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 0.090 % 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%.

Part A

What is the volume of the plate?

Express the volume numerically in cubic centimeters.

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Part B

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

Express your answer numerically using two significant figures.

Explanation / Answer

First find the volume of the plate without accounting for the hole:

V = (15.0 cm)(12.5 cm)(0.350 cm) = 65.62 cm^3

The volume of the hole is: (pi)(1.25 cm)^2(0.350 cm) = 1.7272 cm^3

Subtract the volume of the hole from the rest: 63.9 cm^3

Multiply this by the density of the alloy to find the mass: (8.80 g/cm^3)(63.9cm^3) = 562.32 g.

0.090% of this is Si, so (0.00090)(562.32 g) = 0.506 g is silicon.

The natural abundance is not by mass, but by the number of atoms.

So...i'd use the average atomic mass of silicon and Avogadro's number to find the number of silicon atoms:

(0.506 g)(1 mol/28.0855 g)(6.022E23 atoms/1 mol) = 1.08 E22 atoms of Si.

3.10% of these are Si-30: (0.0310)(1.08 E22 atoms)/1000 = 3.34 E20 atoms of Si-30

Or, with two significant figures, 3.4 E20 atoms

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