Answer:
[tex]\boxed {\boxed {\sf 4.80 \ grams \ Xe}}[/tex]
Explanation:
To convert from atoms to grams, we must first convert atoms to moles, then moles to grams.
To convert from atoms to moles, we must use a special number called Avogadro's number. It tells us the number of particles in 1 mole. In this case, the particles are atoms of xenon.
[tex]6.022 * 10^{23} \ atoms \ / 1 \ mol[/tex]
We can write this number as a ratio or fraction.
[tex]\frac{6.022 * 10^{23} \ atoms} { 1 \ mol}[/tex]
Then, multiply by 2.20 * 10²² atoms.
[tex]2.20 * 10^{22} \ atoms \ Xe *\frac{6.022 * 10^{23} \ atoms \ Xe \ } { 1 \ mol \ Xe}[/tex]
We want the atoms of xenon to cancel, so we flip the fraction.
[tex]2.20 * 10^{22} \ atoms \ Xe *\frac{1 \ mol \ Xe\ } { 6.022 * 10^{23} \ atoms \ Xe }[/tex]
Now, we can multiply and the atoms of xenon will cancel.
[tex]2.20 * 10^{22} \ *\frac{1 \ mol \ Xe\ } { 6.022 * 10^{23} \ }[/tex]
[tex]\frac {2.20 * 10^{22} *1 \ mol \ Xe\ } { 6.022 * 10^{23} \ }[/tex]
[tex]\frac {2.20 * 10^{22} \ mol \ Xe\ } { 6.022 * 10^{23} \ } = 0.03653271338 \ mol \ Xe[/tex]
Now, convert moles to grams. We need to find the molar mass of xenon, which is on the Periodic Table.
Now, use the molar mass as a ratio.
[tex]\frac{131.29 \ g \ Xe}{1 \ mol \ Xe}[/tex]
Multiply by the number of moles we found above.
[tex]0.03653271338 \ mol \ Xe * \frac{131.29 \ g \ Xe}{1 \ mol \ Xe}[/tex]
The moles of xenon will cancel.
[tex]0.03653271338 * \frac{131.29 \ g \ Xe}{1 }[/tex]
The 1 as a fraction is irrelevant, so we can just multiply.
[tex]0.03653271338 * {131.29 \ g \ Xe= 4.79637994 \ g \ Xe[/tex]
The original number (2.20) had 3 significant figures (2,2, and 0). We must round to 3 sig figs, which is the hundredth place.
The 6 in the thousandths place tells us to round the 9 to a 0 in the hundredth place, which bumps the 7 to an 8. We must still leave the 0 though, because it is the third significant figure.
[tex]4.80 \ g \ Xe[/tex]
There are about 4.80 grams of xenon in 2.20 *10²² atoms.
