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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 0.073% Si by mass is used to make a rectangular plate that is 15.0 cm long, 12.5 cm wide, and 2.50mm thick and has a 2.50-cm-diameter hole drilled through its center such that the height of the hole is 2.50mm .

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 and a percent natural abundance of 3.10%

How many silicon-30 atoms are found in this plate?
Express your answer numerically using two significant figures.

Respuesta :

MissPhiladelphia
For the answer to the question above, let us use this formula for finding density.

density = mass / volume 

volume = (15.0 cm) * (12.5 cm) * (0.45 cm) = 84.375 cm^3 

8.80 grams/cm^3 = mass / 84.375 cm^3 
mass = 742.5 grams alloy 

mass of Si in alloy = (742.5 grams alloy) * (0.00041) = 0.304 grams Si 

mass of Si-30 = (0.304 grams Si in metal) * (0.0310) = 0.009424 grams Si-30 

atoms Si-30 = (0.009424 grams Si-30) * (1 mol Si-30 / 29.97376 grams Si-30) * (6.02*10^23 atoms Si-30 / 1 mol Si-30) =

The answer is

1.893*10^20 atoms Si-30 
Dejanras

Answer is: there are 1.82·10²⁰ silicon-30 atoms.

V₁(alloy) = 15 cm · 12.5 cm · 0.25 cm.

V₁(alloy) = 46.875 cm³; volume of the alloy without hole.

V(hole) = 0.25 cm · (1.25 cm)² · 3.14.

V(hole) = 1.23 cm³

V₂(alloy) = 46.875 cm³ - 1.23 cm³.

V₂(alloy) = 45.65 cm³; volume of the alloy with hole.

m(alloy) = V₂(alloy) · d(alloy).

m(alloy) = 45.65 cm³ · 8.80 g/cm³.

m(alloy) = 401.7 g; mass of the alloy.

ω(Si) = 0.073% ÷ 100%.

ω(Si) = 0.00073.

m(Si) = ω(Si) · m(alloy).

m(Si) = 0.00073 · 401.7 g.

m(Si) = 0.293 g; mass of silicon it the alloy.

m(Si-30) = m(Si) · ω(Si-30).

m(Si-30) = 0.293 g · 0.031.

m(Si-30) = 0.0091 g; mass of the silicon-30.

n(Si-30) = m(Si-30) ÷ M(Si-30).

n(Si-30) = 0.0091 g ÷ 29.97376 g/mol.

n(Si-30) = 0.000303 mol; amount of the silicon-30.

N(Si-30) = n(Si-30) · Na (Avogadro constant).

N(Si-30) = 0.000303 mol · 6.022·10²³ 1/mol.

N(Si-30) = 1.824·10²⁰.

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