Question

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)

Answer 1

There are
`1.323* 10^(31) atoms` of mercury in 4,408 metric tons.

Step-by-step 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

`4,408,000,000 g=4.408* 10^9 g`

Mass of mercury =
`4.408* 10^9 g`

Atomic mass of mercury = 200.59 g/mol

Moles of mercury = n

`n=(4.408* 10^9 g)/(200.59 g/mol)`

`1 mole=N_A=6.022* 10^(23)` atoms/molecules/ ions

Number of atoms of mercury in n moles = N

`N=n* N_A`

`N=(4.408* 10^9 g)/(200.59 g/mol)* 6.022* 10^(23)\\=1.323* 10^(31) atoms`

Hence, there are
`1.323* 10^(31) atoms` of mercury in 4,408 metric tons.