volume of Ti cube = 2.723 in3 = 20.12 in3 x 16.39 cm3/in3 = 329.8 cm3
density = 4.50 g/cm3
mass of Ti = density x volume = 4.50 x 329.8 = 1484 g
atomic mass of Ti = 47.88 g/mol
moles of Ti = mass / atomic mass = 1484/47.88 = 31 mol
1 mole of Ti contains 6.02 x 1023 Ti atoms,
Thus,
total Ti atoms number = 31 x 6.02 x 1023 = 1.87 x 1025
Once you convert the edge length (a) to centimetres, the volume in cubic centimetres is calculated as a3.
Multiplying the volume by the density of titanium yileds the mass of the cube in grams.
Then, the atomic mass of titanium can be used to convert the mass in grams to the number of moles.
Lastly, Avogadro's number is used to convert the number of moles to the number of titanium atoms.
The dimensional analysis for these calculations is summarised as follows:
(2.72 in • (2.54cm/1in))3 • (4.50g/1cm3) • (1 mol Ti/47.867g) • (6.022•1023 atoms/1mol)
Therfore, N = 1.87 • 1025 atoms Ti.
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