$(a)$ Calculate the number of moles in $112 \, g$ of iron.
$(b)$ Calculate the mass of $0.5$ mole of sugar $(C_{12}H_{22}O_{11})$.
$(c)$ Calculate the number of atoms in $8 \, g$ of oxygen $(O_2)$ molecules.
(Atomic mass of $Fe = 56 \, u, C = 12 \, u, H = 1 \, u, O = 16 \, u, N_A = 6.022 \times 10^{23} \, mol^{-1}$)

(N/A) Gram atomic mass of $Fe = 56 \, g/mol$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{112 \, g}{56 \, g/mol} = 2 \, moles$.
$(b)$ Molecular mass of sugar $(C_{12}H_{22}O_{11}) = (12 \times 12) + (22 \times 1) + (11 \times 16) = 144 + 22 + 176 = 342 \, u$.
Mass of $0.5 \, mole = 0.5 \, mol \times 342 \, g/mol = 171 \, g$.
$(c)$ Molar mass of $O_2 = 32 \, g/mol$.
Number of moles in $8 \, g$ of $O_2 = \frac{8 \, g}{32 \, g/mol} = 0.25 \, moles$.
Number of molecules $= 0.25 \times 6.022 \times 10^{23} = 1.5055 \times 10^{23} \, molecules$.
Since $1$ molecule of $O_2$ contains $2$ atoms, total atoms $= 2 \times 1.5055 \times 10^{23} = 3.011 \times 10^{23} \, atoms$.