thousandths place ( 0.5662570575) tells us to leave the 6 in the thousandths place.

`0.566 \ mol \ Fe`

3.41 × 10²³ atoms of iron is equal to approximately 0.566 moles of iron.