A few years ago, a newspaper article reported that the Utah Industrial Depot west of Salt Lake
City had made the short list as a possible storage site for 4,408 metric tons of mercury metal.
This material is owned by the Defense National Stockpile Center. Mercury is mined primarily in Algeria, China, Kyrgyzstan, and Ukraine. At least part of this stockpiled material is from
payments to the US made by Spain as part of a WWII war debt. How many atoms of mercury
does this amount represent? (1 metric ton is 1000 kg, and 1 kg is 1000 g)

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Tringa0 Tringa0 · Answer 1 · 2020-09-16T16:34:30+02:00

Answer:

There are [tex]1.323\times 10^{31} atoms[/tex] of mercury in 4,408 metric tons.

Explanation:

Mass of mercury metal = 4,408 metric ton

1 metric ton = 1000 kg

4,408 metric ton = 4,408 × 1000 kg = 4,408,000 kg

1 kg = 1000 g

4,408,000 kg = 4,408,000 × 1000 g = 4,408,000,000 g

[tex] 4,408,000,000 g=4.408\times 10^9 g[/tex]

Mass of mercury = [tex]4.408\times 10^9 g[/tex]

Atomic mass of mercury = 200.59 g/mol

Moles of mercury = n

[tex]n=\frac{4.408\times 10^9 g}{200.59 g/mol}[/tex]

[tex]1 mole=N_A=6.022\times 10^{23}[/tex] atoms/molecules/ ions

Number of atoms of mercury in n moles = N

[tex]N=n\times N_A[/tex]

[tex]N=\frac{4.408\times 10^9 g}{200.59 g/mol}\times 6.022\times 10^{23}\\=1.323\times 10^{31} atoms[/tex]

Hence, there are [tex]1.323\times 10^{31} atoms[/tex] of mercury in 4,408 metric tons.