Question

How many titanium atoms does it contain? Titanium has a density of ( 4.50 , text{g/cm}^3 ). A pure titanium cube has an edge length of ( 2.75 , text{in} ).

a) ( 6.02 times 10^{23} )
b) ( 8.37 times 10^{23} )
c) ( 1.20 times 10^{24} )
d) ( 2.40 times 10^{24} )

Answer 1

To calculate the number of titanium atoms in the cube, convert the edge length to centimeters, find the volume, and use the density to determine mass. Then, convert the mass to moles, and multiply by Avogadro's number. The result is approximately 1.117 x 10^24 atoms, with the closest answer being option (c) (1.20 x 10^24).

Step-by-step explanation:

To determine how many titanium atoms are in the cube, we first need to calculate the volume of the cube. Since the edge length is given in inches and density in grams per cubic centimeter (g/cm3), we'll need to convert the measurements to a consistent unit system. The edge length of 2.75 inches is converted to centimeters using the conversion factor (1 inch = 2.54 cm).

The volume V of the cube is calculated using the formula V = a3, where 'a' is the edge length of the cube:

V = (2.75 in * 2.54 cm/in)3 = 19.734 cm3

We then multiply the volume by the density of titanium to find the mass of titanium:

Mass = Density * Volume = 4.50 g/cm3 * 19.734 cm3 = 88.803 g

Using the molar mass of titanium (47.867 g/mol), we can convert this mass into moles:

Moles of Ti = Mass of Ti / Molar Mass of Ti = 88.803 g / 47.867 g/mol = 1.856 mol

Finally, we use Avogadro's number (6.02 x 1023 atoms/mol) to find the number of atoms:

Number of Titanium atoms = Moles of Ti * Avogadro's number = 1.856 mol * 6.02 x 1023 atoms/mol = 1.117 x 1024 atoms

From the given options, (c) (1.20 x 1024) is the closest to our calculated number of titanium atoms.