Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics

Question

Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics industry. A particular alloy with a density of 8.80 g/cm3 and containing 0.043 % Si by mass is used to make a rectangular plate that is 15.0 cm long, 12.5 cm wide, and 3.50 mm thick and has a 2.50-cm-diameter hole drilled through its center such that the height of the hole is 3.50 mm .

The silicon in the plate is a mixture of naturally occurring isotopes. One of the those isotopes is silicon-30, which has an atomic mass of 29.97376 amu. The percent natural abundance, which refers to the atoms of a specific isotope, of silicon-30 is 3.10%.

How many silicon-30 atoms are found in this plate?

Explanation / Answer

density = mass / volume

volume = (15.0 cm) * (12.5 cm) * (0.35cm) = (65.625) cm3

8.80 grams/cm3 = mass / 65.625 cm3
mass =577.5 grams alloy

mass of Si in alloy = (577.5 grams alloy) * (0.00041) = 0.237 grams Si

mass of Si-30 = (0.237 grams Si in metal) * (0.0310) = 0.007347 grams Si-30

atoms Si-30 = (0.007347 grams Si-30) * (1 mol Si-30 / 29.97376 grams Si-30) * (6.02*1023 atoms Si-30 / 1 mol Si-30)

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