Question

How many moles of silver are there in 6.9 x 10^28 silver atoms?

Answer 1

1.2 x 10⁵ moles Ag (2 sig. figs.)

Step-by-step explanation:

1 mole any substance (elements or compounds) => 6.023 x 10²³ particles of specified substance

∴ 6.9 x 10²⁸ atoms Ag = 6.9 x 10²⁸ Ag atoms / 6.023 x 10²³ Ag atoms/mole Ag

= 1.145608501 x 10⁵ moles Ag (calculator answer)

= 1.2 x 10⁵ moles Ag (2 sig. figs.)

Answer 2

`\boxed {\boxed {\sf 110,000 \ mol \ Ag}}`

Step-by-step explanation:

We are asked to convert 6.9*10²⁸ silver atoms to moles of silver. We can do this in 2 steps.

1. Convert Atoms to Moles

We know that 1 mole of any substance contains the same number of particles: 6.022*10²³ (Avogadro's Number). These particles can be atoms, molecules, formula units, and more. In this case, the particles are atoms of silver (Ag).

So, there are 6.022 *10²³ atoms of silver in 1 mole. Let's set up a ratio using this information.

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

Since we are converting 6.9*10²⁸ silver atoms to moles of silver, we multiply by that value.

`6.9*10^(28) \ atoms \ Ag*(6.022*10^(23) \ atoms \ Ag)/( 1 \ mol \ Ag)`

Flip the ratio. It remains equivalent, but the units if atoms of silver can cancel.

`6.9*10^(28) \ atoms \ Ag*( 1 \ mol \ Ag)/(6.022*10^(23) \ atoms \ Ag)`

`6.9*10^(28) *( 1 \ mol \ Ag)/(6.022*10^(23))`

`(6.9*10^(28) )/(6.022*10^(23)) \ mol \ Ag`

`114579.8738 \ mol \ Ag`

2. Round

The original measurement of silver atoms (6.9*10²⁸) has 2 significant figures, so our answer must have the same.

For the number we calculated, that is the ten thousands place. The 4 in the thousandths place (114579.8738) tells us to leave the 1.

`110,000 \ mol \ Ag`

There are approximately 110,00 moles of silver in 6.9*10²⁸ silver atoms.