Question

If it were possible to have a 9.0 x 1023-atom sample of pure titanium, what would be the mass of this sample, in grams?

Answer 1

The answer is 71.6 g

Step 1: Calculate the number of moles using the Avogadro's number.
Step 2: Calculate the mass using the number of moles and atomic mass of titanium.

Step 1.

Avogadro's number is the number of units in 1 mole of substance:

6.023 × 10²³ units (atom) per 1 mole

Calculate the number of moles by using the proportion:
6.023 × 10²³ atom : 1 mole = 9.0 × 10²³ atom : x
x = 1 mole * 9.0 × 10²³ atom / 6.023 × 10²³ atom
x = 1.4942 moles

Step 2.
The atomic mass of titanium is: Ar = 47.867 g
This means that in 1 mole, there are 47.867 g in 1000 ml
And we need to calculate the number of grams in 1.4942 moles:
47.867 g : 1 mole = x : 1.49 moles
x = 1.4942 moles * 47.867 g / 1 mole
x ≈ 71.6 g

Answer 2

Use the atomic mass of Ti: 47.867 g/mol and Avogadro's number

9.0*10^23 atoms *[1 / ( 6.022*10^23 atoms/mol) ] * 47.867 g/mol = 71.5 g.

The answer is 71.6 g