Chemistry, 21.12.2020 04:40 Ayomide2004

What is the mass of 2.20 x 10^22 atoms of Xe?

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Answer from: alex0123

$\boxed {\boxed {\sf 4.80 \ grams \ Xe}}$

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.

$6.022 * 10^{23} \ atoms \ / 1 \ mol$

We can write this number as a ratio or fraction.

$\frac{6.022 * 10^{23} \ atoms} { 1 \ mol}$

Then, multiply by 2.20 * 10²² atoms.

$2.20 * 10^{22} \ atoms \ Xe *\frac{6.022 * 10^{23} \ atoms \ Xe \ } { 1 \ mol \ Xe}$

We want the atoms of xenon to cancel, so we flip the fraction.

$2.20 * 10^{22} \ atoms \ Xe *\frac{1 \ mol \ Xe\ } { 6.022 * 10^{23} \ atoms \ Xe }$

Now, we can multiply and the atoms of xenon will cancel.

$2.20 * 10^{22} \ *\frac{1 \ mol \ Xe\ } { 6.022 * 10^{23} \ }$

$\frac {2.20 * 10^{22} *1 \ mol \ Xe\ } { 6.022 * 10^{23} \ }$

$\frac {2.20 * 10^{22} \ mol \ Xe\ } { 6.022 * 10^{23} \ } = 0.03653271338 \ mol \ Xe$

Now, convert moles to grams. We need to find the molar mass of xenon, which is on the Periodic Table.

Xenon: 131.29 g/mol

Now, use the molar mass as a ratio.

$\frac{131.29 \ g \ Xe}{1 \ mol \ Xe}$

Multiply by the number of moles we found above.

$0.03653271338 \ mol \ Xe * \frac{131.29 \ g \ Xe}{1 \ mol \ Xe}$

The moles of xenon will cancel.

$0.03653271338 * \frac{131.29 \ g \ Xe}{1 }$

The 1 as a fraction is irrelevant, so we can just multiply.

$0.03653271338 * {131.29 \ g \ Xe= 4.79637994 \ g \ Xe$

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.

$4.80 \ g \ Xe$

There are about 4.80 grams of xenon in 2.20 *10²² atoms.

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