Question

How many moles of gold is 9.75 x 10^24 atoms?

Answer 1

1 Answer. You use the fact that 1 mole of any substance contains exactly 6.022⋅1023 atoms or molecules of that substance - this is known as Avogadro's number. In your case, 1 mole of gold will have exactly 6.022⋅1023 atoms of gold.

Step-by-step explanation:

Answer 2

`\boxed {\boxed {\sf 1.62 \ mol \ Au}}`

Step-by-step explanation:

We are asked to convert atoms to moles.

1. Avogadro's Number

We know that 1 mole of any substance contains the same number of particles (atoms, molecules, formula units etc.) This is Avogadro's Number: 6.022*10²³. For this question, the particles are atoms of gold (Au).

2. Convert Atoms to Moles

Let's set up a proportion using this information.

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

Since we are solving for the moles in 9.75 * 10²⁴ atoms, we multiply by that number.

`9.75*10^(24) \ atoms \ Au*\frac {6.022*10^(23) \ atoms \ Au}{1 \ mol \ Au}`

Flip the proportion. It will be equivalent, but the units of "atoms Au" can cancel.

`9.75*10^(24) \ atoms \ Au*\frac {1 \ mol \ Au}{6.022*10^(23) \ atoms \ Au}`

`9.75*10^(24) *\frac {1 \ mol \ Au}{6.022*10^(23)}`

Condense the problem into 1 fraction.

`\frac {9.75*10^(24) }{6.022*10^(23)}\ mol \ Au`

`1.619063434 \ mol \ Au`

3. Round

The original measurement (9.75) has 3 significant figures. Our answer must have the same. For the number we found, that is the hundredth place.

• 1.619063434

The 9 in the thousandth place tells us to round the 1 to a 2 in the hundredth place.

`1.62 \ mol \ Au`

9.75 * 10²⁴ atoms of gold is approximately equal to 1.62 moles of gold.