Answer:
[tex]\boxed {\boxed {\sf 3.8 \times 10^{24} \ atoms \ Zn}}[/tex]
Explanation:
We are asked to find how many atoms are in 6.3 moles of zinc (Zn). We will 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 problem, the particles are atoms of zinc. Therefore, there are 6.022 ×10²³ atoms of zinc in 1 mole of zinc.
We will convert using dimensional analysis, so set up a ratio using Avogadro's Number and the underlined information.
[tex]\frac {6.022 \times 10^{23} \ atoms \ Zn}{1 \ mol \ Zn}[/tex]
We are converting 6.3 moles of zinc, so we multiply the ratio by this value.
[tex]6.3 \ mol \ Zn * \frac {6.022 \times 10^{23} \ atoms \ Zn}{1 \ mol \ Zn}[/tex]
The units of moles of zinc cancel out.
[tex]6.3 * \frac {6.022 \times 10^{23} \ atoms \ Zn}{1 }[/tex]
A fraction with a denominator of 1 is equal to the numerator. We can disregard the denominator of 1.
[tex]6.3 * 6.022 \times 10^{23} \ atoms \ Zn[/tex]
[tex]3.79386 \times 10^{24} \ atoms \ Zn[/tex]
The original measurement of moles has 2 significant figures, so our answer must have the same. For the number we calculated that is the tenths place. The 9 in the hundredth place tells us to round the 7 in the tenths place up to an 8.
[tex]3.8 \times 10^{24} \ atoms \ Zn[/tex]
6.3 moles of zinc contains approximately 3.8 ×10²⁴ atoms of zinc.
