Question

9. How many moles of Ca are in 7.6 x 10^22 atoms of calcium?

Answer 1

There are 6.02×10²³ atoms of Ca in 1 mol of calcium, so:

6.02×10²³ --- 1 mol

7.6×10²² --- x

x = (7.6×10²²×1)/(6.02×10²³) = 0.13 mol

Answer 2

`\boxed {\boxed {\sf 0.13 \ mol \ Ca}}`

Step-by-step explanation:

We are asked to find how many moles of calcium are in 7.6 × 10²² atoms of calcium.

Avogadro's Number or 6.022 × 10²³ is used to convert atoms to moles. This number is how many particles (atoms, particles, formula units, etc.) in 1 mole of a substance. In this problem, the particles are atoms of calcium.

We use dimensional analysis to convert, so we must set up a conversion factor using Avogadro's Number.

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

We are converting 7.6 × 10²² atoms of calcium, so we multiply by this value.

`7.6 * 10^(22) \ atoms \ Ca *\frac {6.022 * 10^(23) \ atoms \ Ca}{ 1 \ mol \ Ca}`

Flip the conversion factor so the units of atoms of calcium cancel.

`7.6 * 10^(22) \ atoms \ Ca *\frac{ 1 \ mol \ Ca} {6.022 * 10^(23) \ atoms \ Ca}`

`7.6 * 10^(22) *\frac{ 1 \ mol \ Ca} {6.022 * 10^(23) }`

`\frac{ 7.6 * 10^(22) } {6.022 * 10^(23) } \ mol \ Ca`

`0.126203919 \ mol \ Ca`

The original measurement of atoms has 2 significant figures, so our answer must have the same. For this number, 2 sig fig is the hundredth place. The 6 in the thousandth place tells us to round the 2 up to a 3.

`0.13 \ mol \ Ca`

7.6 × 10²² atoms of calcium contains approximately 0.13 moles of calcium.