Question

A pure titanium cube has an edge length of 2.66 in .how many titanium atoms does it contain? titanium has a density of 4.50 g/cm3.

Answer 1

Volume of Cube = edge length^3
V=2.66*2.66*2.66
V=18.82 in^3
because density is in cm^3
so converting V from in^3 to cm^3
V=314.12 cm^3
mass=density * volume
mass= 4.5*314.12
mass=1413.54 g
The molar mass of titanium is 47.88 g/mole
so moles=1413.54/47.88
moles=29.52
now one mole has avogadro number of atoms
so number of atoms=29.52*avogadro number
number of atoms=1.77x10^25

Answer 2

The volume of the cube will be 2.66 × 2.66 × 2.66 = 18.821 cubic inches.
1 cubic inch = 16.387 cubic centimeter.
18.821 cubic inches will be 18.821 × 16.387 = 308.42 cubic centimeter.
Density is 4.5 g/cm³
Therefore, mass will be 308.42 × 4.5 = 1387.89 g
1 mole of Titanium = 47.877 g, so the number of moles will be 1387.89/47.877=28.99 moles.
1 mole = 6.02 × 10^23 atoms
Therefore, 28.99 moles × 6.02 ×10^23 atoms = 1.745 ×10^25 atoms.