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 0.058 % Si by mass is used to make a rectangular plate that is 15.0 cm long, 12.5 cm wide, and 2.50 mm thick and has a 2.50-cm -diameter hole drilled through its center such that the height of the hole is 2.50 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% .

A. What is the volume of the plate?

answer 45.6 cm^3

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

Answer 1

A.

final volume of the plate=volume of the plate-vol. of the hole

= lenghtxbreadthxheight - (pixradius²x height)

= 15x12.5x.25 - (3.14x(1.25²)x.25)

= 45.64 cm^3 = 45.6 cm^3

B.

mass/volume= density

mass= volumex density

= 45.6x8.8 g

= 401.28 g

mass percent of silicon-30 = 3.10 %

mass of silicon-30 = 29.97376 amu.

therefore mass of one mole of silicon-30 = 29.97376 g

so, moles of si-30 present = (3.1/100)* (401.28/29.97376)

= 0.415 moles

no. of atoms in one mole= 6.022x 10^23

so no. of atoms in 0.415 moles= 0415x6.022x10^23 = 2.499 x 10^23 atoms