Answer:
[tex]\boxed {\boxed {\sf 1.62 \ mol \ Au}}[/tex]
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.
[tex]\frac {6.022*10^{23} \ atoms \ Au}{1 \ mol \ Au}[/tex]
Since we are solving for the moles in 9.75 * 10²⁴ atoms, we multiply by that number.
[tex]9.75*10^{24} \ atoms \ Au*\frac {6.022*10^{23} \ atoms \ Au}{1 \ mol \ Au}[/tex]
Flip the proportion. It will be equivalent, but the units of "atoms Au" can cancel.
[tex]9.75*10^{24} \ atoms \ Au*\frac {1 \ mol \ Au}{6.022*10^{23} \ atoms \ Au}[/tex]
[tex]9.75*10^{24} *\frac {1 \ mol \ Au}{6.022*10^{23}}[/tex]
Condense the problem into 1 fraction.
[tex]\frac {9.75*10^{24} }{6.022*10^{23}}\ mol \ Au[/tex]
[tex]1.619063434 \ mol \ Au[/tex]
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.
The 9 in the thousandth place tells us to round the 1 to a 2 in the hundredth place.
[tex]1.62 \ mol \ Au[/tex]
9.75 * 10²⁴ atoms of gold is approximately equal to 1.62 moles of gold.
