Question

Convert particles to moles: 8.3 x 10^20 atoms Cu

Answer 1

`\boxed {\boxed {\sf 0.0014 \ mol \ Cu}}`

Step-by-step explanation:

We are asked to convert particles to moles.

1. Avogadro's Number

1 mole of any substance contains the same number of particles (atoms, molecules, formula units). This is Avogadro's Number or 6.022*10²³.

In this problem, the particles are atoms of copper. So, 1 mole of copper contains 6.022*10²³ atoms of copper

2. Convert Atoms to Moles

Use Avogadro's Number to make a ratio.

`( 1 \ mol \ Cu)/( 6.022*10^(23) \ atoms \ Cu)`

We are trying to convert 8.3*10²⁰ atoms of copper to moles, so we multiply that value by the ratio.

`8.3*10^(20) \ atoms \ Cu*( 1 \ mol \ Cu)/( 6.022*10^(23) \ atoms \ Cu)`

The units of "atoms Cu" will cancel.

`8.3*10^(20)( 1 \ mol \ Cu)/( 6.022*10^(23) )`

Condense the expression into 1 fraction.

`(8.3 *10^(20))/( 6.022*10^(23) ) \ mol \ Cu`

`0.001378279641 \ mol \ Cu`

3. Round

The original measurement of atoms has 2 significant figures, so our answer must have the same. For the number we calculated that is the ten-thousandths place.

• 0.001378279641

The 7 in the hundredth thousandth place tells us to round the 3 up to a 4.

`0.0014 \ mol \ Cu`

8.3*10²⁰ atoms of copper are equal to 0.0014 moles of copper.