To determine the number of atoms and moles of nickel required to plate a steel part with a surface area of 0.14 m^2 and a 0.5 mm thick layer of nickel, we need to use the concept of Avogadro's number and the formula for calculating the number of moles.
(a) To find the number of atoms of nickel required, we need to know the molar mass of nickel. The molar mass of nickel is 58.69 g/mol.
First, we need to convert the thickness of the nickel layer from millimeters to meters. 0.5 mm is equal to 0.0005 meters.
Next, we can calculate the volume of the nickel layer by multiplying the thickness (0.0005 m) by the surface area (0.14 m^2). This gives us a volume of 0.00007 m^3.
To find the number of moles of nickel required, we divide the volume by the molar volume of nickel. The molar volume is the volume occupied by one mole of a substance at standard temperature and pressure (STP). The molar volume of nickel is approximately 0.00699 m^3/mol.
Using the formula: Number of moles = Volume / Molar volume, we can calculate the number of moles of nickel required.
Number of moles = 0.00007 m^3 / 0.00699 m^3/mol = 0.01001 mol.
(b) To find the number of atoms of nickel required, we can use Avogadro's number, which is approximately 6.022 x 10^23 atoms/mol.
To calculate the number of atoms, we multiply the number of moles by Avogadro's number.
Number of atoms = 0.01001 mol * (6.022 x 10^23 atoms/mol) = 6.024 x 10^21 atoms.
Therefore, (a) the number of atoms of nickel required is approximately 6.024 x 10^21 atoms, and (b) the number of moles of nickel required is approximately 0.01001 mol.