How many grams of titanium (Ti, 47.90 g/mol) are in an instrument gear with 5.74x10^22 atoms of Ti

Mass = 45.64 g

Solution:

First of all calculate number of moles for given number of atoms,

As,

6.022 * 10²³ atoms = 1 Mole

So,

5.74 * 10 ²² atoms = X Moles

Solving for X,

X = (1 mol * 5.74 * 10²² atoms) : 6.022 * 10²³ atoms

X = 0.953 Moles

Now converting moles into mass,

As,

Moles = Mass / M. mass

So,

Mass = Moles * M. Mass

Putting Values,

Mass = 0.953 mol * 47.90 g. mol⁻¹

Mass = 45.64 g