Exercise 1 solution

Molar mass of CO2: one C and two O.
  M = 12.01 + 2 x 16.00 = 44.01 g/mol

Moles: n = m / M
  n = 22.0 g / 44.01 g/mol = 0.4999 mol, so 0.500 mol to three figures.

Units: g divided by (g/mol) leaves mol, which is the unit we wanted.
The result is about half a mole, so 22.0 g is about half of the 44.01 g in one mole.

Note: the atomic masses are given in the exercise; the arithmetic was run in Python
(check, my own calculation).