Question

How many moles of iron is equivalent to 4.45 x 10^22 atoms of iron

Answer 1

0.074 moles

Step-by-step explanation:

For every mole (of any element), there are 6.022 x 10^23 atoms.

There are 4.45 x 10^22 atoms of iron.

To find the moles we divide the number of atoms by Avogadro's number

4.45 x 10^22 / 6.022 x 10^23 = 0.0738957

Don't forget sig figs

Answer 2

`\boxed {\boxed {\sf 0.0739 \ mol \ Fe}}`

Step-by-step explanation:

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

We will use Avogadro's Number for this, which is 6.022 × 10²³. This 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. There are 6.022 ×10²³ atoms of iron in 1 mole of iron.

We will also use dimensional analysis to solve this problem. To do this, we use ratios. Set up a ratio using the underlined information.

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

Since we are converting 4.45 × 10²² atoms of iron to moles, we multiply the ratio by that value.

`4.45 \ * 10^(22) \ atoms \ Fe *\frac {6.022 * 10^(23) \ atoms \ Fe} {1 \ mol \ Fe}`

Flip the ratio. The value is the same, but it allows us to cancel the units of atoms of iron.

`4.45 \ * 10^(22) \ atoms \ Fe *\frac {1 \ mol \ Fe}{6.022 * 10^(23) \ atoms \ Fe}`

`4.45 \ * 10^(22) *\frac {1 \ mol \ Fe}{6.022 * 10^(23)}`

Condense into 1 fraction.

`\frac {4.45 \ * 10^(22) }{6.022 * 10^(23)} \ mol \ Fe`

`0.07389571571 \ mol \ Fe`

The original measurement of atoms ( 4.45 × 10²²) has 3 significaint figures, so our answer must have the same. For the number we calculated, that is the ten-thousandths place. The 9 to the right of this place (0.07389571571) tells us to round the 8 up to a 9.

`0.0739 \ mol \ Fe`

There are approximately 0.0739 moles of iron in 4.45 × 10²² atoms of iron.