Question

You want to plate a steel part having a surface area of 160 with a 0.002--thick layer of lead. The atomic mass of lead is 207.19 . The density of lead is 11.36 . How many atoms of lead are required

Answer 1

To answer this question we assumed that the area units and the thickness units are given in inches.

The number of atoms of lead required is 1.73x10²³.

Step-by-step explanation:

To find the number of atoms of lead we need to find first the volume of the plate:

`V = A*t`

Where:

A: is the surface area = 160

t: is the thickness = 0.002

Assuming that the units given above are in inches we proceed to calculate the volume:

`V = A*t = 160 in^(2)*0.002 in = 0.32 in^(3)*((2.54 cm)/(1 in))^(3) = 5.24 cm^(3)`

Now, using the density we can find the mass:

`m = d*V = 11.36 g/cm^(3)*5.24 cm^(3) = 59.5 g`

Finally, with the Avogadros number (
`N_(A)`) and with the atomic mass (A) we can find the number of atoms (N):

`N = (m*N_(A))/(A) = (59.5 g*6.022 \cdot 10^(23) atoms/mol)/(207.19 g/mol) = 1.73 \cdot 10^(23) atoms`

Hence, the number of atoms of lead required is 1.73x10²³.

I hope it helps you!