4. The penny is 97.5% zinc; the copper on the outside is a thin coating. For sim

Question

4. The penny is 97.5% zinc; the copper on the outside is a thin coating. For simplicity, you can make the approximation that it is entirely made of zinc. It has a mass of 2.5 g, a diameter of 19.05 mm, and a thickness (averaging over the surface) of 1.228 mm. The density of zinc is 7140 kg/m3 , and its atomic mass is 65.4 amu (in other words, g/mol). From this data, please show how to calculate:

(a) the volume of a penny.

(b) the number of moles of zinc in the penny.

(c) the number of atoms of zinc in a penny.

(d) the mass, in kg, of a single zinc atom.

(e) the diameter of a single zinc atom.

(f) the number of zinc atoms needed to stretch across the diameter of the penny.

Explanation / Answer

diameter, d = 19.05 mm
r = d/2 = 19.05/2 =9.525 mm = 9.525*10^-3 m
thickness, t = 1.228 mm = 1.228*10^-3 m

a)
volume = pi*r^2*t
= pi*( 9.525*10^-3)^2 *(1.228*10^-3)
= 3.5*10^-7 m^3

b)
mass of Zn = 2.5 g
molar mass of Zinc = 65.4 g
number ofmoles = mass / molar mass
= 2.5 / 65.4
=0.038 mol

c)
number of atoms = number of moles * 6.022*10^23
= 0.038*6.022*10^23
= 2.3 *10^22 atoms

d)
mass of 2.3 *10^22 atoms = 2.5 g
mass of 1 atom = 2.5 /(2.3 *10^22 atoms)
= 1.1*10^-22 g
= 1.1*10^-25Kg

This question has more than 4 parts.i am allowed to answer only 4 parts, Please ask remaining 2 as different question.

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