Answer:
[tex]\boxed {\boxed {\sf 1.53 \ mol \ Au}}[/tex]
Explanation:
We are asked to find how many moles of gold are in 9.23 *10²³ atoms of gold.
Avogadro's Number or 6.022 *10²³ is used to convert atoms to moles. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are atoms of gold.
We convert using dimensional analysis. Set up a conversion factor using Avogadro's Number.
[tex]\frac {6.022 \times 10^{23} \ atoms \ Au}{ 1 \ mol \ Au}[/tex]
We are converting 9.23 * 10²³ atoms of gold to moles, so we multiply by this value.
[tex]9.23 \times 10^{23} \ atoms \ Au *\frac {6.022 \times 10^{23} \ atoms \ Au}{ 1 \ mol \ Au}[/tex]
Flip the conversion factor so the units of atoms of gold cancel.
[tex]9.23 \times 10^{23} \ atoms \ Au *\frac { 1 \ mol \ Au}{6.022 \times 10^{23} \ atoms \ Au}[/tex]
[tex]9.23 \times 10^{23} *\frac { 1 \ mol \ Au}{6.022 \times 10^{23}}[/tex]
[tex]\frac {9.23 \times 10^{23} }{6.022 \times 10^{23} } \ mol \ Au[/tex]
[tex]1.53271338426 \ mol \ Au[/tex]
The original measurement of atoms has 3 significant figures, so our answer must have the same. For the number we found, that is the hundredth place. The 2 in the thousandth place tells us to leave the 3.
[tex]1.53 \ mol \ Au[/tex]
9.23 *10²³ atoms of gold is equal to approximately 1.53 moles of gold.
