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

Answer 1

Answer:

Based on the given question, the dimensions of the plate is 15 cm in length, 12.5 cm in width, and 3.50 mm in thickness (0.350 cm). Now the volume of the plate will be,  

V = 15 cm × 12.5 cm × 0.350 cm = 65.62 cm³

A hole of diameter 2.50 cm is drilled through the center of the plate, at the height of 3.50 mm or 0.350 cm. Now the volume of the hole is π(r)²h,  

= 22/7 × (1.25 cm)² × 0.350 cm = 1.72 cm³

Thus, the volume of the plate will be determined by subtracting the volume of plate with the volume of hole, which will be,  

65.62 cm³ - 1.72 cm³ = 63.9 cm³

The density of the alloy is 8.80 g/cm³, therefore, the mass of the alloy can be determined by using the formula, mass = density * volume  

mass = 8.80 g/cm³ × 63.9 cm³ = 562.32 grams

Of the total alloy, 0.090 percent is Si, that is,  

(0.090/100) × 562.32 g = 0.506 grams of Si

The natural abundance of the element is not determined by mass but by the number of atoms it possess. For this Avogadro's number and atomic mass of Si is used. Now the number of atoms of Si present is,  

(0.506 g) (1 mol/28.0855 g) (6.023 × 10²³ atoms /mol) = 1.08 × 10²² Si atoms

Of these Si atoms, 3.10 percent are Si-30 so,  

= (3.10 / 100) × (1.08 × 10²² atoms) / 1000 = 3.34 × 10²⁰ atoms of Si-30. or 3.4 × 10²⁰ atoms