Answer:
[tex]\boxed {\boxed {\sf 4.60 \times 10^{23} \ atoms \ Mg}}[/tex]
Explanation:
We are asked to find how many atoms of magnesium are in 0.764 moles of magnesium.
We convert moles to atoms using Avogadro's Number or 6.022 × 10²³. 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 magnesium. So, there are 6.022 × 10²³ atoms of magnesium in 1 mole of magnesium.
Convert using dimensional analysis and set up a conversion factor using Avogadro's Number.
[tex]\frac{6.022 \times 10^{23} \ atoms \ Mg}{1 \ mol \ Mg}[/tex]
We are converting 0.764 moles of magnesium to atoms, so we multiply by this value.
[tex]0.764 \ mol \ Mg *\frac{6.022 \times 10^{23} \ atoms \ Mg}{1 \ mol \ Mg}[/tex]
The units of moles of magnesium cancel.
[tex]0.764 *\frac{6.022 \times 10^{23} \ atoms \ Mg}{1 }[/tex]
[tex]0.764 *6.022 \times 10^{23} \ atoms \ Mg[/tex]
[tex]4.600808 \times 10^{23} \ atoms \ Mg[/tex]
The original value of moles (0.764) has 3 significant figures, so our answer must have the same. For the number we calculated, that is the hundredth place. The 0 in the thousandth place tells us to leave the 0 in the hundredth place.
[tex]4.60 \times 10^{23} \ atoms \ Mg[/tex]
0.764 moles of magnesium contains approximately 4.60 × 10²³ atoms of magnesium.
